Re: [EM] PR approval voting
My system isn't quota based and doesn't involve any reweighting or redistribution. It looks at every possible result (potentially problematic in itself) and works out a score for each one. Because there is no redistribution, a voter can lose out more than some other systems by voting too high for a candidate that is going to get elected anyway. But I would argue that it gives the best proportional results for honest voting, and could still potentially deliver good overall results unless some candidates' supporters are much better at adopting strategy than others. A bit like with single-winner range where you wouldn't expect one particular faction of voters to vote approval style and "ruin" the whole thing. (Not that it would necessarily ruin it) From: Ted Stern To: election-methods@lists.electorama.com Cc: Ted Stern Sent: Monday, 3 October 2011, 20:49 Subject: Re: [EM] PR approval voting On 03 Oct 2011 12:23:10 -0700, Toby Pereira wrote: > > I noticed on your page that you suspect that all multi-winner > methods fail participation. I don't think that's the case. I would > suggest that Forest Simmons's Proportional Approval Voting passes > it. Also I think my versions of Proportional Approval Voting and > Proportional Range Voting pass. Since I wrote that, I have come to believe (but still haven't proved) that Approval-based methods will generally pass participation and IIAC. A range based method will pass participation, at least in single-winner, if it doesn't adjust ratings. In many cases my version of Range Transferable Vote will elect winners without having to raise ratings to meet quota. It only fails participation in those cases where the quota is not met, which most often happens on the last or penultimate seat. Is your PRV method quota-based? If so, does it pass Droop proportionality? If so, how do you deal with elevating preferences if no candidate achieves a quota? Ted Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR approval voting
I noticed on your page that you suspect that all multi-winner methods fail
participation. I don't think that's the case. I would suggest that Forest
Simmons's Proportional Approval Voting passes it. Also I think my versions of
Proportional Approval Voting and Proportional Range Voting pass.
From: Ted Stern
To: Election Methods
Cc: Ted Stern
Sent: Monday, 3 October 2011, 19:45
Subject: Re: [EM] PR approval voting
I'd like to stick my oar in here, to point out that I have an
implementation of Range Transferable Vote, which can be used with
Droop or other quotas, that implements PR.
Code for it is located here:
https://github.com/dodecatheon/range-transferable-vote
It reduces to Approval Transferable Vote in the case of range(0,1).
I had to make one change to it recently to fulfill the Droop
proportionality criterion, which states that if a faction distributes
its votes among L candidates, and has enough votes to elect K <= L
quotas, then the method will elect K candidates from the set of L
candidates.
For RTV, this meant that I had to find a way to elevate range
preferences in the event that no candidate achieves a quota.
The way I implement this is to increase non-zero ratings incrementally
(up to maximum score) until at least one candidate makes quota.
This pushes RTV into the territory of Bucklin-style methods, and
therefore it does not satisfy the Independence from Irrelevant
Alternatives criterion, even in the single-winner case.
Ted
On 01 Oct 2011 09:25:45 -0700, Toby Pereira wrote:
>
> Presumably this could also be used for range voting with a fairly
> simple modification. It would just set a limit on the fraction of
> someone's vote that could be used for each candidate. If you scored
> a candidate 3 out of 10, then no more than 0.3 of your vote could go
> to that candidate, regardless of whether the rest remained unused.
>
>
> From: Ross Hyman
> To: election-methods@lists.electorama.com
> Sent: Saturday, 1 October 2011, 5:07
> Subject: [EM] PR approval voting
>
> The following PR approval voting procedure is an approval limit of Schulze STV
>
> A score for each candidate set is determined in the following way: ?? The
> vote of each ballot is distributed amongst the ballot's approved candidates
> in the candidate set.? The score for each candidate set is the largest
> possible vote for the candidate in the set with the smallest vote.? The
> candidate set with the highest score wins the election.
>
> example: 2 seats
> approval voting profile
> 10 a
> ? 6 a b
> ? 2 b
> ? 5 a b c
> ? 4 c
> The possible candidate sets are: {a b}, {a c}, and {b c}.
>
> score for {a b} determined from
> 10 a
> ?11 a b
> ? 2 b
> score for {a b} = 11.5
>
> score for {a c} determined from
> 16 a
> ? 5 a c
> ? 4 c
> score for {a c} = 9
>
> score for {b c} determined from
> ?8 b
> ?5 b c
> ?4 c
> score for {b c} = 8.5
>
> set {a b} wins.
>
>
> Schulze uses a maximum flow algorithm to distribute the votes optimally on
> each ballot for each candidate set.? Here is another algorithm.
>
> v_i,a is the vote assigned to candidate a from the ith ballot.? The optimal
> v_i,a is determined iteratively.
>
> 1) Initially, the vote for each ballot is distributed equally between all the
> candidates in the candidate set that are approved by that ballot.?
>
> 2) The total vote for a candidate in the set is determined from v_a = sum_i
> v_i,a.? The lowest vote is a lower bound for the candidate score.
>
> 3) Form the adjusted vote w_i,a =? v_i,a/v_a.?
>
> 4) The adjusted vote for each ballot is w_i = sum_a w_i,a.
>
> 5) The new v_i,a = w_i,a / w_i.? Proceed to step 2.
>
>
>
> ?? ? ? ??
>
>
>
> ?
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>> Election-Methods mailing list - see http://electorama.com/em for list
>>info
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araucaria dot araucana at gmail dot com
Election-Methods mailing list - see http://electorama.com/em for list info
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Re: [EM] PR approval voting
Presumably this could also be used for range voting with a fairly simple
modification. It would just set a limit on the fraction of someone's vote that
could be used for each candidate. If you scored a candidate 3 out of 10, then
no more than 0.3 of your vote could go to that candidate, regardless of whether
the rest remained unused.
From: Ross Hyman
To: election-methods@lists.electorama.com
Sent: Saturday, 1 October 2011, 5:07
Subject: [EM] PR approval voting
The following PR approval voting procedure is an approval limit of Schulze STV
A score for each candidate set is determined in the following way: The vote
of each ballot is distributed amongst the ballot's approved candidates in the
candidate set. The score for each candidate set is the largest possible vote
for the candidate in the set with the smallest vote. The candidate set with
the highest score wins the election.
example: 2 seats
approval voting profile
10 a
6 a b
2 b
5 a b c
4 c
The possible candidate sets are: {a b}, {a c}, and {b c}.
score for {a b} determined from
10 a
11 a b
2 b
score for {a b} = 11.5
score for {a c} determined from
16 a
5 a c
4 c
score for {a c} = 9
score for {b c} determined from
8 b
5 b c
4 c
score for {b c} = 8.5
set {a b} wins.
Schulze uses a maximum flow algorithm to distribute the votes optimally on each
ballot for each candidate set. Here is another algorithm.
v_i,a is the vote assigned to candidate a from the ith ballot. The optimal
v_i,a is determined iteratively.
1) Initially, the vote for each ballot is distributed equally between all the
candidates in the candidate set that are approved by that ballot.
2) The total vote for a candidate in the set is determined from v_a = sum_i
v_i,a. The lowest vote is a lower bound for the candidate score.
3) Form the adjusted vote w_i,a = v_i,a/v_a.
4) The adjusted vote for each ballot is w_i = sum_a w_i,a.
5) The new v_i,a = w_i,a / w_i. Proceed to step 2.
> Election-Methods mailing list - see http://electorama.com/em for list
> info
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet-Kemeny calculations are not NP-hard
From: Richard Fobes To: election-meth...@electorama.com Sent: Thursday, 29 September 2011, 8:43 Subject: [EM] Condorcet-Kemeny calculations are not NP-hard This is very cryptic. What is this named advantage and why haven't you named it here? Is the unnamed advantage also indescribable? >The only valid disadvantage is that in very rare cases it fails the >"independence of clones" criteria, yet this perceived disadvantage does not >yield unfair results if all aspects of >VoteFair Ranking are used. I'm not sure how rare it would be myself (an exact clone isn't required for a non-cloneproof method to have problems). So VoteFair doesn't use the Kemeny method then? But having said that, failing independence of clones seems to me to be just one aspect of failing independence of irrelevant alternatives, which all Condorcet methods fail. So, for example, the Schulze method might not have problems when there are clones in the Smith Set, but it might have problems caused by a candidate introduced to have specific properties relative to the other candidates in the Smith Set. The Kemeny-Young method might (just speculating) not suffer as badly with this candidate. It's just that among the umbrella of irrelevant alternatives, clones have specifically been given their own criterion. You could probably make up other more obscure criteria under this umbrella but that cause just as many problems. >Some people have questioned why it is worth doing Condorcet-Kemeny >calculations when there are faster Condorcet methods. The answer is that >Condorcet-Kemeny >results offer lots of advantages, including one named >advantage that is currently underappreciated and a significant advantage that >has not yet been named or widely >recognized. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Viewable Interim results with permitted vote changing
This may well have been discussed before, and it wouldn't really be practical for parliamentary elections, but could be used in other situations. You allow a certain period for voting to take place (say a week), and when you cast your vote (logging into a computer with a password), it tells you the current result. Votes can be changed as many times as you want until the voting deadline. This would possibly be a little bit like SODA except that voters aren't putting delegation in the hands of the candidates, but do it all themselves. I think it would potentially remove problems where "weak" winners get in - candidates that people rank/rate highly thinking that they will never get in, perhaps to put a gap between theit favourite and their perceived nearest rival. As for what sort of ballot you'd use with this, I would suggest something simple. First Past the Post probably wouldn't be too horrific with this sort of voting, but I would suggest probably Approval. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Is there any profile where IRV is worse than Plurality?
Andy Candidates can go up the rankings or down when a candidate is eliminated in IRV, and it's possible to do both in different rounds. A plurality winner could slip down and be eliminated in a case where they would have still gone up again and won had they not been eliminated. So: 30: A>B>C>D 26: B>A>C>D 24: C>A>B>D 10: D>B>A>C 10: D>C>A>B Round 1: A: 30 B: 26 C: 24 D: 20 D eliminated Round 2: B: 36 C: 34 A: 30 A eliminated Round 3: B: 66 C: 34 B wins the IRV election whereas A would have been the plurality winner and the (quite strong) Condorcet winner. A>B: 64-36 A>C: 66-34 A>D: 80-20 Toby From: Andy Jennings To: EM Sent: Saturday, 24 September 2011, 0:13 Subject: [EM] Is there any profile where IRV is worse than Plurality? Since we're discussing IRV quite a bit lately, here's a question: - Is there any voter profile where IRV gives a worse result than plurality? I can't seem to think of one. So is it true that, mathematically, IRV dominates Plurality, that is IRV is always at least as good as plurality and sometimes strictly better? Even if that is true, I still believe that IRV is harmful, socially. By successfully avoiding the traditional spoiler problem (where spoilers are very weak), it leads people to believe that it is immune to the spoiler problem. Then it leads them directly into the second-tier spoiler scenarios where a large group of voters will, by voting honestly, cause their least favorite candidate to win. ~ Andy Election-Methods mailing list - see http://electorama.com/em for list info
[EM] PR >> Best Single-Winner Method > FPTP
Most of the discusssion on this group is about single-winner methods and while it's important to get things right for elections with single winners, I don't think I can be alone in thinking that with parliamentary elections, the gap (in quality) between any half-decent PR method and the "best possible" single-winner method would be greater than the gap between the best possible single-winner method and FPTP. I don't know so much about in America or other places (in terms of how realistic it is), but I certainly think that in the UK, that is where we should be concentrating. I don't think it's particularly realistic in the UK anyway, but I think we're probably more likely to get some form of PR than any of Approval/Range/Condorcet/Majority Judgement - and not forgetting SODA. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] [CES #3650] FairVote folks are not the friendliest bunch
From: James Gilmour >> I don't think I would have a problem with C winning here, if >> the votes were all sincere. >Even if all the votes are sincere, it is irrelevant what you or I think. It >is what ordinary electors would think about such a >winner, with only 5% of the first preferences. And those electors would not >be left in peace to reflect quietly on the potential of >their (weak) "Condorcet winner". Their views would be whipped up by partisan >politicians and by a hostile press and media. That >Condorcet winner would still be the Condorcet winner, but that's not how such >an outcome would be portrayed. The world of real >politics is a very brutal, nasty and dirty place, but that's where practical >electoral reformers have to work (at least for the time >being) if they really want to change anything. >James Gilmour In the example, A would win in a FPTP system, so all of B's voters would be better off under this outcome. So while the A supporters might kick up a massive fuss, it's not as if everyone, or even a majority, would probably be doing so. It's difficult to tell exactly what reaction we'd get, but the press are over-the-top on many matters, so it wouldn't be anything new! Toby Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] [CES #3650] FairVote folks are not the friendliest bunch
From: James Gilmour I don't think I would have a problem with C winning here, if the votes were all sincere. But that's the problem. They might not be. A and B supporters might just be putting C ahead of their perceived main rival. I suppose this is similar to the "DH3" problem - http://rangevoting.org/DH3.html - except with two main rivals instead of three. As far as I understand, range, approval and Majority Judgement should do OK here (and not forgetting SODA of course). But in the sincere case, every voter has ranked C above one of A or B, and if it happened that C and only one of A and B were running, then C would win and no-one would be bothered at all. Toby >But suppose the votes had been (again ignoring irrelevant preferences): > 48 A>C > 47 B>C > 5 C >"C" is still the Condorcet winner - no question about that. But I doubt >whether anyone could successfully sell such a result to the >electorate, at least, not here in the UK. >And I have severe doubts about how effective such a winner could be in office. >Quite apart from the sceptical electorate, the >politicians of Party A and of Party B would be hounding such an office-holder >daily. And the media would be no help - they would >just pour fuel on the flames. The result would be political chaos and totally >ineffective government. >The flaw in IRV is that it can, sometimes, fail to elect the Condorcet >winner. But IRV avoids the "political" problem of the weak >Condorcet winner. I suspect that's why IRV has been accepted for many public >and semi-public elections despite the Condorcet flaw. >James Gilmour Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Median-based PR systems
Except that this wouldn't give proportional results. From: Toby Pereira To: election-methods Sent: Saturday, 17 September 2011, 16:56 Subject: [EM] Median-based PR systems In Forest Simmons's system of Proportional Approval Voting each voter's satisfaction score is based on the number of elected candidates they voted for - 1 + 1/2 + 1/3 + ... + 1/n and the set of candidates giving the highest mean satisfaction score wins. This could be changed to highest median. (Other versions such as 1 + 1/3 + 1/5 etc can be used.) As I think has been dicussed in this mailing list, this can be extended to Range Voting by using harmonic numbers which give a continuous function for summing reciprocals. If you gave three elected candidates 3/10, 4/10 and 9/10, the number of elected candidates that you voted for would be considered to be 0.3+0.4+0.9=1.6. As before you could find the set of candidates with highest median satisfaction score. Toby Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Median-based PR systems
In Forest Simmons's system of Proportional Approval Voting each voter's satisfaction score is based on the number of elected candidates they voted for - 1 + 1/2 + 1/3 + ... + 1/n and the set of candidates giving the highest mean satisfaction score wins. This could be changed to highest median. (Other versions such as 1 + 1/3 + 1/5 etc can be used.) As I think has been dicussed in this mailing list, this can be extended to Range Voting by using harmonic numbers which give a continuous function for summing reciprocals. If you gave three elected candidates 3/10, 4/10 and 9/10, the number of elected candidates that you voted for would be considered to be 0.3+0.4+0.9=1.6. As before you could find the set of candidates with highest median satisfaction score. Toby Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Kemeny challenge
I don't think it is about exact clones though. First Past the Post is a bad voting system because it is not cloneproof and this shows itself with the problem of vote splitting. Voting methods that are not cloneproof suffer when there are similar candidates - they do not need to be identical. From: Richard Fobes To: election-meth...@electorama.com Sent: Wednesday, 14 September 2011, 18:32 Subject: Re: [EM] Kemeny challenge The Condorcet-Kemeny method does allow candidates to be ranked at the same preference level, and no special calculations are needed to handle these ballots. Such "ties" can occur at any combination of preference levels. The interactive ballots at VoteFair.org allow such "ties" and, more broadly, allow any one oval to be marked for each choice. (On a paper-based version, if a voter marks more than one oval, only the left-most marked oval is used.) I've addressed the "clone dependence" issue previously, yet I'll repeat the important points: Exact clones (which is what clone dependence assumes) are very rare in real elections, and circular ambiguity (that includes the winner) is not common (because Condorcet winners are more common), so the combination of these two events -- which is what must occur in order to fail the clone independence criteria -- is extremely rare. When I get time to reply to Warren's other message I'll address the "computational intractability" misconception. Richard Fobes On 9/13/2011 2:39 PM, fsimm...@pcc.edu wrote: > The problems with Kemeny are the same as the problems with Dodgson: > (1) computational intractability > (2) clone dependence > (3) they require completely ordered ballots (no truncations or equal > ranking), so they do not readily adapt to Approval ballots, for example. > In my posting several weeks ago under the title "Dodgson done right" I > showed how to overcome these three problems. (The same modifications do > the trick for both methods.) However, much of the simplicity of the > statements of these two methods (Dodgson and Kemeny) gets lost in the > translation. Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Kemeny challenge
>From what I understand it's independent of Smith-dominated alternatives. So >ranking the Smith Set should be sufficient. From: Jameson Quinn To: electionmeth...@votefair.org Cc: election-meth...@electorama.com Sent: Wednesday, 14 September 2011, 18:21 Subject: Re: [EM] Kemeny challenge 2011/9/14 Richard Fobes Large pairwise-count numbers do not increase the likelihood of a longer computation time. They just test the processor's integer limit, or the language-specified integer limit, or the efficiency of big-integer algorithms. > >Based on lots and lots of calculations using lots and lots of real data, I've >learned that just a few ballots (which corresponds to small pairwise-count >numbers) are more likely to increase the computation time. This makes sense >when you stop and think about it. > >If you come up with a ballot-based version of this challenge (rather than this >pairwise-count version), I'd like to try it out. > >Regardless of the results, remember that real elections only require >identifying the winner, whereas here we are discussing the computation time >for producing a full ranking. > Is there any way to prove that X is the winner, if they aren't the CW and you don't have the full ranking? JQ >Richard Fobes > > > >On 9/12/2011 12:00 PM, Warren Smith wrote: > >KEMENY CHALLENGE >>= >> >>Here is an attempt by me to intentionally create small elections for >>which it is difficult to determine the Kemeny winner. >> >>Consider this pairwise matrix: >> http://www.RangeVoting.org/Tourn27.html >>and replace all the +1s by random numbers in the interval >> [A, B] >>and all the -1s by ditto but negated, to get the pairwise margins matrix >>for a 27-candidate election. >>Here B>A>0 are two parameters chosen by the Devil to try to cause >>these problems to be hardest [I'd originally suggested A=9million >>B=10million, but maybe some other choice like A=0 and B=10billion >>would tend to make it harder]. Also of course randomly permute the 27 >>candidate-names in a way unknown to the solver, before giving the >>problem to the solver [equivalently permute both the rows and columns >>of the 27x27 matrix by one random permutation]. >> >>THE CHALLENGE: Find the Kemeny winner or order... can anybody do >>either reliably for 27-candidate elections of this class, or is this >>usually beyond humankind's abilities? >> >> >> >> > > >Election-Methods mailing list - see http://electorama.com/em for list info > Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] [CES #3605] Re: Kemeny Condorcet method. Apparently not a good choice for those of us who want to know who won in our lifetimes.
Your point 2 was why I initially saw it as the "natural" method when I first read about Condorcet methods. I don't know about anyone else, but my post wasn't intended to be related to whether it should be included in the declaration. As long as we're going along with mentioning specific Condorcet methods, it's probably worthy of inclusion. Regarding the cloneproof thing, I agree that it's probably not very exploitable in practice. First of all there needs to not be a Condorcet winner. And if you've got a cycle of A>B>C>A>... I think whichever candidate is cloned is likely to end up in the middle rather than either as winner or loser. Is that right? I think it effectively multiplies the power of the pairwise results involving the cloned candidate. I wonder if you could cloneproof it by looking at correlations between candidates and reducing the effect of comparisons involving "similar" candidates. I think that would remove it's simplicity and elegance though, arguably making the modified version have no advantages over other competing cloneproof methods. From: Andy Jennings To: Toby Pereira Cc: "electionscie...@googlegroups.com" ; election-methods Sent: Monday, 12 September 2011, 19:04 Subject: Re: [EM] [CES #3605] Re: Kemeny Condorcet method. Apparently not a good choice for those of us who want to know who won in our lifetimes. Kemeny has a couple things going for it: 1. Peyton Young argues here (http://www.econ.ucsb.edu/~tedb/Courses/UCSBpf/readings/PeytonYoungCondorcet.pdf) that it is probably the rule that Condorcet himself had in mind. 2. It is mathematically simple and elegant, so it is easier to prove things about it than the other Condorcet methods. Hence, it appears in lots of theoretical papers. In my opinion, these are the reasons that it is one of the "frontrunners" among the Condorcet methods. It is interesting that neither of these reasons relates to its performance (either in terms of worst-case runtime or criterion compliance), so I am fine that we question it here. However, I don't know that we can ever dethrone it as one of the "frontrunners", so maybe it's worth leaving in the declaration on those grounds alone... I, personally, feel that Warren's points are well-made and that NP-complete worst case behavior is of some concern, but it's not a deal-killer for me. Also, Kemeny is not cloneproof, but I think the fault is sufficiently difficult to exploit that it will be very rare. Famous last words, right? So my mind can be changed on these opinions. I'm just saying at this point that I, personally, feel that Kemeny is good enough. But I'm interested to hear from others... Andy On Mon, Sep 12, 2011 at 10:07 AM, Toby Pereira wrote: How much support does the Kemeny method actually have? I know Richard Fobes supports it obviously. But as far as I understand, is problems run deeper than runtime. Like not being cloneproof. > >When I first found out about Condorcet methods, I thought it looked like the >most "natural" one and seemed the best to me. It has a "maximum likelihood >estimator" property, but that doesn't apply to real life. It assumes that >there is "an objectively 'correct', but unknown preference order over the >alternatives, and voters receive noisy signals of this true preference order" >(from Wikipedia). In real life, people aren't all working towards trying to >find the "objectively best" candidate in this way. > >It may be the best (ignoring runtime) at finding a winner when voters are >"neutral" and not all with their own opinions, and also I've heard that it's >good at producing a full order. But in single-winner elections those don't >apply. Other Condorcet systems can find a full order anyway, even if they >aren't as "good" at it. And you wouldn't want to decrease the quality of the >winner in a single-winner method just to improve the rest of the order. > >Also, I wonder where Kemeny and others (such as Schulze) differ in the winner, >why they differ. Is it in most cases because Kemeny-Young is not cloneproof? >If so, that's a point against Kemeny-Young. Is it to do with margins/winning >votes? That's probably not an important factor anyway, because methods can >generally be converted from winning votes to margins or vice versa. > >From: Jameson Quinn >To: electionscie...@googlegroups.com >Cc: Kristofer Munsterhjelm ; election-methods > >Sent: Monday, 12 September 2011, 16:00 >Subject: Re: [CES #3605] Re: [EM] Kemeny Condorcet method. Apparently not a >good choice for those of us who want to know who won in our lifetimes. > > > >I wonder if there aren'
Re: [EM] [CES #3605] Re: Kemeny Condorcet method. Apparently not a good choice for those of us who want to know who won in our lifetimes.
How much support does the Kemeny method actually have? I know Richard Fobes supports it obviously. But as far as I understand, is problems run deeper than runtime. Like not being cloneproof. When I first found out about Condorcet methods, I thought it looked like the most "natural" one and seemed the best to me. It has a "maximum likelihood estimator" property, but that doesn't apply to real life. It assumes that there is "an objectively 'correct', but unknown preference order over the alternatives, and voters receive noisy signals of this true preference order" (from Wikipedia). In real life, people aren't all working towards trying to find the "objectively best" candidate in this way. It may be the best (ignoring runtime) at finding a winner when voters are "neutral" and not all with their own opinions, and also I've heard that it's good at producing a full order. But in single-winner elections those don't apply. Other Condorcet systems can find a full order anyway, even if they aren't as "good" at it. And you wouldn't want to decrease the quality of the winner in a single-winner method just to improve the rest of the order. Also, I wonder where Kemeny and others (such as Schulze) differ in the winner, why they differ. Is it in most cases because Kemeny-Young is not cloneproof? If so, that's a point against Kemeny-Young. Is it to do with margins/winning votes? That's probably not an important factor anyway, because methods can generally be converted from winning votes to margins or vice versa. From: Jameson Quinn To: electionscie...@googlegroups.com Cc: Kristofer Munsterhjelm ; election-methods Sent: Monday, 12 September 2011, 16:00 Subject: Re: [CES #3605] Re: [EM] Kemeny Condorcet method. Apparently not a good choice for those of us who want to know who won in our lifetimes. I wonder if there aren't also Kemeny optimizations similar to IRV's multiple-elimination, which would work well for real data. That is to say, that in real life, with enough candidates to make the problem hard, there are even more likely to be Condorcet losers (also-rans) than Condorcet winners. By successively peeling off the Condorcet loser, you could quickly reduce the problem. This much is a clear, easy optimization, and could easily bring an untractable 60 candidates down to a tractable 20. The analogy with the IRV case is that if you had a Smith set of condorcet losers, but they all (by some measure similar to IRV's summing) were "far enough behind" all other candidates, then it might be safe to treat them as a bloc, enabling a divide and conquer of the Kemeny problem. Or even if it weren't 100% safe, it would certainly be a good first guess. This part is just an intuition of mine, and it would certainly take further thought before you could use this idea. Jameson Quinn 2011/9/12 Warren Smith one very simple algorithm for Kemeny ranking >is the "quicksort" method. > >That is, you pick a random candidate X. You then >partition the others into two sets: above and below Xm, >by consulting random voters. >You then recursively sort the two resuitling subsets of candidates. > >This method produces random ordering of the candidates selected from a >non-uniform distribution, which is biased in a good direction. In >particular if the votes >all agree then it will get the best permutation immediately. >The point is that this bias means, that if you keep trying this over >and over, you will find the best permutation faster than if you just >tried uniform-random permutations over and over. > >There are many other such heuristic hacks. >One of the better ones seems to be based on Copeland voting plus local search. > > > > > >On Mon, Sep 12, 2011 at 10:32 AM, Warren Smith wrote: >>> Well, I can only speak from experience, but I've implemented the >>> Kemeny-Young method in quadelect as an integer program, and the vast >>> majority of the time (more than 90%), the LP linearization gives an optimal >>> result. >>> >>> NP-complete problems usually have phase transitions, i.e. there are some >>> regions of the problem that are easy and some that are very hard. It seems >>> that at least for the ballots generated by my opinion-space model, the >>> Kemeny instances tend to end up on the easy side. >>> >>> I could be wrong, of course, so any independent verification would be >>> welcome. >> >> --can you give more details? >> For example, if you make N candidates, what percentage of time do you >> succeed, as a function of N? >> [make a graph or table for N=3..100, say] >> >> If you have in mind the idea that this is an integer program, but the >> fact it is an INTEGER rather than LINEAR program happens not to matter >> in 90% of your >> cases (I think that is what you are saying) that's nice, >> but you lose for 10% of your cases. >> >> The Conitzer et al paper (a local copy is now at >> http://rangevoting.org/AAAI06-099.pdf ) >> had a randomized method for generating Kemeny elections whi
Re: [EM] [CES #3586] How to measure somebody's utilities
I wouldn't say that this method makes Joe's utilities measurable. It puts him
in a position where it's in his best interests to consider the utilities and
come up with the best approximation he can. But it doesn't mean he'll get it
right. But by getting people to think in terms of B being equal to a coin toss
between A and C when the average utility of A and C is equal to the utility of
B then this could help people's thinking (maybe).
Also, when it comes to the meaning of a normal range ballot, then it still
makes sense to talk about utility in these terms - the relative scores you give
to candidates. But not everyone would give 0 to their least candidate and the
top score to their favourite. If there are two candidates in a range voting
election, and someone gives scores of 10 out of 10 and 8 out of 10, what would
you say this means? I'm not sure that 0 and 10 or any absolute score can be
said to have a set definition when not everyone uses the full range.
From: Jameson Quinn
To: electionscie...@googlegroups.com
Cc: election-methods
Sent: Friday, 9 September 2011, 21:12
Subject: Re: [EM] [CES #3586] How to measure somebody's utilities
The problem is, what if Joe doesn't understand?
In a separate thread, Dodeca proposes a definition of utility that is
intuitively easy. The problem is, it's probably not the perfect definition of
"utility" for range voting... especially when you consider that you'd have to
rescale strategically to vote in range.
That's one of the reasons why I like MJ. As long as the voters agree on what
the numbers/grades mean, it works, even if nobody is rescaling and the scale
isn't even linear.
JQ
2011/9/9 Warren Smith
It is often erroneously claimed that utilities are "unmeasurable."
>
>Here is a way to do it. This kind of idea was one ingredient in F.W.Simmons's
>invention of various honesty-inducing voting methods,
>such as "double range voting," but it is worth isolating this ingredient since
>it is of interest by itself.
>
>We suppose there are N items, alternatives, events, candidates, or
>whatever you want to call them.
>We want to know Joe's N utilities for those N events.
>We make a machine to carry out the following
>
>UTILITY-REVELATION ALGORITHM:
>STEP 1. Machine tells Joe:
>"Please tell me your utility values (real numbers U_1, U_2, ..., U_N)
>for the N events,."
>
>STEP 2. [Joe tells.]
>
>STEP 3. Machine chooses 3 events A,B,C at random from the N
>with (say) U_A <= U_B <= U_C
>
>STEP 4. Machine now chooses a random real p with 0<=p<=1.
>
>STEP 5. Machine now GIVES to Joe, either B, or {A with probability p
>and C with probability 1-p},
>whichever of these two has greater utility according to the U-values
>Joe had told us in step 2.
>The utility of the former is U_B and of the latter is p*U_A + (1-p)*U_C.
>
>The end.
>
>THEOREM:
>No matter what the random processes are in steps 3 and 4 (provided they
>cause positive probability for each triple {A,B,C}, and no subsegment of the
>real p-interval [0,1] has probability=0, and the randomness is not
>predictable by Joe),
>Joe's uniquely best (expected-utility-maximizing) strategy is
>to give honest (perhaps rescaled) utility values in step 2.
>
>(Certain weaker conditions on the triples also would be acceptable.)
>
>
>--
>Warren D. Smith
>http://RangeVoting.org <-- add your endorsement (by clicking
>"endorse" as 1st step)
>
Election-Methods mailing list - see http://electorama.com/em for list info
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] "Meaning" of a vote (or lack thereof)
From: Warren Smith warren@gmail.com I wasn't denying that the honest sub-ballots had a meaning, but that the meaning of a score on a range ballot is probably less clear to mot people than the meaning of a score on a ranked ballot. This was my point, not that the range ballot lacked meaning in any objective sense (yes, I know this is tangential to your main point). >Voting "A>B>C", while it may be "clear" to you, in fact may cause A to lose, >or C to win, in every deterministic non-dictatorial ranked-voting scheme... >This is the Gibbard-Satterthwaite theorem. >This suggests that the problem is not that A>B>C has meaning and rnage-style >ballots do not. It is that you have a wrong perception of that. But the whole >point of my post waas to correct this wrong perception. If you now say >"but this wrong perception exists!" that does not refute my post. It supports >my post's raison d'etre. Well, I don't think every ranked voting system fails the participation criterion (e.g. Borda Count), so I don't think the above is strictly true, although I'm not denying that there will always be certain strategic considerations beyond just voting honestly. But I would argue that none of this is really relevant to what your ballot actually means (unless we're going to debate what "means" means). If I vote A>B>C, it means that I am stating my preference is for A to be elected first and foremost, but that I'd rather B be elected than C. The fact that voting that way may not always be best for me is irrelevant to what my ballot actually means. It is also irrelevant that my true preference might be A>C>B and that I'm voting tactically. I'm essentially lying on the ballot in that case. Voting A>B>C is a statement that that is your preference order even if it is not a true statement, or if it is a true statement but ends up giving a worse result for me. So it's clear to me what a ranked ballot means. And as someone previously suggested, you can devise a partially random ranked system where honest voting is the best strategy, so this is nothing against ranked ballots per se anyway. Also, while double range voting requires voters to use a specific meaning for what the scores mean in order to maximise their utility, I don't think that this is necessarily the same meaning that they'd use for a normal range voting election, so the meaning of a range ballot is arguably more voting-method-specific than a ranked ballot. I think double range works on affine scores, so scores of 10 and 0 for two candidates would be the same as 1 and 0, whereas this is not the case for ordinary range voting. This is a true difference of meaning rather than a strategical consideration. All ranked-ballot systems (ones that aren't simply absurd) have the same fundamental meaning for a ballot, even if strategical considerations can affect what people do in practice. >>It would be very difficult for someone to calculate/guess. >--Sure, some people, or even more likely, some lower animals, >may have trouble. That's just a speculation unsupported by, and in >fact flatly contradicted by, the actual evidence measuring e.g. >elapsed time taken for range-style voters versus rank-order-style >voters (the latter take longer, indicating more mental effort for rank >ordering). My point is that they won't necessarily be able to make a very good guess at the comparative utilities of the candidates. Voting more quickly doesn't mean they've calculated the utilities correctly. >But the question here was not about what a naive uninformed guesser >might think their mental effort would be; it was about the inherent >presence or absence of meaning. And the person involved was not a >lower animal, but in fact a Nobel prize winning expert on Voting, Ken >Arrow, and another Nobelist, E.Maskin. OK, fair enough. But I think there's always room for tangential discussion. But also, since you argue that strategic considerations strip away meaning from ranked voting systems, the same would apply for normal range voting as well. And since normal range voting doesn't have the specific pinpoint meaning of the honest sub-ballot of double range voting in the first place coupled with the fact that different range methods can have different ballot meanings (as argued above), one could argue that there is a gap in meaning here. >--the scores on honest-sub-ballots have a clear "meaning." If you deny it, >then find an example election in which voting any way other than honest >expected utilities, helps that voter. You cannot. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Executive Summary for Declaration
I think the executive summary needs to mention that plurality = First Past the Post. The term plurality is basically never used in the UK and most people wouldn't know what it means, so to cover as many countries as we can, we need to use the terms that each country uses. From: Andy Jennings To: electionmeth...@votefair.org Cc: election-meth...@electorama.com Sent: Thursday, 8 September 2011, 6:49 Subject: Re: [EM] Executive Summary for Declaration I do like the executive summary. Maybe it's a little too long? I think we could do without the sentence "Some good Condorcet methods are:..." I do think the PR section could be significantly shortened. I made a few changes. Feel free to review, roll back, and discuss if you think I have erred. ~ Andy Jennings On Wed, Sep 7, 2011 at 9:25 PM, Richard Fobes wrote: On 9/7/2011 2:09 PM, Peter Zbornik wrote: >> I still think the 12 page declaration (incl table of contents) needs an >> executive summary. The table of contents does not in my honest opinion >> give good enough information. > > >I agree that the declaration needs an executive summary. Here is what I've >come up with as a first draft: > >- Executive Summary - > >This declaration, which has been signed by election-method experts from around >the world, publicly denounces the use of plurality voting in governmental >elections. Plurality voting mistakenly assumes that the candidate who >receives the most ballot marks – on single-mark ballots – is the most popular. > Plurality voting also suffers from vote splitting, which is what forces >political parties to offer only a single choice in each election. > >As replacements for plurality voting, this declaration recommends four >significantly fairer election methods, namely, in alphabetical order: Approval >voting, any Condorcet method, Majority Judgment voting, and Range voting. >These methods use better ballots – namely the Approval ballot, Ranked ballot, >and Score ballot – to collect much more preference information compared to >plurality's primitive single-mark ballot. > >The lack of awareness about plurality voting's unfairness arises from its use >of single-mark ballots, which not only fail to collect enough information to >correctly identify the most popular candidate, but also fail to collect enough >information to produce proof or evidence of the unfair results. > >Computer technology now makes it easy to count better ballots and correctly >identify who deserves to win. All the supported methods are based on the fact >that a majority of voters, not just a plurality of voters, must approve or >prefer the winning candidate in order to produce fairer results. > >In spite of the academically recognized, well-known unfairness of plurality >voting, it is used throughout Canada, the United Kingdom, the United States, >and to some extent nearly every democracy around the world. As a consequence >of adopting fairer election methods, this declaration's signers expect the >benefits to include a dramatically reduced gap between voters and government, >more easily -- and fairly -- resolved political conflicts, and significantly >increased economic prosperity for any region that adopts fairer election >methods. > >Significantly the election-method experts do not support the use of >instant-runoff voting, which is also known as the alternative vote. This >method is based on the mistaken belief that the candidate with the fewest >plurality votes is the least popular candidate. > >The four supported methods also can be adopted for use in non-governmental >situations, such as electing an organization's officers, making democratic >decisions, and electing corporate board members. > >The signers of this declaration do not share any common political beliefs, and >are confident that the recommended election reforms will not favor any >particular political parties or political orientations. Their clearly stated >goal is to improve election fairness by replacing primitive plurality voting >with any of the fairer supported methods. Their expectation is that a higher >level of democracy will lead to higher standards of living, reduced conflicts, >and widespread greater economic prosperity, just as replacing monarchies and >dictatorships with plurality voting has produced dramatic and widespread >benefits. > >The signers urge everyone to learn more about how voting should be done – >using Approval voting, Condorcet methods, Majority Judgment voting, or Range >voting – and begin adopting the supported voting methods in whatever >situations currently, yet inappropriately, use plurality voting. > >- end - > >It mentions some concepts that currently aren't in the declaration itself, so >if this executive summary is liked, adjustments will need to be made in either >this summary or in the declaration. > >Also note that this summary does not mention PR. We still need to decide what >to do about that s
Re: [EM] "Meaning" of a vote (or lack thereof)
I think part of the problem then is that as far as I can see there is no clear and easily understandable description of Double range voting in existence. Also, it's not intuitively obvious to everyone what the different scores should mean. Voting A>B>C in a ranked list is clear. I know there are strategic considerations that mean you don't necessarily vote in order of favourite, but you are essentially telling the ballot that that is your preference order, even if it isn't strictly true. That's essentially what it means. I understand about utility and score votes but it wouldn't be clear to everyone, and also people wouldn't know in reality what level of utility to expect from each candidate. It would be very difficult for someone to calculate/guess. As had been stated, giving scores of 10, 5, and 0 out of 10 means that your middle candidate would have the same utility to you as a coin toss between your favourite and least favourite but it wouldn't always be obvious to a voter which has higher utility for them. They are, however, far more likely to be able to order the candidates. I'm not saying that ranked ballots are better than range ballots, but while they both might have a meaning, the ranked ballot's meaning would be far clearer to most voters. From: Warren Smith To: election-methods Sent: Thursday, 8 September 2011, 0:31 Subject: [EM] "Meaning" of a vote (or lack thereof) >Lundell: > How does it keep me honest in that scenario? Presumably I'd vote 1-0-0; >what's my motivation to do otherwise? > >Quinn: > Because there's a small chance that your (first "honest" range) vote actually > will decide between a lottery of some chance of A or C and a certainty of B. > If you haven't voted honestly, then that could make the wrong decision. And > such decisions are all your "honest" ballot is ever used for, so there is no > motivation to strategize with it. >Lundell: That's always the case with strategic voting when we don't have perfect knowledge of the other votes. There's a larger chance (in this example) that a sincere vote will cause B to defeat A. The more I know about the state of other voters, the more motivation I have to vote insincerely. This is true, of course, of any manipulable voting rule. --wrong. There is NOT a "larger chance" that a sincere (double range voting) vote will cause B to defeat A. There is in this example ZERO chance of that, Also double range voting is NOT a "manipulable voting rule" (or more precisely, it cannot be advantageously manipulated by altering the "please be honest" range-style sub-ballot, and indeed any such manipulation whatsoever will be strictly disadvantageous) As far as I can tell, Lundell has either never read, or has not comprehended, what "double range voting" is. That's a pity because it is a major theoretical advance with considerable philosophical implications, which was sort of the whole point of this whole thread. -- Warren D. Smith http://RangeVoting.org Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] [CES #3566] Re: Declaration of Election-Method Experts and Enthusiasts: final stretch
I agree that it's too long. I've had another go at culling come parts of it, but if anyone objects, feel free to revert some or all. From: Warren Smith To: electionscie...@googlegroups.com; election-methods Sent: Wednesday, 7 September 2011, 16:17 Subject: Re: [EM] [CES #3566] Re: Declaration of Election-Method Experts and Enthusiasts: final stretch this "declaration" is suffering from exactly what everybody most-complains about re the rangevoting.org website. I.e. it tried to cover everything and got large. In fact, enormous. That for a website is a flaw that is not necessarily an insurmountable obstacle since one can put short "summary" pages (or try...) and use of lots of hyperlinks, so it isn't just a flat document, it's easier to get to information. But for a "consensus statement" it is a major problem since (a) nobody is going to sign it and (b) nobody is going to read it. Well, "nobody" is an exaggeration. But not by much. This statement (4328 words) is now over 3 times the length of the USA's "Declaration of Independence" (1315 words) and also longer than the entire USA constitution (as un-amended) at 4318 words. Have you seen my attempt to study what election experts and/or Joe Public actually agree on? The total amount of true consensus out there, is extremely small. So you could have an extremely short statement, if you wished to summarize what is the current consensus. If you have the more ambitious goal of creating consensus by actually changing minds... well, I doubt you can do it with one single document. It's very hard to get people to sign statements, and the difficulty increases with the length. Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] SODA unfairly hobbles nonparanoid voters.
I'm not sure that three of those are unmatched by other systems. Point 1 - I don't think it is the simplest system. I certainly don't think it's any simpler than straight approval, and they've also got to decide whether to delegate or not and they've also got to understand that their vote can be delegated only if they vote for one candidate. You say they don't need to defensively strategize, but I'm not sure how well the benefits of SODA would get across to the general public. So it's not clear whether voters will see the strategy as simpler. Even if the task of voting is relatively simple, understanding the system and why it works like it does is not simple, and I think you have to include that in the simplicity of a system. Overall I'd say it's an above averagely complex system. And I don't know about in America (although I can't imagine it would be much different from the UK), but in the UK I simply canot see people ever accepting this idea of delegating votes. It's a major paradigm shift and I think it renders it a non-starter as a serious system to elect parliaments, if I'm being honest (along with any other asset system). Also, if it is better for a voter to bullet vote and allow delegation (from their point of view), then voters who like a candidate but don't like their delegation list are presumably at a disadvantage to begin with, which they may perceive as unfair. Point 2 - You've said yourself that IRV satisifes this, but then I notice you've qualifed this earlier by saying any good system. Clever. Point 3 - The chicken problem - yeah maybe. I'd have to get back to you. Point 4 - I imagine this is the one where it isn't unmatched by other good systems. So if we're allowing point 2 on this technicality, I still think it's only 2 out of 4, because I think it fails simplicity, and fails it badly. Toby From: Jameson Quinn To: ⸘Ŭalabio‽ Cc: EM Sent: Monday, 5 September 2011, 19:31 Subject: Re: [EM] SODA unfairly hobbles nonparanoid voters. SODA was initially designed as a single-winner system. I believe that as such, it has four independent advantages, three of which are unmatched by any other good system. 1. It is the easiest possible system for voters. No spoiled ballots, bullet voting works, and no need to defensively strategize. 2. It is "later-no-harm" enough to satisfy political incumbents who don't want to be defeated by centrist nonentities. (This is also true of IRV, but IRV has other problems) 3. It resolves the chicken problem better than any other system I know of. 4. I believe it would give good results overall - like Approval, Condorcet, MJ, or Range. So if you are thinking of SODA as just being Asset shoehorned into a single-winner case, then you don't understand the motivation, and either you don't understand the system or I don't. JQ 2011/9/5 ⸘Ŭalabio‽ 2011-09-05T09:28:14Z, “Jameson Quinn” : > > 0thly, I recommend that you read this article: > > >http://web.archive.org/web/20080113211450/http://www.greenend.org.uk/rjk/2000/06/14/quoting.html > > >> Basically, ⸘Ŭalabio‽'s objection is that SODA does not allow >> non-bullet votes to be delegable. The reason that SODA is designed that way >> is not "paranoia", as ⸘Ŭalabio‽ claims, but rather simplicity. > > Simplicity is in the eye of the beholder. What is simple for me is >choosing people whom I trust to represent my interests in the >Asset-Negotiations and leave them to their work. If some of them screw me >during Asset-Negotiations, I shall never vote for the bad 1s again. As far as >simplicity goes, SODA seems more complex to me than Asset-Voting. > > >> To see why multiple delegable votes would be confusing, consider the >> following scenario. Let us say that I vote for A and B. After the votes are >> counted, it turns out that all the other voters voted for X or Y, in a 50/50 >> proportion. My delegated vote could be decisive. But A approves X, and B >> approves Y. So both of these approvals are added to my delegated vote, which >> ends up being useless in deciding between X and Y. > > Either A or B would eventually by won over to the other side by >policy-concessions. > > >> Also, making multiply-delegated votes possible would entirely ruin >> SODA's summability. This would make a number of useful anti-fraud measures >> impossible, including precinct-level counting, sampled count audits, and >> voter-auditable cryptographic ballot receipts like those of heliosvoting.org. > > Just make the allowable votes a fixed number. This is required in 1 >form or another in proportional systems. Indeed, most of the problems with >SODA is that it is based on a system designed for creating a proportional >legislature, but is modified for both creating proportional legislatures and >for single-winner. These are 2 different domains and should use different >systems. The simplest methods for these domains ar
Re: [EM] This mailing list as a forum?
Andy It certainly can be a problem if some people move and others don't, but from my own limited experience, I don't think it will happen. I was on a Yahoo group that converted to a forum, and while some people were reluctant to make the change, virtually everyone ended up doing so. Not only that, but there was an increase in new members and a dramatic increase in posts. I think people feel freer to post in threads on a forum than to a mailing list, where every post is the next in line and inevitably in the spotlight. Even Google Groups (which I only know from the range voting group) seems to be a hybrid between a forum and a mailing list, so I don't think is as good as a full forum. Having said that, because it can be used as a mailing list, it is, as you say, a strict improvement over what we have now. Toby From: Andy Jennings To: Toby Pereira Cc: electorama list Sent: Saturday, 3 September 2011, 6:43 Subject: Re: [EM] This mailing list as a forum? Toby, I agree that it is a pain to try to reply to the digest. I've switched to receiving every message as a separate email and it seems much easier. The downside, as you say, is that there are a lot of messages sometimes. I would support moving to Google Groups because I think it would be a strict improvement over what we have now: after the adjustment period, life would be worse for no one and strictly better for some. But there would, no doubt, be a learning curve for some people. And then there's the risk of what happened on the range voting list. Someone created a Google Group with the intent of moving from Yahoo Groups to Google, but then some people didn't want to move and so now there are two lists to follow. One on Yahoo and one on Google. ~ Andy On Fri, Sep 2, 2011 at 10:40 AM, Toby Pereira wrote: I don't know if this has been discussed before, but most discussion groups on the internet (certainly the ones I use) use forums with separate threads for topics, rather than a mailing list. I think forums are easier to use and the threads are easier to follow. It's awkward to reply to topics on here unless you have individual e-mails sent to your inbox and it's a full-time job to put them into a separate folder. You can't reply via the central "hub". Mailing lists are the FPTP of the internet discussion world! Any thoughts? > >Election-Methods mailing list - see http://electorama.com/em for list info > > Election-Methods mailing list - see http://electorama.com/em for list info
[EM] This mailing list as a forum?
I don't know if this has been discussed before, but most discussion groups on the internet (certainly the ones I use) use forums with separate threads for topics, rather than a mailing list. I think forums are easier to use and the threads are easier to follow. It's awkward to reply to topics on here unless you have individual e-mails sent to your inbox and it's a full-time job to put them into a separate folder. You can't reply via the central "hub". Mailing lists are the FPTP of the internet discussion world! Any thoughts? Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Voting reform statement; a clearer and more inspiring version
I've just been looking at the statement - https://docs.google.com/document/d/1oyJLxI9dciXBbowM5mougnbGHzkL3Ue1QkD8nnMwWLg/edit?hl=en_US&pli=1# I think overall it's pretty good, but there are a couple of things I thought I'd mention. It seems to repeat itself: "Four of the counting methods that we agree would produce significantly better results compared to plurality voting are, in alphabetical order:" And then: "Yet most of us also agree that we will support the adoption of any of the supported methods, namely, in alphabetical order:" followed by the same list. I think that it can therefore be shortened a bit. I think it can probably also be shortened elsewhere, but it depends on how long you think is reasonable for it to be. Also in the second list it individually lists the Condorcet methods. It also says "the Condorcet methods" implying that it is an exhaustive list. But anyway, I don't think it is probably necessary to list them at all. Also, and I think this has been mentioned, it refers to election-method experts, and that may put some of us off signing. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Range Voting - Is adding up the scores really the best way?
Very simple case - two voters and two candidates. Candidate A get scores of 0/10 and 10/10. Candidate B gets 5/10 and 5/10. Under normal range voting, it would be a draw. But to me, candidate B seems the much fairer choice. Although there's only a single winner, we can apply some PR thinking. Either way, 10 "points" will be handed out to voters. If candidate A is elected, one voter gets all 10, but if B is elected, the points are shared equally. Normal range voting seems a little simplistic to me in terms of calculating the winner. When I developed my own form of proportional range voting, it didn't collapse into normal range voting in the single winner case, since the PR thinking continued. http://www.tobypereira.co.uk/voting.html Presumably PRV that's based on proportional approval voting using harmonic numbers of non-integers would also not collapse into normal range voting for one winner. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
From: Kevin Venzke To: election-meth...@electorama.com Sent: Sun, 24 July, 2011 23:49:24 Subject: Re: [EM] PR for USA or UK Hello again. >Sorry, I mean, I don't believe it is hopeless to try doing what you >want with a rated ballot. Range does use a rated ballot. Off the top >of my head I don't have any really great method suggestions here, >because it seems to me to be extremely difficult to design a method so >that it maximizes utility. If the method is strategy-proof, it will >tend to elect the sincere Condorcet winner. If it's not strategy-proof, >you can't fully trust the information you collect. Something in-between >seems to be needed, but I would bet nobody will feel very happy with >whatever is invented. Yes, range more than some other systems is vulnerable to strategy. The sort of Range PR that I would use may cause problems computationally, and a version of it that does a bit of strategy for you is likely to make the problem worse. But to summarise a possibility - everyone submits their range ballots. Then the computer calculates what would be the winning set of candidates under these votes. Then each ballot is looked at again by the computer and it works out the "optimum" vote for each voter on the basis of what everyone else has done. These new votes are then "submitted". Obviously everyone's changes at once so the goalposts move. But they could be recalculated a few times, and it might approach some form of equilibrium. But I'm not entirely sure at the moment how you would decide the optimum vote for someone based on the current situation. I'll think about it though. What I like about the range ballot here is that it sets out in advance each voter's preference for whole sets of candidates. It would work on the basis that how a voter rates a set of candidates is realted to their total score given to them. So if there are two to be elected then two candidates they give 5 out of 10 to is the same as a 10 and a 0. I would set that out as how the scores are essentially defined. With ranks I don't know if 1st and 4th is better or worse than 2nd and 3rd. >Kevin Venzke Toby >Hi Toby, Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
From: Jameson Quinn To: Toby Pereira Cc: EM Sent: Sun, 24 July, 2011 19:45:06 Subject: Re: [EM] PR for USA or UK >I don't necessarily think sophisticated voters are required in order to ensure >reasonable PR under PRV. I think as long as you don't get some candidates who >>have much better strategic voters than others, it should do OK. >You should read some of Schulze's papers about the history of free riding. It >seems clear from those examples that there are examples of parties with better >or >worse free-riding vote-management capabilities. So I would worry about >this >distorting results. OK, I might look into it. But you could probably legislate against blatant suggestions to vote in a specific way from certain parties. It would still exit "unofficially" with discussions online and elsewhere but anyone would have access to the information. I'm sure Warren's got an answer too. ;) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
From: Kevin Venzke To: election-meth...@electorama.com Sent: Sun, 24 July, 2011 20:34:33 Subject: Re: [EM] PR for USA or UK Hello again. --- En date de : Dim 24.7.11, Toby Pereira a écrit : >>Strategy-resistant systems do have certain advantages as you say, >>but in the single-winner case it would end up reducing range to a >>Condorcet method, which arguably isn't as good, and ends up pushing >>out a "better-liked" candidate for one that strictly more people >>prefer. And this is what I like about range - it's not just about >>which candidates you prefer to which other ones, but by how much. >I think the Range method itself is pretty incapable of this, but you >could do it either with rated ballots or with a rank ballot that has >truncation incentive. Is a range ballot not a rated ballot? >>And as long as strategy isn't performed better by voters of some >candidates >>than others, the fact that there would still be some >> >>honest voters would mean that the advantages of range would still >>remain to an extent, meaning that overall better-liked candidates >>stand a better chance, and it therefore reflects better the overall >>preferences of the electorate! >That paragraph makes sense if you're comparing Range to Approval, but >not Range to anything else. If large numbers of voters use strategy in >Range (and I'm pretty sure they would be encouraged to; personally I >wouldn't need any encouraging) this will destroy so much information >that the only way Range will win out is if the rank methods you compare >it to contain even more destructive incentives than Range has. With a single-winner election, the full strategy option is to vote approval style, but I'm not sure if this is as clear for PR. You say you wouldn't need any encouraging to vote strategically - I wouldn't either to be honest - but what is the optimal strategy? In any case, if range does turn out to be problematic, proportional approval voting would be my next choice. I don't like ranked ballots because you don't know how much the voter actually likes each candidate or whether they like them at all. >Can you explain your position without saying "party"? Because if you >didn't see the parties, and only saw voters, it would be indefensible >to give a seat to the 32%. There would be nothing special about that >group. Candidates A and B are both fairly similar and 68% of voters vote for both of these approval-style and no-one else. Candidates C and D are also similar to each other and 32% of voters vote for both of these approval style and no-one else. That's the example set out without parties. And it's the same as before - if 50% of the voters voted for A and B it would be exactly the right proportion (without rounding due to a specific number of seats) for one of A or B to be elected, and if 100% voted for them, it would eb exactly the right proportion for both seats. 75% is halfway. >Hi Toby, Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
I've replied to Jameson and Kevin in the same post here, so hopefully it's come out alright! From: Jameson Quinn To: Toby Pereira Cc: EM Sent: Sun, 24 July, 2011 2:50:12 Subject: Re: [EM] PR for USA or UK >I agree that PRV would give better results, with sophisticated voters, than >most >forms of PR. However, it does fail my criterion 4 (simple ballots) and do >worse >>than SODA-PR on criteria 5(smooth transition) and even arguably 1(true >proportionality - because separate districts spoil the proportionality). If >you >don't think >these criteria are reasonable, you should give that argument. > >I started out with a list of criteria because I think that's the right place >to >start when you're looking for a practical system. >JQ I don't necessarily think sophisticated voters are required in order to ensure reasonable PR under PRV. I think as long as you don't get some candidates who have much better strategic voters than others, it should do OK. I would argue that my system doesn't fail on simple ballots. It's not all or nothing. Yes, there are simpler ballots, but if I was rating simplicity of ballots approval style, I'd approve range ballots! But seriously, scores out of 6 is quite simple, and it could be made quite clear that you only need to rate candidates that you have any positive feeling towards. Blanks would count as zero. Some may argue for an average score to be given to blanks, but I think that would actually encourage people to fill out a load of zeros anyway. SODA-PR is probably simpler, but I think the delegable/non-delegable thing would be a bit confusing for voters and so wouldn't be simple in their minds. I know that it's arguably better to have the one vote and let your favourite candidate delegate (given that they probably have similar views to you) than dilute with several approvals, but why not just let candidates have their own delegation list - i.e. STV - and do away with the approval aspect completely (since you don't approve of voters actually voting approval style under your system yourself)? Smooth transition - yes, PRV a bigger step from FPTP in some ways than SODA-PR (giving candidates a score is further from a single X than approval-style votes), but the idea of giving your vote to the candidates to delegate is a pretty big paradigm shift in itself, and arguably causes it to fail on this criterion. Still, if we ever were to have PR in the UK, it would probably be STV anyway (don't know about in the US), which I would argue is no more or less smooth a transition than PRV from the starting point of FPTP. So for smooth transition, I don't think PRV fails, because I think it ties with the realistic (UK) frontrunner. Separate constituencies do spoil proportionality to an extent, yes. There would only be a certain number of seats available in each. If it was six, then a party with constant 10% support across the county would struggle to get anything. What's the alternative? We could have bigger constituencies, but that means bigger ballots, or party lists, but I don't like them. I'm not sure I get your district/co-district thing though. In any case, I think this is a problem of how we sort out districts/constituencies, rather than anything against PRV per se. Also, I don't get the whole thing about write-ins. Maybe it's a UK/US divide thing, but surely if you want to be elected then you stand for election. Therefore your name would be on the ballot. From: Kevin Venzke To: election-meth...@electorama.com Sent: Sun, 24 July, 2011 5:38:18 Subject: Re: [EM] PR for USA or UK >Hi Toby, Hello. >I really don't know what "dishonest results" means. Judging by your >example below it apparently requires comparing two different methods. >So, I can make any method give "dishonest results" just by inventing >a different method that requires dishonesty from everyone. Now every >other method in the world is cheating. I suppose what I mean is that by transferrig your vote for you, STV ends up producing the same result (in my simple case) as PRV with strategic voting, and to me it's an ugly result. >It's not a bad description that strategy-resistant systems "do the >strategy for you." This has important results: >1. The voters do not need to do the strategy >2. So the playing field is leveled >3. So votes should have correct effect in proportion to the number, >meaning the outcome is more accurate. That is, it reflects better the >overall preferences of the electorate. Strategy-resistant systems do have certain advantages as you say, but in the single-winner case it would end up reducing range to a Condorcet method, whi
Re: [EM] PR for USA or UK
My preferred system of proportional representation is proportional range voting. Each voter gives the candidates a score and the result are calculated from this. I have my own system of PRV - http://www.tobypereira.co.uk/voting.html - which I prefer to Warren's Reweighted Range Voting for various reasons. Mine can also be converted to a sequential method if computing power deems it necessary. So we would have geographical constituencies with several seats available in each, and candidates would be elected accordingly. No need to vote for parties. You would purely be voting for the candidates in your geographical constituency. Why range voting? I make an argument here - http://www.tobypereira.co.uk/voting2.html - but I'll summarise. First of all, I think that the argument for range ballots over ranked ballots is (even) greater for PR than it is for single-winner elections. STV with ranked ballots assumes that you want to get your first choice elected over any number of your next preferences, and so only when that is settled, will your vote be used further down your preference list (if it still can be). 1st choice > 2nd + 3rd + 4th. But it's not as if it can make any other assumption either because that would be a guess too. Also there's Warren's example here - http://rangevoting.org/PRcond.html. By submitting a range ballot, you are indicating how much you like each candidate. Strategy aside, I would argue that a proportional form of range voting is probably the purest form of PR there is. So what about strategy? Would strategy ruin the "purity" of proportional range voting? I don't think it would too much. Unless the voters of some candidates are better at voting strategically than the voters of others, then I don't see it as too much of a problem. And no system would be entirely free from strategy. Specifically under PRV, people might vote down some of their preferences if they think it's likely they'll be elected anyway. It's a bit of a risk though, so I'm not sure it would happen too much. If we can trust Warren's Bayesian Regret figures for single-winner cases and range voting generally comes out on top there, I don't think it would be too much of a stretch to imagine that it might also come out on top for multiple winners. And I would argue that more "strategy-resistent" systems generally work by basically doing the strategy for you, so already give "dishonest" results. So it's not that they give better results. On my website I give an example where party A has 68% of the support and party B 32%. There are two seats and so each party fields two candidates. Assuming everyone would vote approval style, under my system, they would win one each. Party A would need over 75% of the votes to win the second seat. I would argue that this is a fair result (75% being bang in the middle between 50% and 100% - the amount to exactly earn one and two seats). Of course party A voters could coordinate themselves and split into two factions of 34% to take both seats, but this would be very hard for them to achieve. STV (Droop quota anyway) would transfer the votes above the quota accordingly so that party A would win both seats, and give what I would regard as the less fair result. By the way, I tend to think quotas, whether Droop or Hare, all end up being fairly arbitrary. Droop is supposed to be the "best" because it's supposedly set as low as possible, but in reality it isn't. It's not as if all elected candidates ever end up exactly on the quota so unless you have a moveable quota then it always ends up being too high and more votes could be transferred away. I'm probably not acquainted enough with SODA or SODA-PR to give a full argument against it, but generally I think that voters would regard the idea of giving their votes to candidates in a delegable manner as just too weird. I'm not sure people would really get the point of it and would just want to have their own ranked list of candidates instead (and as we know, ranking isn't as good as range!) I'm not sure it would give better result than PRV anyway, or even Proportional Approval Voting (again, my version of it), and I'd have PAV as my second choice if PRV was deemed too complicated. I don't think it is too complicated though. It's not any more complicated for the voter than STV, and scores can be out of a low number if need be. 6 would be fine. From: Jameson Quinn To: EM Sent: Sat, 23 July, 2011 15:45:04 Subject: [EM] PR for USA or UK We had a discussion about the best practical single-winner proposal, which, while it certainly wasn't as conclusive as I'd hoped, seemed productive to me. I think we should have a similar discussion about PR. Obviously, the situations in the UK and in the USA are very different in this regard. The UK is, as far as I know, the origin of the PR movement (in the 1860s and 1870s, liberals gained seats disproporti
Re: [EM] General PR question
Normal Proportional Approval Voting would give it to ABC, ABD or ABE based on satisfaction. Everyone has voted for one of the elected candidates and some get two. Whereas with CDE, it's purely one each, but as you say this is envy-free. While I can see the merits of the envy-free argument, I would probably go for the ABC, ABD or ABE option. Perhaps a slightly weird analogy - you have an apple to give away on Thursday. John is the only person around, so you give it to him. Then on Friday you have two apples to give away. Fred is the only person to come along. You can give him one apple which would be envy-free, but the other one would get thrown away and wasted. Or you could give him both. But he might tell John who would then experience "envy". John doesn't materially lose anything by Fred getting two apples, so really I think Fred should get them both. It's slightly different with voting, because the people who get the extra candidate could get more of their preferred legistlation through at the expense of the others - so it's not purely envy, but possible material loss. But where do you draw the line? Maybe I'll think of an example later but perhaps you could have a case where the only envy-free solution is for everyone to end up with much less representation than they would in the envy result. So would our ideal system be the one that flattens representation out as much as possible? From: Andy Jennings To: EM Sent: Fri, 22 July, 2011 19:42:06 Subject: [EM] General PR question Forest and I were discussing PR last week and the following situation came up. Suppose there are five candidates, A, B, C, D, E. A and B evenly divide the electorate and, in a completely orthogonal way, C, D, and E evenly divide the electorate. That is: One-sixth of the electorate approves A and C. One-sixth of the electorate approves A and D. One-sixth of the electorate approves A and E. One-sixth of the electorate approves B and C. One-sixth of the electorate approves B and D. One-sixth of the electorate approves B and E. It is obvious that the best two-winner representative body is A and B. What is the best three-winner representative body? CDE seems to be the fairest. As Forest said, it is "envy-free". Some methods would choose ABC, ABD, or ABE, which seem to give more total satisfaction. Is one unequivocally better than the other? I tend to feel that each representative should represent one-third of the voters, so CDE is a much better outcome. Certain methods, like STV, Monroe, and AT-TV (I think) can even output a list of which voters are represented by each candidate, which I really like. I also note that if there was another candidate, F, approved by everybody, it is probably true that ABF would be an even better committee than CDE. Is there a method that can choose CDE in the first case and ABF in the second case? Andy Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] HBH
I'm not sure I've followed everything about how to determine the pecking order and how to calculate the distance between candidates, and why it's good to base the challenge order on this, but I'll go along with it! Could we work on a similar distance basis for STV? There are S candidates to be elected, so we could start with the bottom S in the pecking order. For the challenger (single candidate), can distance be measured between a set of candidates and a single candidate? I'm sure it can, so we could calculate the most distant candidate from the current "champion set". Then we need to see which of the S+1 candidates is to be eliminated. We now need to determine the order of comparison here as well. Essentially there's two orders of comparison we need to worry about. The first, as already described, is which candidate is to be pitted against the current "champion set". Then, once this is determined, we need to determine the order of comparison of the S+1 sets that contain all members of the "champion set" and the challenger candidate. Each set here will have just one of the S+1 candidates missing so in terms of starting at the bottom of the pecking order, we probably want to start off with the set that excludes the candidate at the top of the pecking order (the top out of the S+1 that are being considered here). Then on the basis that we can probably calculate distance between a set and a candidate, we can also probably calculate the distance between two sets. So we take our "champion set" containing S of the S+1 candidates, and compare it against the most distant other remaining set that still remains in this group. When only one of these sets remains, this becomes the new "champion set", and we find the most distant challenger and continue as before. Also, the winner in the set comparisons can be done as in Schulze STV (or another one if you prefer) as Schulze STV compares sets that differ by only one candidate anyway, so it seems fit for purpose. So, Forest, is this of any potential use? From: Toby Pereira To: fsimm...@pcc.edu Cc: election-methods@lists.electorama.com Sent: Thu, 21 July, 2011 12:19:36 Subject: Re: [EM] HBH Excellent - if you think it's a good idea it must be! I don't think it would be as simple as checking one possible result against one other that differs by one candidate. How would we decide which of the "current champion set" to remove to put the new candidate in for our comparison? We'd have to check the merits of each possible result. There wouldn't be that many though. So if S candidates are to be elected, the "current champion set" would obviously have S members. Then we introduce a challenger candidate giving us S+1 candidates. There will then only be S+1 possible sets of S members involving these candidates (one for each candidate's absence). Instead of comparing each of these sets against each other, we can stick to the principle of HBH and its winner-stays-on nature. So when we determine the winning set of S out of the S+1 candidates, we eliminate the candidate not in the winning set. Then we pick another challenger and so on, one at a time, until S candidates remain. These S are elected. As for deciding the order of comparison, I'm not sure I'm as well qualified as you! From: "fsimm...@pcc.edu" To: Toby Pereira Cc: election-methods@lists.electorama.com Sent: Thu, 21 July, 2011 2:22:03 Subject: Re: [EM] HBH Good idea. Let's play with it. - Original Message - From: Toby Pereira Date: Wednesday, July 20, 2011 4:44 pm Subject: Re: [EM] HBH To: fsimm...@pcc.edu Cc: election-methods@lists.electorama.com > I was thinking - Schulze STV compares every result against every > other result > that differs by just one candidate, which could be a lot of work > for a computer! > So could your HBH system be used for STV elections? Determine > the order of > comparison and compare two results that differ by one candidate > and the "losing > candidate" is eliminated. So each pairwise comparison eliminates > a candidate and > it's all done much more quickly. > > > > > > From: "fsimm...@pcc.edu" > To: fsimm...@pcc.edu > Cc: election-methods@lists.electorama.com > Sent: Mon, 18 July, 2011 19:25:01 > Subject: [EM] HBH > > HBH stands for Hog Belly Honey, the name of an inerrant > "nullifier" invented by > a couple of R.A. Lafferty > > characters. The HBH is the only known nullifier that can "posit > moral and > ethical judgments, set up and > > enforce categories, discern and make full philosophical > pronouncements,"
Re: [EM] HBH
Excellent - if you think it's a good idea it must be! I don't think it would be as simple as checking one possible result against one other that differs by one candidate. How would we decide which of the "current champion set" to remove to put the new candidate in for our comparison? We'd have to check the merits of each possible result. There wouldn't be that many though. So if S candidates are to be elected, the "current champion set" would obviously have S members. Then we introduce a challenger candidate giving us S+1 candidates. There will then only be S+1 possible sets of S members involving these candidates (one for each candidate's absence). Instead of comparing each of these sets against each other, we can stick to the principle of HBH and its winner-stays-on nature. So when we determine the winning set of S out of the S+1 candidates, we eliminate the candidate not in the winning set. Then we pick another challenger and so on, one at a time, until S candidates remain. These S are elected. As for deciding the order of comparison, I'm not sure I'm as well qualified as you! ____ From: "fsimm...@pcc.edu" To: Toby Pereira Cc: election-methods@lists.electorama.com Sent: Thu, 21 July, 2011 2:22:03 Subject: Re: [EM] HBH Good idea. Let's play with it. - Original Message - From: Toby Pereira Date: Wednesday, July 20, 2011 4:44 pm Subject: Re: [EM] HBH To: fsimm...@pcc.edu Cc: election-methods@lists.electorama.com > I was thinking - Schulze STV compares every result against every > other result > that differs by just one candidate, which could be a lot of work > for a computer! > So could your HBH system be used for STV elections? Determine > the order of > comparison and compare two results that differ by one candidate > and the "losing > candidate" is eliminated. So each pairwise comparison eliminates > a candidate and > it's all done much more quickly. > > > > > > From: "fsimm...@pcc.edu" > To: fsimm...@pcc.edu > Cc: election-methods@lists.electorama.com > Sent: Mon, 18 July, 2011 19:25:01 > Subject: [EM] HBH > > HBH stands for Hog Belly Honey, the name of an inerrant > "nullifier" invented by > a couple of R.A. Lafferty > > characters. The HBH is the only known nullifier that can "posit > moral and > ethical judgments, set up and > > enforce categories, discern and make full philosophical > pronouncements," in > other words eliminate the > > garbage and keep what's valuable. The main character, the "flat > footed genius," > Joe Spade, picks the > > name "Hog Belly Honey," for it "on account it's so sweet." > > The whole idea of HBH is just starting at the bottom of a > pecking order and > pitting (for elimination) the > > current champ against the most distant challenger. I hope you > will keep that in > mind as we introduce > > the necessary technical details. > > HBH is based on range style ballots that allow the voters to > rate each > alternative on a range of zero to > > some maximum value M. [Keep this M in mind; we will make > explicit use of it > presently.] > > Once the ballots are voted and submitted, the first order of > business is to set > up a "pecking order" for > > the purpose of resolving ties, etc. Alternative X is higher in > the pecking > order than alternative Y if > > alternative X is rated above zero on more ballots than Y is > rated above zero. > If both have the same > > number of positive ratings, then the alternative with the most > ratings greater > than one is higher in the > > pecking order. If that doesn't resolve the tie, then the > alternative with the > greatest number of ratings > > above two is higher, etc. > > In the practically impossible case that two alternatives have > exactly the same > number of ratings at each > > level, ties should be broken randomly. > > The next order of business is to establish a proximity relation > between > alternatives. For our purposes > > closeness or proximity between two alternatives X and Y is given > by the number > > Sum over all ballots b, min( M*(M-1), b(X)*b(Y) ). > > [The minimization with M*(M-1) clinches the method's resistance > to compromise, > as explained below.] > > This proximity value is a useful measure of a certain kind of > closeness of the > two alternatives: the larger > > the proximity number the closer the alternatives in this limited
Re: [EM] HBH
I was thinking - Schulze STV compares every result against every other result that differs by just one candidate, which could be a lot of work for a computer! So could your HBH system be used for STV elections? Determine the order of comparison and compare two results that differ by one candidate and the "losing candidate" is eliminated. So each pairwise comparison eliminates a candidate and it's all done much more quickly. From: "fsimm...@pcc.edu" To: fsimm...@pcc.edu Cc: election-methods@lists.electorama.com Sent: Mon, 18 July, 2011 19:25:01 Subject: [EM] HBH HBH stands for Hog Belly Honey, the name of an inerrant "nullifier" invented by a couple of R.A. Lafferty characters. The HBH is the only known nullifier that can "posit moral and ethical judgments, set up and enforce categories, discern and make full philosophical pronouncements," in other words eliminate the garbage and keep what's valuable. The main character, the "flat footed genius," Joe Spade, picks the name "Hog Belly Honey," for it "on account it's so sweet." The whole idea of HBH is just starting at the bottom of a pecking order and pitting (for elimination) the current champ against the most distant challenger. I hope you will keep that in mind as we introduce the necessary technical details. HBH is based on range style ballots that allow the voters to rate each alternative on a range of zero to some maximum value M. [Keep this M in mind; we will make explicit use of it presently.] Once the ballots are voted and submitted, the first order of business is to set up a "pecking order" for the purpose of resolving ties, etc. Alternative X is higher in the pecking order than alternative Y if alternative X is rated above zero on more ballots than Y is rated above zero. If both have the same number of positive ratings, then the alternative with the most ratings greater than one is higher in the pecking order. If that doesn't resolve the tie, then the alternative with the greatest number of ratings above two is higher, etc. In the practically impossible case that two alternatives have exactly the same number of ratings at each level, ties should be broken randomly. The next order of business is to establish a proximity relation between alternatives. For our purposes closeness or proximity between two alternatives X and Y is given by the number Sum over all ballots b, min( M*(M-1), b(X)*b(Y) ). [The minimization with M*(M-1) clinches the method's resistance to compromise, as explained below.] This proximity value is a useful measure of a certain kind of closeness of the two alternatives: the larger the proximity number the closer the alternatives in this limited sense, while the smaller the number the more distant the alternatives from each other (again, in this limited sense). For the purposes of this method, if two alternatives Y and Z have equal proximity to X, then the one that is higher in the pecking order is considered to be closer than the other. In other words, the pecking order is used to break proximity ties. Next we compute the majority pairwise victories among the alternatives. Alternative X beats alternative Y majority-pairwise if X is rated above Y on more than half of the ballots. For the purposes of this method, the "victor" of a pair of alternatives is the one that beats the other majority pairwise, or in the case where neither beats the other majority-pairwise it is the one that is higher in the pecking order. Of the two, the non-victor alternative is called the "loser." In other words, the pecking order decides pairwise victors and losers when there is no majority defeat. [This convention on victor and loser is what makes the method plurality compliant, as explained below.] Next we initialize an alphanumeric variable V with the name of the lowest alternative in the pecking order, and execute the following loop: While there remain two or more discarded alternatives discard the loser between V and the alternative most distant from V, and replace V with the name of the victor of the two. EndWhile Finally, elect the alternative represented by the final value of V. This HBH method is clone free, monotone, Plurality compliant, compromise resistant, and burial resistant. Furthermore, it is obviously the case that if some alternative beats each of the other alternatives majority pairwise, then that alternative will be elected. Let's see why the method is plurality compliant: If there is even one majority defeat in the sequence of eliminations, every value of V after that will be the name of an alternative that is rated positively on more than half of the ballots. If none of the victories are by majority defeat, then the winner is the alternative highest on the pecking order, i.e. the one with the greatest number of positive ratings. Let's see why the method is monoton
Re: [EM] Correspondences between PR and lottery methods (was Centrist vs. non-Centrists, etc.)
Regarding this, it might be an idea to perform some sort of transformation on
the satisfaction score for a result before using it to correspond to
probability
of coming out in the lottery. For the simple case of Proportional Approval
Voting with D'Hondt divisors (so 1 + 1/2 + 1/3 etc), take the average
satisfaction score for each voter under the result. Then find the inverse
harmonic number of this. This might correspond better to level of
representation
for a voter so it could be this number that's proportional to the probability
of
this result being picked.
(Under my versions of PAV and PRV, the "representation score" of a result
corresponds more to this this normalised version.)
________
From: Toby Pereira
To: Kristofer Munsterhjelm
Cc: election-methods@lists.electorama.com; fsimm...@pcc.edu
Sent: Tue, 19 July, 2011 15:46:52
Subject: Re: [EM] Correspondences between PR and lottery methods (was Centrist
vs. non-Centrists, etc.)
OK, thanks for the information. But what I meant regarding a result (group of
winners) having a score itself is that this score is just the total
satisfaction
score for a particular result, and then it is this number that is proportional
to the probability of that set of candidates being elected. So rather than
looking at each candidate's chances in the lottery individually, you could look
at whole results and the candidates are elected as one. I was thinking that
this
might be an analogue to random ballot in the single winner case.
From: Kristofer Munsterhjelm
To: Toby Pereira
Cc: fsimm...@pcc.edu; election-methods@lists.electorama.com
Sent: Tue, 19 July, 2011 15:15:15
Subject: Re: [EM] Correspondences between PR and lottery methods (was Centrist
vs. non-Centrists, etc.)
Toby Pereira wrote:
> For proportional range or approval voting, if each result has a score, you
>could make it so that the probability of that result being the winning result
>is
>proportional to that score. Would that work?
For a lottery derived from PAV or PRV, each winner has a single score, which is
the probability that the winner would be selected in that lottery. However, an
entire assembly (group of winners) does not have a single score as such.
That is, you get an output of the sort that {A: 0.15, B: 0.37, C: 0.20, D:
0.17,
E: 0.11}, which means that in this lottery, A would win 15% of the time. It's
relatively easy to turn this into a party list method - if party A wins 15% of
the time, that just means that party A should get 15% of the seats. You could
also use it in a system where each candidate has a weight, but to my knowledge
that isn't done anywhere.
However, if A can only occupy one seat in the assembly, it's less obvious
whether or not A should win (or how often, if it's a nondeterministic system)
in
a two-winner election. In his reply to my question, Forest gave some ideas on
how to figure that out.
> Also, how is non-sequential RRV done? Forest pointed me to this a while back
> -
>http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026425.html
> - the bit at the bottom seems the relevant bit. Is that what we're talking
>about?
Very broadly, you have a function that depends on a "prospective assembly"
(list
of winners) and on the ballots. Then you try every possible prospective
assembly
and you pick the one that gives the best score.
In proportional approval voting, each voter gets one satisfaction point if one
of the candidates he approved is in the outcome, one plus a half if two
candidates, one plus a half plus a third if three candidates, and so on. The
winning assembly composition is the one that maximizes the sum of satisfaction
points. It's also possible to make a Sainte-Laguë version where the point
increments are 1, 1/3, 1/5... instead of 1, 1/2, 1/3 etc.
Proportional range voting is based on the idea that you can consider the
satisfaction function (how many points each voter gets depending on how many
candidates in the outcome is also approved by him) is a curve that has f(0) =
0,
f(1) = 1, f(2) = 1/2 and so on. Then you can consider ratings other than
maximum
equal to a fractional approval, so that, for instance, a voter who rated one
candidate in the outcome at 80%, one at 100%, and another at 30%, would have a
total satisfaction of 1 + 0.8 + 0.3 = 2.1.
All that remains to generalize is then to pick an appropriate continuous curve,
because the proportional approval voting function is only defined on integer
number of approvals (1 candidate in the outcome, 2 candidates, 3 candidates).
That's what Forest's post is about.
(Mathematically speaking, the D'Hondt satisfaction function f(x) is simply the
xth harmonic number. Then one can see that f(x) = integral from 0 to 1 of (1 -
x^n)/(1-x) dx. This can be a
Re: [EM] Correspondences between PR and lottery methods (was Centrist vs. non-Centrists, etc.)
OK, thanks for the information. But what I meant regarding a result (group of
winners) having a score itself is that this score is just the total
satisfaction
score for a particular result, and then it is this number that is proportional
to the probability of that set of candidates being elected. So rather than
looking at each candidate's chances in the lottery individually, you could look
at whole results and the candidates are elected as one. I was thinking that
this
might be an analogue to random ballot in the single winner case.
From: Kristofer Munsterhjelm
To: Toby Pereira
Cc: fsimm...@pcc.edu; election-methods@lists.electorama.com
Sent: Tue, 19 July, 2011 15:15:15
Subject: Re: [EM] Correspondences between PR and lottery methods (was Centrist
vs. non-Centrists, etc.)
Toby Pereira wrote:
> For proportional range or approval voting, if each result has a score, you
>could make it so that the probability of that result being the winning result
>is
>proportional to that score. Would that work?
For a lottery derived from PAV or PRV, each winner has a single score, which is
the probability that the winner would be selected in that lottery. However, an
entire assembly (group of winners) does not have a single score as such.
That is, you get an output of the sort that {A: 0.15, B: 0.37, C: 0.20, D:
0.17,
E: 0.11}, which means that in this lottery, A would win 15% of the time. It's
relatively easy to turn this into a party list method - if party A wins 15% of
the time, that just means that party A should get 15% of the seats. You could
also use it in a system where each candidate has a weight, but to my knowledge
that isn't done anywhere.
However, if A can only occupy one seat in the assembly, it's less obvious
whether or not A should win (or how often, if it's a nondeterministic system)
in
a two-winner election. In his reply to my question, Forest gave some ideas on
how to figure that out.
> Also, how is non-sequential RRV done? Forest pointed me to this a while back
> -
>http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026425.html
> - the bit at the bottom seems the relevant bit. Is that what we're talking
>about?
Very broadly, you have a function that depends on a "prospective assembly"
(list
of winners) and on the ballots. Then you try every possible prospective
assembly
and you pick the one that gives the best score.
In proportional approval voting, each voter gets one satisfaction point if one
of the candidates he approved is in the outcome, one plus a half if two
candidates, one plus a half plus a third if three candidates, and so on. The
winning assembly composition is the one that maximizes the sum of satisfaction
points. It's also possible to make a Sainte-Laguë version where the point
increments are 1, 1/3, 1/5... instead of 1, 1/2, 1/3 etc.
Proportional range voting is based on the idea that you can consider the
satisfaction function (how many points each voter gets depending on how many
candidates in the outcome is also approved by him) is a curve that has f(0) =
0,
f(1) = 1, f(2) = 1/2 and so on. Then you can consider ratings other than
maximum
equal to a fractional approval, so that, for instance, a voter who rated one
candidate in the outcome at 80%, one at 100%, and another at 30%, would have a
total satisfaction of 1 + 0.8 + 0.3 = 2.1.
All that remains to generalize is then to pick an appropriate continuous curve,
because the proportional approval voting function is only defined on integer
number of approvals (1 candidate in the outcome, 2 candidates, 3 candidates).
That's what Forest's post is about.
(Mathematically speaking, the D'Hondt satisfaction function f(x) is simply the
xth harmonic number. Then one can see that f(x) = integral from 0 to 1 of (1 -
x^n)/(1-x) dx. This can be approximated by a logarithm, or calculated by use of
the digamma function. Forest gives an integral for the corresponding
Sainte-Laguë satisfaction function in the post you linked to, and I give an
expression in terms of the harmonic function in reply:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026437.html
)
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Correspondences between PR and lottery methods (was Centrist vs. non-Centrists, etc.)
For proportional range or approval voting, if each result has a score, you could make it so that the probability of that result being the winning result is proportional to that score. Would that work? Also, how is non-sequential RRV done? Forest pointed me to this a while back - http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026425.html - the bit at the bottom seems the relevant bit. Is that what we're talking about? (I have my own ways of course - http://www.tobypereira.co.uk/voting.html) From: "fsimm...@pcc.edu" To: Kristofer Munsterhjelm Cc: election-methods@lists.electorama.com Sent: Tue, 19 July, 2011 2:00:40 Subject: [EM] Correspondences between PR and lottery methods (was Centrist vs. non-Centrists, etc.) - Original Message - From: Kristofer Munsterhjelm Date: Monday, July 18, 2011 1:12 pm Subject: Re: [EM] Centrist vs. non-Centrists (was A distance based method) To: fsimm...@pcc.edu Cc: election-methods@lists.electorama.com > fsimm...@pcc.edu wrote: > > > > - Original Message - > > From: Kristofer Munsterhjelm > > Date: Wednesday, July 13, 2011 2:12 pm > > Subject: Re: [EM] Centrist vs. non-Centrists (was A distance > based method) > > To: fsimm...@pcc.edu > > Cc: Jameson Quinn , election-methods@lists.electorama.com > > >> I think you said that these are related, even: that PR > methods and > >> stochastic single-winner methods are similar, seeking > >> proportionality (the former in seats, the latter in time). > >> > > > > Precisely. Andy Jennings was the one who hit on the key idea for > > constructing a lottery directly from a PR method; just do an N- > winner> PR method for large N, and treat the candidates like we > treat parties > > in a party list method; keep the candidates in the running > after they > > have already won a seat. Then the number of seats won by the > > candidate divided by the total number of seats is the candidate's > > probability in the lottery. > > How would that work with combinatorial methods like PAV -- would > you > just clone each candidate a very large number of times? (I guess > the > question is academic because running a combinatorial method with > a very > large number of candidates would take too much time anyway.) An interesting question here is whether PAV woould give the same proportions as sequential PAV in the limit. Also, as usual, proposed slates (with repeats allowed) could be tested to see which gives the largest PAV score. > > Also, is there any way of going in the reverse direction? I can > see how > one could turn the lottery into a party list PR allocation: just > give > each party a number of seats proportional to the chance they > have in the > lottery, resolving rounding problems by apportionment algorithm > of > choice. That works when the number of seats is large. Right. Also if the lottery is the Ultimate Lottery, it is the lottery that maximizes the product of ballot expectations, so for apportionment you can choose the apportionment that maximizes the corresponding product under the constraint that there are n candidates and each gets 1/n of the probability. This is more of an indirect conversion based on the method of getting the lottery instead of just the lottery probabilities themselves. >There > might be too > little information to go to individual member multiwinner > methods from a > lottery, though. > Perhaps something to the effect of, when picking n members, just > spin a > roulette wheel with zones of size proportional to the chances in > the > lottery. If the ball lands on a zone of an already elected > candidate, > spin again, otherwise elect the candidate in question. Repeat > until n > candidates have been elected. That is nondeterministic, however. You could make it deterministic by using the conditional probabilities, i.e. the probabilities that are conditioned on the exclusion of the candidates that have already been chosen. Another way is to amalgamate the factions by averaging the ballots that have the same top choice (weighted average if more than one candidate rated equal top). The lottery then gives a certain weight to each faction that may or may not be equal to the random ballot lottery. The factions with probability in excess of the quota can pass the excess down, just as the factions with a deficiency pass their entire probability down to lower rated candidates on their amalgamated rating ballots. It seems like STV could be thought of as using the random ballot lottery probabilities in a similar way. Andy and I were thinking mostly of Party Lists via RRV. His question was that if we used RRV, either sequential or not, would we get the same result as the Ultimate Lottery Maximization. I was able to show to our satisfaction, that at least in the non-sequential RRV version, the results would be the same. It seems li
[EM] A Condorcet-like, STV-like, rank-based PR system
I was thinking about the problem Warren outlined here - http://rangevoting.org/PRcond.html - and how you might get around it using a ranked PR system. So here's my attempt: Each voter ranks the candidates in order of preference. Ties are allowed. For n winners, each set of n candidates is compared against each other set. For two sets being compared, x and y, each member of x is compared against each member of y. For example, in a two-seat election, candidates A and B are being compared against C and D. There are four pairwise comparisons - AC, AD, BC and BD. So under each result (A, B or C, D), a voter will have a score from 0 to 4. Based on these 0-4 scores, a representation score is calculated for each of the two results. The representation score is calculated in the same way as in my proportional range/approval voting (http://www.tobypereira.co.uk/voting.html) with each pairwise comparison treated as a "candidate" or qandidate. So in this example, four qandidates are elected. The representation score for each of the two sets of candidates (the actual candidates, as opposed to qandidates) are then recorded next to each other. This is the pairwise result for the two sets of candidates. Once every possible winning set of candidates has been compared against every other one, the winning set is calculated using an off- the-shelf pairwise Condorcet method such as Kemeny-Young or Schulze. If one set of candidates beats all others then it is the equivalent of a Condorcet winner. When two sets of candidates are being compared against each other, the same candidate will often appear in both lists (e.g. AB versus AC). So when a candidate is compared against itself, you could give a score of, say, 0, 0.5 or 1 to each voter for the tied result. The way the representation scores work, it won't make a difference to the numerical difference between the representation scores for each set of candidates. If we use the above example, by giving 0 for the repeated candidate, the two sets of candidates may have a representation score of 0.5 and 0.4 respectively. By giving a score of 1, this will simply add 0.25 onto each score so the difference between them will still be 0.1. (0.25 because there are four qandidates and the overall representation score is out of 1.) So whatever score is given won't make any difference at least under Kemeny-Young (which I understand better than Schulze). It may actually be best to simply ignore these comparisons altogether, so when comparing AB against AC, there would be three qandidates (AC, BA and BC). This is what I will go with for now. Where voters have ranked two different candidates at the same level, I think it may make more of a difference to things. These scores can't be ignored unless a voter has ranked every candidate in both sets at the same level (in which case we could ignore that voter entirely) or every voter has ranked the two candidates at the same level (not likely). To maintain equivalence with Kemeny-Young in the one-winner case, you can split the voter in two halves and award scores of 0 and 1 to each half respectively. In the full version, every possible winning set of candidates would have to be compared against every other set, which would probably not be viable computationally in most cases. A sequential system could be used. The most basic version of this would be to find the best single winner, and then compare all two-winner sets that contain this winner and so on. I'm not entirely sure what sort of results this would produce but in a few very simple cases, it seemed not to be too bad. One thing I've noticed - with loyal party voting and a comparison of (A1, A2 ... An) against (A1, A2, ... An-1, B), the B voters seem to be better off by ordering the A candidates in the same order as the A voters. It could be tested against other proportional systems, to see if it produced similar results, including against my proportional range system. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Quotaless STV
I did wonder that myself and considered mentioning in the post for some reason didn't. I'm not 100% sure. If it does make a difference you could easily add in some sort of rule to determine how to do it, although the more rules the uglier. You could do it in stages. At the first stage everyone transfers away any votes above the 1/(n+1) threshold where there are n candidates. Any votes that might get transferred to a candidate already above this would automatically go to third choice, fourth etc. Once this is done, it would be clear that some candidates would be stuck at higher than 1/(n+1) votes due to voters not having made enough ranked choices. So a new quota would be calculated and the same process would happen again until no votes can be transferred. All candidates have their votes transferred simultaneously so there would be no ordering to it. I know I've mentioned the word "quota" but it's not a specific set quota like Droop or Hare and it's always up for renewal if it can be reduced further, so I'd still essentially call this quotaless STV. From: Warren Smith To: election-methods Sent: Sat, 9 July, 2011 21:38:15 Subject: [EM] Quotaless STV --that's an interesting idea. This may be a dumb question, but is it clear that when we are "transferring away everything you can" that order is irrelevant? Or might it be that the order in which the candidates activate their "transfer it all away" actions, makes a difference, i.e. can cause the results to differ? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Median-based Proportional Representation
Is this just the Instant Run-off version of STV that you're talking about that pays no attention to who you ranked below top? Also your example here - http://rangevoting.org/PRcond.html - would that be resolved under any form of STV in existence? From: Warren Smith To: Jameson Quinn Cc: election-methods Sent: Sat, 9 July, 2011 19:38:13 Subject: Re: [EM] Median-based Proportional Representation > In AT-TV, suppose > 30% of the voters vote Red=9, Blue=Green=0; > 30% of the voters vote Blue=9, red=green=0; > 40% of the voters vote Green=5, red=blue=4. > Will it then elect 30% reds, 30% blues, and 40% greens? > And do you consider that the right thing to do? --(in this situation, by the way, I think RRV would elect <=20% Greens and the rest would be evenly split between reds and blues.) RRV incentivizes exaggerating in your vote to max and min scores; but it also de-incentivizes that because if you exaggerate then your vote gets de-weighted more when your guy wins a seat. So the net result is probably that you are incentivized to exaggerate on candidates whose winning chances seem poor, but to try to "free ride" for candidates that seem sure-thing winners by dishonestly not giving them high scores. With STV, a big flaw is that it pays no attention to anybody you ranked below top. If you ranked Bush>Gore>>>Hitler, it pays no attention to the "Gore>>>Hitler" part of your vote, until after Bush is elected. And basically, any party voter-bloc which ranks Green-party candidates above all others, will have zero effect on non-Green winners until after the last Green has won, then some small fraction of "leftover" green power will be able to exert some (tiny and varying with the size of the leftover in a rather random-seeming way) effect. This ignoring, seems a very serious flaw of STV, that is not present with RRV. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Quotaless STV
I was wondering if you could run a Single Transferable Vote election without worrying about having a Droop/Hare etc. quota.* I'm sort of thinking out loud and I'm not sure what sort of results this might produce. In the fist round, all candidates transfer away as many votes as they can get away with so that they don't end up in last place. So if there are 10 candidates, then having more than 1/(n+1) votes will guarantee not finishing in last place. Because not every voter will rank every candidate, some candidates will be "stuck" at much higher than 1/(n+1) and so others may get away with transferring more away and end up with less than this and still not finish last. 1/(n+1) isn't a specific quota. The candidate in last place is then eliminated. In each subsequent round, the transferred votes are all reset (de-transferred) and the process starts again. Continue until the right number of candidates remain for the number of available seats. Obviously any candidate reaching the Droop Quota will automatically get elected, but no quota is actually built into the system at any point. You could also use this system for single winners as an alternative to the Alternative Vote (Instant Run-off). But by eliminating one candidate at a time, it's not a very "Condorcety" method but could possibly be adapted. You could certainly compare set of candidates that differed only by one. I might come back to that. *Actually, I don't know much about STV methods - is Schulze STV quotaless? I've had a look at its Wikipedia article, and although in some parts it's as clear as mud, it appears not to have a specific quota. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Has this idea been considered?
> > >Why are the votes only delegable if you bullet vote (or is that obvious)? >Because if you vote for several, which one would get to assign the delegated >votes? Can't they all delegate the votes that they get from you? Also, just out of interest, is there a multi-winner version? > >SODA outputs approval ballots (which can also be considered as 3-rank Bucklin >ballots). Any proportional method with approval ballots as an input can then >>be >used. With the number of dimensions on which such systems can vary, I could >easily list two dozen distinct methods (although results would tend to agree >>across many of them). With a proportional approval system, it wouldn't always be obvious who would get elected under a particular result before going into the calculations. So when it gets to the delegation stage, wouldn't it be a headache for the candidates to work out what would happen depending on how they delegated? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Median-based Proportional Representation
I had a look at your system - http://www.mail-archive.com/election-methods@lists.electorama.com/msg07066.html - I think I might have to look at it again to get it! But one thing about percentiles. As I understand it, people often disagree about how to calculate percentiles. The one I agree with on here - http://en.wikipedia.org/wiki/Percentile - is the one recommended by NIST. Where P is the percentile and N is the population, the ranked posistion would be P/100 * (N+1). Does your system have an inbuilt assumption about this? From: Jameson Quinn To: Toby Pereira Cc: electorama list Sent: Sat, 9 July, 2011 0:27:12 Subject: Re: [EM] Median-based Proportional Representation I've told Warren to change that, and he hasn't given me a clear criterion for what I have to do so he will. I've created a system called AT-TV which is PR and reduces to a median-based system in the single-winner case. It's Bucklin-like, in that there is a falling approval threshold, and when a candidate gets enough approvals to be elected (a Droop quota) they are, which "uses up" those votes (except for the excess). So in a one-winner case, it's based on 50th percentile (median), but in, for instance, a 3-winner case, it would be (pseudo-)maximizing the elected candidates' 75th-percentile score, not their 50th-percentile. I think this is the appropriate thing to do in the multi-winner "median" case. JQ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Median-based Proportional Representation
Just to clarify this, for the nth "permeantile", I think you'd weight each point on the n side (100-n)^2 and on the (100-n) side it would be n^2 . ____ From: Toby Pereira To: electorama list Sent: Sat, 9 July, 2011 0:19:30 Subject: [EM] Median-based Proportional Representation *I was thinking about how you would calculate permeantiles. In a uniform distribution between 0 and 1, the 25th permeantile would be 0.25. If you weight the averages of each side 3 to 1 in favour of the smaller side of the permeantile (0 to 0.25), and average these, then you get 0.25. (3*0.125 + 1*0.625) / 4 = 0.25. So for the 10th permeantile, you have (9*0.05 + 1*0.55) / 10 = 0.1 and so on. I imagine this would work for non-uniform distributions too. (Sorry for going off topic.) Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Median-based Proportional Representation
While discussing median-based range voting - http://rangevoting.org/MedianVrange.html, Warren Smith says "Average-based range voting generalizes to a multiwinner proportional representation voting system called reweighted range voting. (See papers 78 and 91 here.) But there currently is no known way to generalize median-based range voting to do that." So I was thinking about how you might get a median-based PR system, using range voting, or some other score system, such as Borda Count. I don't think there is necessarily a "perfect" method but I did come up with something (possibly ridiculous). You find a way to convert the scores of the candidates so that a candidate's median score becomes their mean score. For example, if a candidate's mean was 5 (out of 10) and their median was 7, their scores would undergo some sort of transformation so that their mean score became 7. Likewise if someone had a mean of 7 and a median of 5, their scores would undergo a transformation to reduce the mean to 5. One way to do this is as follows: Convert the range so that it becomes 0 to 1 (so in a 0-10 case, just divide all scores by 10). Then for each candidate you convert their score s to s^n where n is the number for that particular candidate that will make the original median score the mean of the transformed scores. For n over 1 the score will be reduced and for n under 1, the score will increase. So each candidate has their own value of n. Once all the scores have been converted, you can just do whatever you would have done in your non-median-based PR system to find the winning candidates. Obviously, this is a bit of a fudge because although we are fixing the mean for each candidate to what we want, the rest of the scores just end up how they end up. There would be different conversion systems that convert median to mean but give different values for the other scores. Just looking at the median and mean here could be seen as a bit arbitrary. As well as converting median to mean, we would ideally also want to convert other percentiles accordingly. We'd want to convert the 25th percentile score to the 25th "permeantile"*, or whatever the term is. (Is there a term?) But it would actually be impossible to do this properly. With repeated scores (which would always happen where there are more voters than possible scores), different percentile values will have the same score. For example, if someone's median score is 5, it's likely to also be 5 at the 51st percentile. But, as far as I understand it, the "permeantile" would not be able to have a flat gradient at any point, unless it's flat all the way across. So we couldn't have a "perfect" system that worked on this basis. So for simplicity we can just use the system as described. Of course, with range voting, people might vote approval style, so many candidates might simply have a median of 0 or 10. In that case the only "reasonable" conversion would be to convert all their scores to 0 or 10 respectively. This problem wouldn't occur to the same degree under Borda Count, however. *I was thinking about how you would calculate permeantiles. In a uniform distribution between 0 and 1, the 25th permeantile would be 0.25. If you weight the averages of each side 3 to 1 in favour of the smaller side of the permeantile (0 to 0.25), and average these, then you get 0.25. (3*0.125 + 1*0.625) / 4 = 0.25. So for the 10th permeantile, you have (9*0.05 + 1*0.55) / 10 = 0.1 and so on. I imagine this would work for non-uniform distributions too. (Sorry for going off topic.) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Has this idea been considered?
I can see the point about strategic range just being approval, but strategic First-Past-The-Post is just ignoring everyone except the top two candidates, and you wouldn't just cut out all other candidates in an election to make it simpler. (I think I nicked that point from Warren Smith). If range voting does still produce some honest voters then it might still give a better winner than approval. I suppose the main worry is that under First-Past-The-Post, people know that if they are voting for someone who's unlikely to win then they are "wasting" their vote, whereas under range voting, the best strategy isn't necessarily as obvious so people lose voting power by not understanding the ins and outs of tactical voting. To me, that's probably the biggest point against range voting. Having said that, if it's as simple as always give 0 or 10 (if it's out of 10), then I imagine it should catch on pretty quickly, although who to give the 0s and 10s to might not always be as obvious. But anyway, I would use range voting for multi-winner elections. For me the biggest problem is not which particular system we use to elect a single winner, but that there is a single winner that takes everything. When we had the referendum for Alternative Vote (Instant Run-off) in the UK, I think most people that preferred it to First-Past-The-Post agreed that it was just scratching the surface and that although it seemed nicer in principle it wouldn't really make much of a material difference (and generally for single-winner systems). And I think most people who voted for Alternative Vote really wanted a proportional system. Anyway, the point I was going to make is that I wonder what strategies people would adopt under a proportional range system - would it always be 0 or 10? From: Andrew Myers To: election-methods@lists.electorama.com Sent: Fri, 8 July, 2011 19:41:27 Subject: Re: [EM] Has this idea been considered? To me, Range remains a non-starter for political settings, though I can see some valid uses. I have implicitly argued that the real barrier to adoption of other voting method is simply the complexity of constructing one's ballot. Range voting is more complex than producing an ordering on candidates. For me the problem of determining my own utility for various candidates is quite perplexing; I can't imagine the "ordinary voter" finding it more pleasant. Range also exposes the possibility of strategic voting very explicitly to the voters. Only a chump casts a vote other than 0 or 10 on a 10-point scale. Range creates an incentive for dishonesty. So if the lazy voters are voting approval style because they don't want to sort out their utilities, and the motivated voters are voting approval style because that's the right strategy, who's left? It seems to me that we might as well have Approval and keep the ballots simple rather than use Range. -- Andrew Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Has this idea been considered?
The thing about SODA is that it's harder to "get" than Approval Voting. I haven't exactly read through all the posts on it here thoroughly but I've looked at the page - http://wiki.electorama.com/wiki/Simple_Optionally-Delegated_Approval - and I do find myself thinking "What?" All of its advantages over other systems may be within the posts on this board, but they are not that clear to me from reading the article. The method is explained and also the criteria it satisfies but I'm not happy that I've been convinced why it works. Why are the votes only delegable if you bullet vote (or is that obvious)? Also it seems like a lot of work for just the people who bullet vote (and also allow delegation). Do we know in practice what proportion of people do bullet vote in Approval Voting? Might SODA reduce this number anyway? From the page: "If any candidate has an absolute majority at this point, or cannot possibly be beaten by any other candidate using the delegable votes and candidate rankings available, then they win immediately." Does absolute majority just mean over 50%? But with Approval 50% isn't a particular threshold. You can get over 50% and still be beaten. Maybe I'm just unclear on "absolute majority", but it's been put as distinct from "cannot possibly be beaten by any other candidate using the delegable votes and candidate rankings available". And it still seems strange to me that candidates pre-declare their delegation order but then still get to negotiate. Yes, there's an explanation, but I'm not really sure I get it. "The system as it stands allows them to see, after the votes are counted, which of them deserves to win. That one will not delegate their votes, and the other one (of necessity) will." Couldn't there be a way in the system to decide who deserves to win (e.g. based on who would get more votes after the delegation or who had more to start with)? Also, just out of interest, is there a multi-winner version? From: Andy Jennings Cc: election-methods@lists.electorama.com Sent: Fri, 8 July, 2011 20:57:52 Subject: Re: [EM] Has this idea been considered? On Fri, Jul 8, 2011 at 3:56 AM, Jameson Quinn wrote: > >So, I guess the question is: is there anyone who would support Approval but >not >SODA? Respond in text. Also, I made a poll on betterpolls - go >vote. http://betterpolls.com/v/1425 > Wow, that results page is hard to read when the poll is about voting systems and the results are analyzed with lots of different voting methods. Very "meta". In any case, I went and voted. I was pretty hard on SODA. Even though I like where it's going, I, like Kristofer, don't think it's been analyzed enough to become our endorsed system at this point. Let's keep working on it... Andy Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Toby Pereira, PR voting methods
I'm not sure I exactly followed that. Jameson's option 2 is to look at the nominated slates and see which is best. You could also still use one of the other methods to find a possible winner and then compare it with the best nominated slate (if they are different). Is that anything like what you're saying? From: Juho Laatu To: election-methods Methods Sent: Thu, 7 July, 2011 22:51:45 Subject: Re: [EM] Toby Pereira, PR voting methods I'd like to add one more option. It is actually close to option 2 below. Specify separately how to compare two slates (which one is better) and what optimization algorithm will be used when trying to find the best slate. The optimization algorithm may change from one election to the next, but the comparison rule stays the same. Also in this method algorithmic improvements can improve the method. Juho On 7.7.2011, at 23.17, Jameson Quinn wrote: Assume you have some way to score the "goodness" of a slate of representatives. You want to find the best possible such slate, but you don't have the computational resources to score all possible slates. The options are: > > >1. Add candidates one at a time. Advantages: deterministic and simple. >Disadvantages: not very optimal. >2. Use the best nominated slate. Advantages: takes advantage of any future >algorithmic improvements without needing new rules. Disadvantage: could >provide >an edge to those with more computational resources; requires time for people >to >nominate slates. >3. Add candidates N at a time, with N being as big as your computer can handle. > > >All of the above have been discussed. But there's another possibility, which >is >probably better than 3: > > >4. "One out and two in" - at each step, find the best slate which differs from >the prior step by removing M candidates and then adding M+N. This is almost >certainly computationally feasible for N=M=1. > > >2011/7/7 Toby Pereira > >On my web page where I describe my Proportional Range Voting System >(http://www.tobypereira.co.uk/voting.html), I have suggested that it should be >possible for a computer to sort out the result in a reasonable amount of time. >Of course, this may not actually be the case considering the number of >possible >winning sets of candidates that you might get in some elections. >> >>So as with other systems, a sequential system could be used. Calculate who >>would >>be the winning candidate in a single-winner election and then find the best >>combination of two winners, given that the single winner is elected. Then >>with >>these two elected, find the best combination of three and so on. Then if this >>takes it too far the other way and makes it too "easy" for a computer to >>calculate you can select candidates in blocks of two or three. I think I've >>seen >>Forest Simmons and others discussing this hybrid version of >>sequential/non-sequential systems. >> >>I think this would still be a very different system to Reweighted Range >>Voting, >>especially consdering that it elects single winners in a different way. >> >> >> >> From: Warren Smith >>To: election-methods >>Sent: Sun, 3 July, 2011 20:25:35 >>Subject: [EM] Toby Pereira, PR voting methods >> >> >>Two are RRV >> http://rangevoting.org/RRV.html >>and asset voting >> http://rangevoting.org/Asset.html >> >>A recent real-world election that used RRV is described here: >> June2011RealWorldRRVvotes.txt >> >>In T.P.'s essay it'd be nice if he subdivided it into smaller chunks >>with subheading titles, and summarized whatever he concluded >>concisely. >> >>-- >>Warren D. Smith >>http://RangeVoting.org <-- add your endorsement (by clicking >>"endorse" as 1st step) >>and >>math.temple.edu/~wds/homepage/works.html >> >>Election-Methods mailing list - see http://electorama.com/em for list info >> >> >>Election-Methods mailing list - see http://electorama.com/em for list info >> >> > >Election-Methods mailing list - see http://electorama.com/em for list info > Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Toby Pereira, PR voting methods
On my web page where I describe my Proportional Range Voting System (http://www.tobypereira.co.uk/voting.html), I have suggested that it should be possible for a computer to sort out the result in a reasonable amount of time. Of course, this may not actually be the case considering the number of possible winning sets of candidates that you might get in some elections. So as with other systems, a sequential system could be used. Calculate who would be the winning candidate in a single-winner election and then find the best combination of two winners, given that the single winner is elected. Then with these two elected, find the best combination of three and so on. Then if this takes it too far the other way and makes it too "easy" for a computer to calculate you can select candidates in blocks of two or three. I think I've seen Forest Simmons and others discussing this hybrid version of sequential/non-sequential systems. I think this would still be a very different system to Reweighted Range Voting, especially consdering that it elects single winners in a different way. From: Warren Smith To: election-methods Sent: Sun, 3 July, 2011 20:25:35 Subject: [EM] Toby Pereira, PR voting methods Two are RRV http://rangevoting.org/RRV.html and asset voting http://rangevoting.org/Asset.html A recent real-world election that used RRV is described here: June2011RealWorldRRVvotes.txt In T.P.'s essay it'd be nice if he subdivided it into smaller chunks with subheading titles, and summarized whatever he concluded concisely. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Toby Pereira, PR voting methods
Thank you for your comments, Warren. I've modified the page a bit and put in some subheadings. You'll notice at the bottom of the page that I've mentioned that my version of Proportional Range Voting is not equivalent to normal Range Voting where there is a single winner. It's not simply a case of adding up the scores. I imagine it might be a pain from a programming point of view, but I'd be interested to see how it came out in your Bayesian Regret tables. From: Warren Smith To: election-methods Sent: Sun, 3 July, 2011 20:25:35 Subject: [EM] Toby Pereira, PR voting methods Two are RRV http://rangevoting.org/RRV.html and asset voting http://rangevoting.org/Asset.html A recent real-world election that used RRV is described here: June2011RealWorldRRVvotes.txt In T.P.'s essay it'd be nice if he subdivided it into smaller chunks with subheading titles, and summarized whatever he concluded concisely. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] What's wrong with the party list system?
The problem I have with party list systems is that you do not elect individuals but organisations, who can then put in who they like. Politicians are going to form groups with each other (parties) and that's fine but I don't think that it should be fundamentally built into the system. I'm not an expert on party list systems, but I presume they are intrinsically biased against independents. >Someone from Europe on this list recently said that they did not like >the party list system. Why not? Party list seems like a fair, simple >system of electing legislators who represent people in approximately >the same proportion that they exist in the electorate. I have not >found a better-sounding proportional system yet. So, what's wrong with >the party list system? >-- >Kathy Dopp Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Proportional Range and Approval Voting
Hello. I've read with interest some of the posts in here over the last few months from the archive so thought I might join and post! I got interested in voting systems because of the Alternative Vote (or Instant Runoff) referendum we had in the UK. I didn't think it was much of an improvement over our current system of First Past the Post (Plurality) and started looking at other systems. I've always been a supporter of Proportional Representation, with Single Transferable Vote probably the "main" one that gets talked about, in the UK at least (and I'm not a fan of party lists). I came across Forest Simmons's Proportional Approval Voting, which is very interesting, although if you type "Proportional Range Voting" into Google you get surprisingly little. Anyway, I looked into Proportional Approval/Range Voting myself and came up with my own systems of them. (I don't think anyone else has described the same systems - apologies if they have). So I thought I might see what people here make of them. http://www.tobypereira.co.uk/voting.html Election-Methods mailing list - see http://electorama.com/em for list info
