[EM] Losing Votes (ERABW)
Kristofer Munsterhjelm wrote (13 Dec 2012): "The method should provide good results and/or strategy resistance and then whether or not it pays attention to the top is secondary. Which leads to marketing. Perhaps having the method elect most from the tops is a marketing advantage. However, it may come at a cost of results (or strategy resistance). In that case, what is better? Should one pick a method for marketability and try to build upon it to go further later, or try to make one leap instead of two?" I agree with the first sentence above, but "good results" can be a bit subjective and some people think that "paying attention to the top" is part of it. When I wrote that my suggested version of Schulze (Losing Votes) has a feature that might help with marketing, I wasn't admitting that anything in terms of "results (or strategy resisatnce)" had been sacrificed for greater "marketability". With regard to "strategy resistance" in Condorcet methods, it seems that we have to choose between trying to reduce Compromise incentive for voters whose main concern is to prevent the election of their Greater Evil and trying to reduce defection incentive by voters trying to get their Favourite elected versus the "sincere CW". The Losing Votes method I advocate goes for the latter. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Losing Votes (ERABW)
On 12/14/2012 06:12 PM, Richard Fobes wrote: On 12/13/2012 11:31 AM, Kristofer Munsterhjelm wrote: On 12/13/2012 05:28 PM, Chris Benham wrote: Of the various proposed ways of weighing "defeat strengths" in Schulze, Losing Votes is the one that elects most from the "tops of the ballots". Given that we are seeking to convert supporters of FPP (and to I hope a lesser extent, IRV), I think that is a marketing advantage. On the other hand, we know that only paying mind to the tops of the ballots is a bad idea. That's what Plurality does. IRV pays less attention to the top (so that it can pass mutual majority, for instance), but Australia and Burlington seem to indicate it's not enough unlike Plurality. In a sense, IRV pays too much attention to the "bottom of the ballot". First, consider that plurality voting assumes that the candidate with the _most_ first-choice votes is most popular. Relatedly, IRV assumes that the candidate with the _fewest_ first-choice votes is least popular. Well, it still pays attention to the top of the ballot. It just derives a different metric from the top of the ballot: a measure of how bad something is, rather than of how good something is. The reasoning is more indirect, so IRV passes things like mutual majority. In a way it's similar to how Nanson and Baldwin's logic is more indirect than Borda (upon which they are based), so that Nanson and Baldwin passes majority and Condorcet but Borda does not. Both beliefs are mistaken rather often. IRV works fine if there are only two dominant candidates and other minor candidates, but what's the point of adopting a better ballot if the counting method only allows two main candidates? Of course long-time folks here know all this, but there are a few folks here who are in the process of learning more about voting methods. There are people on this list who like IRV or think it's not too bad, so I won't put words in their mouths. It feels a bit like IRV is an incremental upgrade to Plurality, though, like someone sat down and tried to find out how to solve Plurality's most obvious problem (minor no-hopes interfering with the outcome). IRV does solve that most obvious problem, but whether intentional or not, the patch doesn't extend far enough: another problem appears when the parties grow to the size where they're no longer no-hopes. Yet the feeling can be deceiving. Knowing IRV's actual history, I don't think someone sat down to patch Plurality. STV came first, and STV *does* work. In STV with many seats, the Droop proportionality criterion (DPC) makes sure that there's at least some measure of representation, and as the number of seats increases, the leeway within DPC decreases, so there's less of a chance for it to go wrong. Then a certain organization decided that getting IRV for single-winner elections would be a good stepping stone to STV. The rest, we all know :-) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Losing Votes (ERABW)
On 12/13/2012 11:31 AM, Kristofer Munsterhjelm wrote: On 12/13/2012 05:28 PM, Chris Benham wrote: Of the various proposed ways of weighing "defeat strengths" in Schulze, Losing Votes is the one that elects most from the "tops of the ballots". Given that we are seeking to convert supporters of FPP (and to I hope a lesser extent, IRV), I think that is a marketing advantage. On the other hand, we know that only paying mind to the tops of the ballots is a bad idea. That's what Plurality does. IRV pays less attention to the top (so that it can pass mutual majority, for instance), but Australia and Burlington seem to indicate it's not enough unlike Plurality. In a sense, IRV pays too much attention to the "bottom of the ballot". First, consider that plurality voting assumes that the candidate with the _most_ first-choice votes is most popular. Relatedly, IRV assumes that the candidate with the _fewest_ first-choice votes is least popular. Both beliefs are mistaken rather often. IRV works fine if there are only two dominant candidates and other minor candidates, but what's the point of adopting a better ballot if the counting method only allows two main candidates? Of course long-time folks here know all this, but there are a few folks here who are in the process of learning more about voting methods. Richard Fobes Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Losing Votes (ERABW)
On 12/13/2012 05:28 PM, Chris Benham wrote: Of the various proposed ways of weighing "defeat strengths" in Schulze, Losing Votes is the one that elects most from the "tops of the ballots". Given that we are seeking to convert supporters of FPP (and to I hope a lesser extent, IRV), I think that is a marketing advantage. On the other hand, we know that only paying mind to the tops of the ballots is a bad idea. That's what Plurality does. IRV pays less attention to the top (so that it can pass mutual majority, for instance), but Australia and Burlington seem to indicate it's not enough unlike Plurality. So we might ask ourselves how much attention we should pay to the top. Of course, it's easy to find a method that pays very much (or very little) attention to the top and still gives bad results. To Plurality there is Antiplurality. Thus the question, inasfar as mechanism design goes, doesn't actually seem to be "how much attention should we pay to the top". The method should provide good results and/or strategy resistance and then whether or not it pays attention to the top is secondary. Which leads to marketing. Perhaps having the method elect most from the tops is a marketing advantage. However, it may come at a cost of results (or strategy resistance). In that case, what is better? Should one pick a method for marketability and try to build upon it to go further later, or try to make one leap instead of two? I'm asking as that question has come up before. It has, for instance, in the question of whether to support IRV or go straight to Condorcet. How much do we give for marketing? Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Losing Votes (ERABW)
I recently proposed (16 Nov 2012) the "Losing Votes (Equal-Ranking Above-Bottom Whole)" method: *Voters rank from the top however many candidates they wish. Equal-ranking is allowed. The result is determined from a pairwise matrix. On that matrix, ballots that rank above bottom any X=Y contribute one whole vote to X>Y and another to Y>X. Ballots that truncate both X and Y have no effect on the X>Y and Y>X entries in the pairwise matrix. With the thus created pairwise matrix, decide the winner with Schulze (Losing Votes).* 35 A 10 A=B 30 B>C 25 C A>B 35-30 (ignoring the 10 A=B ballots unlike my proposal, according to which A>B 45-40) B>C 40-25 C>A 55-45 (This is an old example from Kevin Venke in a different discussion.) B is pairwise beaten and positionally dominated by A and is the least "approved" (ranked above bottom) candidate. C is the most approved candidate and has the biggest single pairwise score (55 verus A). A has the most top rankings. Both Winning Votes and Margins (using the Schulze or equivalent algorithm) elect B, the clearly weakest candidate. Notice that electing B is another outrageous failure of Later-no-Help. Losing Votes elects A. Part of the case against electing C is that the 25 C truncators could be defecting from a sincere BC coalition (and if so, shouldn't be rewarded). Part (at least) of the case for electing C is that if the 30 B>C voters are sincere (and detest A) they have a strong incentive to order-reverse and maybe C has a disincentive to run. But other than in effect just portraying the Margins or Winning Votes algorithms as in themselves standards, there is no case for electing B. Of the various proposed ways of weighing "defeat strengths" in Schulze, Losing Votes is the one that elects most from the "tops of the ballots". Given that we are seeking to convert supporters of FPP (and to I hope a lesser extent, IRV), I think that is a marketing advantage. Chris Benham But there is no case for electing B, other than Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Losing Votes (ERABW)
On 16 Nov 2012 07:29:52 -0800, Chris Benham wrote: > > >It isn't a big deal if Ranked Pairs or River are used instead of >Schulze. "Losing Votes" means that the pairwise results are weighed >purely by the number of votes on the losing side. The "weakest >defeats" are those with the most votes on the losing side, and of >course conversely the "strongest victories" are those with the >fewest votes on the losing side. Ted Stern wrote (16 Nov 2012): Hi Chris, Just so I understand this correctly: You're saying that the pairwise contest A:3 > B:1 should be weighted more strongly than C:3,000,001 > D:2,999,999? Even though only 4 people care to vote in the A vs. B contest? Ted -- Ted, I now see that my previous terse reply was very bad from the POV of *marketing*, something that normally doesn't interest me and seems a bit premature just after the method has been defined/suggested. But to play ball: Losing Votes is very similar to (but better than) Smith//FPP. In your example the 2 pairwise contests involve completely different candidates, so why does it matter to you which is the one counted as stronger? But anyway, "locking defeats" in Ranked Pairs in effect disqualifies the pairwise defeated candidate. So, is it really a problem for you that in an election with at least 5 million ballots a candidate with no more than one first-place vote (B in your example) is disqualified? (It isn't like the voters will be given a ballot with just all the pairwise match-ups on it.) BTW, the "ERABW" stands for Equal-Ranking Above-Bottom (Whole). Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Losing Votes (ERABW)
On 16 Nov 2012 07:29:52 -0800, Chris Benham wrote: > > >It isn't a big deal if Ranked Pairs or River are used instead of >Schulze. "Losing Votes" means that the pairwise results are weighed >purely by the number of votes on the losing side. The "weakest >defeats" are those with the most votes on the losing side, and of >course conversely the "strongest victories" are those with the >fewest votes on the losing side. Hi Chris, Just so I understand this correctly: You're saying that the pairwise contest A:3 > B:1 should be weighted more strongly than C:3,000,001 > D:2,999,999? Even though only 4 people care to vote in the A vs. B contest? Ted -- Ted, Yes. I'm not interested in "moral arguments" about this or that part of an algorithm. If you don't like it, give an example with a result you don't like. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Losing Votes (ERABW)
2012/11/16 Ted Stern > On 16 Nov 2012 07:29:52 -0800, Chris Benham wrote: > > > > > > It isn't a big deal if Ranked Pairs or River are used instead of > > Schulze. "Losing Votes" means that the pairwise results are weighed > > purely by the number of votes on the losing side. The "weakest > > defeats" are those with the most votes on the losing side, and of > > course conversely the "strongest victories" are those with the > > fewest votes on the losing side. > > Hi Chris, > > Just so I understand this correctly: > > You're saying that the pairwise contest A:3 > B:1 should be weighted > more strongly than C:3,000,001 > D:2,999,999? Even though only 4 > people care to vote in the A vs. B contest? > Well, on at least 2,999,998 ballots, and probably more like 5,999,996, A and B are rated equal-bottom. So chances that either of them will be in the Smith set are pretty slim. But if they were, you would be sure not to elect B. I don't think that's such a bad thing, really. If A and B were rated equal-non-bottom on the 5,999,996 ballots, then it would be A:5,999,999 > B:5,999,997. Jameson > > Ted > -- > araucaria dot araucana at gmail dot com > > 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] Losing Votes (ERABW)
On 16 Nov 2012 07:29:52 -0800, Chris Benham wrote: > > > It isn't a big deal if Ranked Pairs or River are used instead of > Schulze. "Losing Votes" means that the pairwise results are weighed > purely by the number of votes on the losing side. The "weakest > defeats" are those with the most votes on the losing side, and of > course conversely the "strongest victories" are those with the > fewest votes on the losing side. Hi Chris, Just so I understand this correctly: You're saying that the pairwise contest A:3 > B:1 should be weighted more strongly than C:3,000,001 > D:2,999,999? Even though only 4 people care to vote in the A vs. B contest? Ted -- araucaria dot araucana at gmail dot com Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Losing Votes (ERABW)
Looks good. Similar to ICT, I think, and simpler (from my perspective).
What does "ERABW" stand for? This should have a good name; "Least
Disappontment Condorcef" or something of the kind.
2012/11/16 Chris Benham
> I propose the following as a reasonably practical, "summable", Condorcet
> method:
>
> *Voters rank from the top however many candidates they wish. Equal-ranking
> is allowed.
>
> The result is determined from a pairwise matrix. On that matrix, ballots
> that rank above bottom
> any X=Y contribute one whole vote to X>Y and another to Y>X.
>
> Ballots that truncate both X and Y have no effect on the X>Y and Y>X
> entries in the pairwise
> matrix.
>
> With the thus created pairwise matrix, decide the winner with Schulze
> (Losing Votes).*
>
> It isn't a big deal if Ranked Pairs or River are used instead of
> Schulze. "Losing Votes" means
> that the pairwise results are weighed purely by the number of votes on the
> losing side. The "weakest
> defeats" are those with the most votes on the losing side, and of course
> conversely the "strongest
> victories" are those with the fewest votes on the losing side.
>
> This has these advantages over Winning Votes: it appears to meet the
> "Approval Bad Example"
> defection-related criterion, it can't fail to elect a positionally
> dominant Smith-set member, and it
> doesn't have any zero-info random-fill incentive.
>
> Instead, in the "acceptables versus unacceptables" situation it has the
> more natural zero-info
> strategy of just equal-top ranking the acceptables and truncating the
> unacceptables.
>
> It doesn't share Winning Votes' compliance with Minimal Defense
> (incompatible, or effectively so,
> with ABE compliance).
>
> It has these advantages over Margins: it meets the Plurality criterion and
> it meets Steve Eppley's old
> "Non-Drastic Defense" criterion.
>
> That says that if more than half the voters rank X above Y and X no lower
> than equal top, then Y
> can't win.
>
> 46: A>C ("sincere" may be A>B)
> 10: B>A
> 10: B>C
> 34: C=B ("sincere" may be C>B)
>
> More than half the voters rank B above A and B no lower than equal-top,
> but Margins elects A.
> If the method were Bucklin, B would be the only candidate with a majority
> score in the first round.
>
> Using the rules of my suggested method, the pairwise comparisons go:
>
> B>A 54>46,A>C 56-44,C>B 80-54 (the 34 C=B have been added to
> both sides).
>
> The weakest defeat (as measured by Losing Votes) is B's, so B wins. Or in
> terms of Ranked Pairs,
> the strongest pairwise result is A>C so that is locked and the next
> strongest is B>A so that is locked
> and then C>B is skipped because it's incompatible with an already locked
> result; so the final order is
> B>A>C.
>
> Enough for the time being.
>
> Chris Benham
>
>
>
>
>
>
> 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] Losing Votes (ERABW)
I propose the following as a reasonably practical, "summable", Condorcet method:
*Voters rank from the top however many candidates they wish. Equal-ranking is
allowed.
The result is determined from a pairwise matrix. On that matrix, ballots that
rank above bottom
any X=Y contribute one whole vote to X>Y and another to Y>X.
Ballots that truncate both X and Y have no effect on the X>Y and Y>X entries
in the pairwise
matrix.
With the thus created pairwise matrix, decide the winner with Schulze (Losing
Votes).*
It isn't a big deal if Ranked Pairs or River are used instead of Schulze.
"Losing Votes" means
that the pairwise results are weighed purely by the number of votes on the
losing side. The "weakest
defeats" are those with the most votes on the losing side, and of course
conversely the "strongest
victories" are those with the fewest votes on the losing side.
This has these advantages over Winning Votes: it appears to meet the "Approval
Bad Example"
defection-related criterion, it can't fail to elect a positionally dominant
Smith-set member, and it
doesn't have any zero-info random-fill incentive.
Instead, in the "acceptables versus unacceptables" situation it has the more
natural zero-info
strategy of just equal-top ranking the acceptables and truncating the
unacceptables.
It doesn't share Winning Votes' compliance with Minimal Defense (incompatible,
or effectively so,
with ABE compliance).
It has these advantages over Margins: it meets the Plurality criterion and it
meets Steve Eppley's old
"Non-Drastic Defense" criterion.
That says that if more than half the voters rank X above Y and X no lower than
equal top, then Y
can't win.
46: A>C ("sincere" may be A>B)
10: B>A
10: B>C
34: C=B ("sincere" may be C>B)
More than half the voters rank B above A and B no lower than equal-top, but
Margins elects A.
If the method were Bucklin, B would be the only candidate with a majority score
in the first round.
Using the rules of my suggested method, the pairwise comparisons go:
B>A 54>46, A>C 56-44, C>B 80-54 (the 34 C=B have been added to both
sides).
The weakest defeat (as measured by Losing Votes) is B's, so B wins. Or in terms
of Ranked Pairs,
the strongest pairwise result is A>C so that is locked and the next strongest
is B>A so that is locked
and then C>B is skipped because it's incompatible with an already locked
result; so the final order is
B>A>C.
Enough for the time being.
Chris Benham
Election-Methods mailing list - see http://electorama.com/em for list info
