Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
On Nov 29, 2009, at 6:37 PM, James Gilmour wrote: Robert Bristow-Johnson wrote (9 Nov 2009): Of course IRV, Condorcet, and Borda use different methods to tabulate the votes and select the winner and my opinion is that IRV (asset voting, I might call it commodity voting: your vote is a commodity that you transfer according to your preferences) is a kabuki dance of transferred votes. and there is an *arbitrary* evaluation in the elimination of candidates in the IRV rounds: 2nd- choice votes don't count for shit in deciding who to eliminate (who decided that? 2nd-choice votes are as good as last-choice? under what meaningful and consistent philosophy was that decided?), then when your candidate is eliminated your 2nd-choice vote counts as much as your 1st-choice. These statements suggest a misunderstanding of how STV voting works and what preferences (US rankings) mean in the STV voting system. i know earlier someone (it might've been James, i dunno) wrote that STV (i think that's what it's called in Australia) is called IRV in the US. i dunno to what extent that is true, but assuming it is, i understand exactly how IRV works as used by a few municipalities in the US, specifically what was used in Burlington VT which i think is identical to how it is in Cambridge MA, SF CA, someplace in NC, and Mpls/StP MN. to how the method works in Australia, i do not know first hand. also, i case you're interested, i voted for IRV for Burlington in 2005 (it has been used in two elections since), and in the referendum it faces this coming spring, i'll likely vote against recalling (abolishing in favor of the FPTP/delayed_runoff we had before) IRV. the issue to me is that the single-transferrable vote (as done in our domestic IRV) is the wrong algorithm to tabulate the votes in a multi- candidate election where no candidate gets a majority of 1st-pick votes. In all STV elections, the preferences are contingency choices. that is true. i fully support a contingency choice is multi-party/ multi-candidate elections. Your vote is transferred to your second choice only in the event that your first choice cannot secure election or does not need you support to secure election. that is *one* way to use the information of the contingency choices. if you are working out a complex problem with multiple directions of interest (which an election with more than 2 sincere candidates would be), you don't necessarily quantify votes as a commodity with some fixed value, and then, as i still point out, transfer these commodities around according to a candidate viability metric that arbitrarily says that 2nd-choice is no better than the last choice. you still haven't demonstrated why this contingent-choice information is the logical way to resolve a bunch of different competing contingency interests. we know how, if there were only two candidates, to decide between the two (assuming they don't tie). we know how to vote in that case (our sincere vote is the same as our tactical vote, easy), plurality = majority. assuming no funny business, no one can dispute the popular legitimacy of the winner. what we don't want to happen (assuming we want honest and democratic elections where tactical voting is not likely to work) is resolve an election differently between any two candidates differently than we would if those two were among a larger group of candidates. we don't want to have to think how we would vote differently in the two cases. if there is a Condorcet winner, and you are not that person, that Condorcet winner beat you, as far as the electorate is concerned. if it was just the two of you, he beats you. if it was you two along with N-2 other candidates, he still beats you (as well as beating everyone else). This is most easily seen in single-winner STV elections (US = IRV), where the sequence of rounds is exactly analogous to the sequence of rounds in an exhaustive ballot (eliminating one candidate at a time in successive ballots). please don't patronize me. there is nothing you're saying here that i don't know. it is in how IRV does that that is the problem. it doesn't accomplish the very goals we had when we adopted IRV (not rewarding tactical voting thus eliminating the need to consider tactical voting so we can vote the way we want to and not worry about contributing to defeating our own political interest - voter regret). The only difference is that in an STV (IRV) election you don't know what all the other voters did in Round 1 when you come to give your second choice. you mean you don't have transparency on how the rounds were performed or is it that your STV is a delayed runoff where you come in later? because i can't see the difference. in the IRV i am familiar with, you order your candidates before knowing how any round turns out. no one is returning to any polls.
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
On Nov 25, 2009, at 10:05 AM, Chris Benham wrote: Robert Bristow-Johnson wrote (9 Nov 2009): Of course IRV, Condorcet, and Borda use different methods to tabulate the votes and select the winner and my opinion is that IRV (asset voting, i might call it commodity voting: your vote is a commodity that you transfer according to your preferences) is a kabuki dance of transferred votes. and there is an *arbitrary* evaluation in the elimination of candidates in the IRV rounds: 2nd- choice votes don't count for shit in deciding who to eliminate (who decided that? 2nd-choice votes are as good as last-choice? under what meaningful and consistent philosophy was that decided?), then when your candidate is eliminated your 2nd-choice vote counts as much as your 1st-choice. Regarding IRV's philosophy: each voter has single vote that is transferable according to a rule that meets Later-no-Harm, Later-no-Help and Majority for Solid Coalitions. I rate IRV (Alternative Vote with unlimited strict ranking from the top) as the best of the single-winner methods that meet Later-no-Harm. On Nov 25, 2009, at 2:41 PM, Warren Smith wrote: Are there any other voting methods besides IRV, meeting the 'later no harm' criterion? my understanding is that the later-no-harm result happens only if the case of a Condorcet cycle (the prevalence of which i am dubious about). where there is a Condorcet winner and that person is elected, is there still possible later harm? i hadn't thought of it before but i s'pose that since Condorcet *does* give preference to centrist candidates over solid coalition candidates (in comparison to IRV rules). i knew before that Condorcet sorta favors centrist candidates because voters in either the left or right fringes (that do not pick the centrist candidate as their 1st-choice) likely pick the centrist as their 2nd-choice. that's nice for political interests of centrist voters, but that is no reason to pick an election method. the reason that IRV or *any* non-Condorcet method is problematic for the interest of democracy is that any candidate elected that is not the Condorcet winner is elected despite the fact that the majority of voters expressed that they wanted someone else *specifically* on their ballots. when IRV or Borda or whatever happens to elect the Condorcet winner, they seem to do pretty well. when they fail to do that, voters have reason to wonder: didn't more of us prefer that other guy? how'd this guy get elected? isn't that what democracy is about?: if more of us prefer Candidate A to Candidate B, then it isn't Candidate B who gets elected. other than the possible cycle, in which some kinda pathologies can happen, i still don't see a pimple on it. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
robert bristow-johnson wrote: my understanding is that the later-no-harm result happens only if the case of a Condorcet cycle (the prevalence of which i am dubious about). where there is a Condorcet winner and that person is elected, is there still possible later harm? As far as I remember, Condorcet and LNHarm has the property that LNHarm isn't, by itself, violated as long as there is a CW, but the transition from CW to no CW (or vice versa) makes it inevitable that there will be a LNHarm-violating discontinuity *somewhere*. In other words, as long as you stay within the CW domain, there is no LNHarm failure, but there is no way to engineer a completion rule to maintain this for every CW-no CW transition. I'm not entirely sure about that, though - can anyone confirm? Not that this bothers me - LNHarm seems to me to be a criterion of don't take the full picture into account. Consider a negotiation situation: if everybody keeps their cards close to their chests (i.e. vote bullet style), there can be no compromise; but if they're willing to reach further, one might find an option that, while not the favorite of any, is good enough for all. An LNHarm-respecting method has to act as if people are voting cautiously before it can consider any additional information, and thus it misses such opportunities for compromise. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
On Nov 25, 2009, at 3:26 PM, Kristofer Munsterhjelm wrote: robert bristow-johnson wrote: my understanding is that the later-no-harm result happens only if the case of a Condorcet cycle (the prevalence of which i am dubious about). where there is a Condorcet winner and that person is elected, is there still possible later harm? As far as I remember, Condorcet and LNHarm has the property that LNHarm isn't, by itself, violated as long as there is a CW, but the transition from CW to no CW (or vice versa) makes it inevitable that there will be a LNHarm-violating discontinuity *somewhere*. the degree of inevitability is an issue. if inevitable is measured as a binary value, the i s'pose it's inevitable. if inevitable is measured as a probability of a cycle occurring per election-year, then i think it's a small number. if cycles are rare, the mean percentage of elections that have Condercet cycles is small. when we somehow figure out a merit metric for an election system, a low- likelihood of a pathology that has low cost (say, if a cycle happens you elect using IRV rules, how bad can that be?) should contribute (negatively) negligibly to the merit metric. In other words, as long as you stay within the CW domain, there is no LNHarm failure, but there is no way to engineer a completion rule to maintain this for every CW-no CW transition. sure, but i'm still dubious about the product of likelihood times cost of occurrence of that. I'm not entirely sure about that, though - can anyone confirm? and i continue to wonder (really) how a possibly rare occurrence of a no-CW election (with its LNHarm consequence) becomes a greater concern than that of the likelihood and cost of electing a candidate against the expressed wishes of a majority of the electorate. i think that cost (electing the wrong candidate) is reasonably high and that the likelihood of it happening is definitely non-zero because it has happened in the Vermont town i am a resident of. Not that this bothers me - LNHarm seems to me to be a criterion of don't take the full picture into account. Consider a negotiation situation: if everybody keeps their cards close to their chests (i.e. vote bullet style), there can be no compromise; but if they're willing to reach further, one might find an option that, while not the favorite of any, is good enough for all. i would call that the essential measure of a popular election. it's utilitarian: we maximize satisfaction for the franchised about the governance of whatever organization by pleasing more people with a decision than we displease. that's the reason we have elections, we could adopt rules to give it to the minority candidate if that candidate reaches a certain threshold, but we don't do that for binary decisions, we consistently give it to the majority. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Trying to sort this out as to Condorcet and LNH: Seems that cycles are involved before, after, or both. And the voters change their votes, getting more affect on result than they might expect. So what, assuming the counters properly read the vote? I agree with those who expect cycles to be rare. Still, it is the more important races that are more likely to result in cycles. What I see as important is that, assuming analysis of the election is done both officially and by others, it should be practical to decide whether the official result was correct, considering the N*N vote count. In other words, the official analysis should not be complex - especially not to gain trivial improvement in quality of official result. Dave Ketchum On Nov 25, 2009, at 3:08 PM, robert bristow-johnson wrote: On Nov 25, 2009, at 10:05 AM, Chris Benham wrote: Robert Bristow-Johnson wrote (9 Nov 2009): Of course IRV, Condorcet, and Borda use different methods to tabulate the votes and select the winner and my opinion is that IRV (asset voting, i might call it commodity voting: your vote is a commodity that you transfer according to your preferences) is a kabuki dance of transferred votes. and there is an *arbitrary* evaluation in the elimination of candidates in the IRV rounds: 2nd- choice votes don't count for shit in deciding who to eliminate (who decided that? 2nd-choice votes are as good as last-choice? under what meaningful and consistent philosophy was that decided?), then when your candidate is eliminated your 2nd-choice vote counts as much as your 1st-choice. Regarding IRV's philosophy: each voter has single vote that is transferable according to a rule that meets Later-no-Harm, Later-no-Help and Majority for Solid Coalitions. I rate IRV (Alternative Vote with unlimited strict ranking from the top) as the best of the single-winner methods that meet Later-no-Harm. On Nov 25, 2009, at 2:41 PM, Warren Smith wrote: Are there any other voting methods besides IRV, meeting the 'later no harm' criterion? my understanding is that the later-no-harm result happens only if the case of a Condorcet cycle (the prevalence of which i am dubious about). where there is a Condorcet winner and that person is elected, is there still possible later harm? i hadn't thought of it before but i s'pose that since Condorcet *does* give preference to centrist candidates over solid coalition candidates (in comparison to IRV rules). i knew before that Condorcet sorta favors centrist candidates because voters in either the left or right fringes (that do not pick the centrist candidate as their 1st-choice) likely pick the centrist as their 2nd-choice. that's nice for political interests of centrist voters, but that is no reason to pick an election method. the reason that IRV or *any* non-Condorcet method is problematic for the interest of democracy is that any candidate elected that is not the Condorcet winner is elected despite the fact that the majority of voters expressed that they wanted someone else *specifically* on their ballots. when IRV or Borda or whatever happens to elect the Condorcet winner, they seem to do pretty well. when they fail to do that, voters have reason to wonder: didn't more of us prefer that other guy? how'd this guy get elected? isn't that what democracy is about?: if more of us prefer Candidate A to Candidate B, then it isn't Candidate B who gets elected. other than the possible cycle, in which some kinda pathologies can happen, i still don't see a pimple on it. r b-j r...@audioimagination.com Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting? (long)
On Nov 10, 2009, at 7:40 AM, Matthew Welland wrote: Also, again, your single vote is irrelevant. except in a close election. It is the aggregate of thousands or millions of votes that will make or break A vs. B. How many feel so strongly against A that they cannot vote for him or her? The binary nature of approval is washed out by large numbers just as a class D amplifier can directly produce smooth analog waveforms out of a pure 1 or 0 signal. the mathematical function that does that is the low-pass filter on the output. it's sorta the same idea that these 1-bit A/D (a.k.a. sigma-delta) converters use. if we were voting with a range ballot, and our continuous range value gets a zero-mean uniform p.d.f. random dither signal added to it (or, to use your PWM example, a zero-mean number drawn sequentially, in chronological order of the vote submission) and that gets quantized to a yes/no Approval vote (i s'pose if the threshold is set to 50%), then you would have a comparable situation. i just dunno if i like the idea of a zero-mean (and even symmetrical p.d.f.) random variable actually going into a governmental election. how well i approve or disapprove of a particular candidate that i am not actively supporting is a function of how i'm feeling on Election Day. but it's less likely how i rank that candidate w.r.t. the other candidates would change. like grading papers, sometimes to come up with a numerical score, we get out our dartboard and see how good our toss is. but students might like a more deterministic method. for governmental elections, i only support a system that is fully deterministic (and repeatable) except, i s'pose, if there is a dead heat, then i s'pose, some kind of drawing of lots would be necessary. it should require enough information from voters that the system knows how any voter would choose between any subset of candidates (the ranked ballot does that, but the approval ballot does not). and it shouldn't force voters to bring their dartboard (or dice or spinner, etc) to the polls to come up with a numerical approval rating for each candidate, because of GIGO. the other principle that is important is that of anonymity of vote. it shouldn't matter if you really, really, really like your candidate and i only tepidly support his/her opponent. my vote for the opponent should count just as much as your more enthusiastic vote for your candidate. there should be nothing that tips the scale in favor of your candidate based on how enthusiastically she is supported, only by the numbers of voters that supports her. our votes should have equal weight. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting? (long)
In large elections with evenly spread voters and candidates and no strategies the distribution of Approval votes may indeed be such that the best candidate regularly wins. The situation may however be also different. I gave one simple example where the left wing had two candidates and the right wing had only one. The distribution of votes may not bring fair results in this type of set-up. The assumption was that the right wing voters would predominantly approve only their own candidate while many left wing voters would be tempted to indicate which one of the left wing candidates they prefer over the other (despite of clearly preferring both left wing candidates over the right wing candidate). The end result could therefore be biased. The right wing candidate might easily win even if right wing would have considerably smaller than 50% support. With small number of candidates and with a candidate set-up that is not symmetric or well balanced Approval may well produce biased results. Methods that are capable of providing richer information (ranked methods) are likely to provide more balanced input data (and results). Juho On Nov 12, 2009, at 2:28 AM, robert bristow-johnson wrote: On Nov 10, 2009, at 7:40 AM, Matthew Welland wrote: It is the aggregate of thousands or millions of votes that will make or break A vs. B. How many feel so strongly against A that they cannot vote for him or her? The binary nature of approval is washed out by large numbers just as a class D amplifier can directly produce smooth analog waveforms out of a pure 1 or 0 signal. the mathematical function that does that is the low-pass filter on the output. it's sorta the same idea that these 1-bit A/D (a.k.a. sigma-delta) converters use. if we were voting with a range ballot, and our continuous range value gets a zero-mean uniform p.d.f. random dither signal added to it (or, to use your PWM example, a zero-mean number drawn sequentially, in chronological order of the vote submission) and that gets quantized to a yes/no Approval vote (i s'pose if the threshold is set to 50%), then you would have a comparable situation. i just dunno if i like the idea of a zero-mean (and even symmetrical p.d.f.) random variable actually going into a governmental election. how well i approve or disapprove of a particular candidate that i am not actively supporting is a function of how i'm feeling on Election Day. but it's less likely how i rank that candidate w.r.t. the other candidates would change. like grading papers, sometimes to come up with a numerical score, we get out our dartboard and see how good our toss is. but students might like a more deterministic method. for governmental elections, i only support a system that is fully deterministic (and repeatable) except, i s'pose, if there is a dead heat, then i s'pose, some kind of drawing of lots would be necessary. it should require enough information from voters that the system knows how any voter would choose between any subset of candidates (the ranked ballot does that, but the approval ballot does not). and it shouldn't force voters to bring their dartboard (or dice or spinner, etc) to the polls to come up with a numerical approval rating for each candidate, because of GIGO. the other principle that is important is that of anonymity of vote. it shouldn't matter if you really, really, really like your candidate and i only tepidly support his/her opponent. my vote for the opponent should count just as much as your more enthusiastic vote for your candidate. there should be nothing that tips the scale in favor of your candidate based on how enthusiastically she is supported, only by the numbers of voters that supports her. our votes should have equal weight. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. 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] Anyone got a good analysis on limitations of approval and range voting? (long)
Matthew Welland wrote:
So, to re-frame my question. What is the fatal flaw with approval? I'm
not interested in subtle flaws that result in imperfect results. I'm
interested in flaws that result in big problems such as those we see
with plurality and IRV.
IMHO, it is that you need concurrent polling in order to consistently
elect a good winner. If you don't have polling and thus don't know where
to put the cutoff (between approve and not-approve), you'll face the
Burr dilemma: If you prefer A B C, if you approve both A and B,
you might get B instead of A, but if you approve only A, you might get C!
Thus the kind of Approval that homes in on a good winner employs
feedback. The method is no longer Approval alone, but Approval plus
polling. That /can/ work (people approve {Nader, Gore} if Nader has
fewer votes than Gore, so that Bush doesn't win from the split, but only
approve either Nader or Gore if both are large), but why should we need
to be burdened with the feedback?
Some, like Abd, argue that we always reason based on others' positions
to know how much we can demand, and so that this is a feature rather
than a bug. That doesn't quite sound right to me. In any event, if you
want Approval + bargaining (which the feedback resolves to), make that
claim. Approval alone, without feedback, will be subject to the flaws
mentioned earlier, however.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting? (long)
On Tue, Nov 10, 2009 at 10:37 AM, Kristofer Munsterhjelm km-el...@broadpark.no wrote: IMHO, it is that you need concurrent polling in order to consistently elect a good winner. If you don't have polling and thus don't know where to put the cutoff (between approve and not-approve), you'll face the Burr dilemma: If you prefer A B C, if you approve both A and B, you might get B instead of A, but if you approve only A, you might get C! However, the same logic can be applied to plurality voting. If people had to vote blind, then the results would be even worse. History with plurality has shown that it is reasonable to expect people to know who the top-2 candidates are. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting? (long)
On Tuesday 10 November 2009 03:37:56 am Kristofer Munsterhjelm wrote:
Matthew Welland wrote:
So, to re-frame my question. What is the fatal flaw with approval? I'm
not interested in subtle flaws that result in imperfect results. I'm
interested in flaws that result in big problems such as those we see
with plurality and IRV.
IMHO, it is that you need concurrent polling in order to consistently
elect a good winner. If you don't have polling and thus don't know where
to put the cutoff (between approve and not-approve), you'll face the
Burr dilemma: If you prefer A B C, if you approve both A and B,
you might get B instead of A, but if you approve only A, you might get
C!
This seems to me to be a minor, not major, flaw. Having to vote A B to
hedge your bets is not ideal but you might even be able to argue some
benefits to it. A will see B as a serious threat and vice versa. They may
make adjustments to their stands on issues to accommodate voters like you.
Approval voting is enough to bring competition for votes back into the arena
and I think it makes negative campaigning a very risky strategy.
Also, again, your single vote is irrelevant. It is the aggregate of
thousands or millions of votes that will make or break A vs. B. How many
feel so strongly against A that they cannot vote for him or her?
The binary nature of approval is washed out by large numbers just as a class
D amplifier can directly produce smooth analog waveforms out of a pure 1 or 0
signal.
Thus the kind of Approval that homes in on a good winner employs
feedback. The method is no longer Approval alone, but Approval plus
polling. That /can/ work (people approve {Nader, Gore} if Nader has
fewer votes than Gore, so that Bush doesn't win from the split, but only
approve either Nader or Gore if both are large), but why should we need
to be burdened with the feedback?
Sure, in any real election there will be many dynamics at work. Feedback
polls, debates etc. will all improve an election. Approval might benefit from
feedback but I don't see why it becomes fatally flawed without it, only
mildly flawed.
Some, like Abd, argue that we always reason based on others' positions
to know how much we can demand, and so that this is a feature rather
than a bug. That doesn't quite sound right to me. In any event, if you
want Approval + bargaining (which the feedback resolves to), make that
claim. Approval alone, without feedback, will be subject to the flaws
mentioned earlier, however.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Jobst Heitzig wrote: Dear Kristofer, both Approval Voting and Range Voting *are* majoritarian: A majority can always get their will and suppress the minority by simply bullet-voting. So, a more interesting version of your question could be: Which *democratic* method (that does not allow any sub-group to suppress the rest) has (usually or on average or in the worst case) the least Bayesian Regret. Yes. A majority that acts in a certain way can get what it wants. That's true for Range and Approval, and it's true for Condorcet, Plurality, etc. However, my point was that Range goes further: a minority that acts in a certain way can get what it wants, too; all that's required is that the majority does not vote Approval style (either max or min) and that the minority does, and that the minority is not too small. It is in that respect I mean that Range is more radical, because it permits a minority to overrule a majority that otherwise agrees about which candidates it prefers. For those who mean that elections have to be, at least, majoritarian, Range may contain a surprise. I conjecture that at least when the nomination of additional options is allowed, the method SEC described recently is a hot candidate for this award, since it seems that SEC will lead to the election of the option at the *mean* (instead of the median) voter position, and I guess that in most spacial utility models the mean position is in many senses better and will in particular have less Bayesian Regret than the median position. (Recall that in a one-dimensional spacial model where additional options can be nominated, all majoritarian methods likely lead to median positions being realized and are thus basically all equivalent.) You could probably devise a whole class of SEC-type methods. They would go: if there is a consensus (defined in some fashion), then it wins - otherwise, a nondeterministic strategy-free method is used to pick the winner. The advantage of yours is that it uses only Plurality ballots. I suppose the nondeterministic method would have to be bad enough to provide incentive to pick the right consensus, yet it shouldn't be so bad as to undermine the process itself if the voters really can't reach a consensus. Assume (for the sake of simplicity) that we can get ranked information from the voters. What difference would a SEC with Random Pair make, with respect to Random Ballot? It would lead to a better outcome if the consensus fails, but so also make it more likely that the consensus does fail. Or would it? The reasoning from a given participant's point of view is rather: do I get something *I* would like by refusing to take part in consensus -- not, does *society* get something acceptable. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Hello Kristofer, you wrote: However, my point was that Range goes further: a minority that acts in a certain way can get what it wants, too; all that's required is that the majority does not vote Approval style (either max or min) and that the minority does, and that the minority is not too small. It is in that respect I mean that Range is more radical, because it permits a minority to overrule a majority that otherwise agrees about which candidates it prefers. For those who mean that elections have to be, at least, majoritarian, Range may contain a surprise. That's true. Methods in which a group can suppress the rest are certainly bad, even more so when the group can be small... You could probably devise a whole class of SEC-type methods. They would go: if there is a consensus (defined in some fashion), then it wins - otherwise, a nondeterministic strategy-free method is used to pick the winner. The advantage of yours is that it uses only Plurality ballots. The hard point is, I think, to define what actually a potential consensus option is. And here the idea was to say everything unanimously preferred to some benchmark outcome qualifies as potential consensus. The benchmark then cannot be any feasible option but must be a lottery of some options, otherwise the supporters of the single option would block the consensus. But which lottery you take as a benchmark could be discussed. I chose the Random Ballot lottery since it seems the most fair one and has all nice properties (strategy-freeness, proportional allocation of power). I suppose the nondeterministic method would have to be bad enough to provide incentive to pick the right consensus, yet it shouldn't be so bad as to undermine the process itself if the voters really can't reach a consensus. Although I can hardly imagine real-world situations in which no consensus option can be found (maybe be combining different decisions into one, or using some kind of compensation scheme if necessary). Assume (for the sake of simplicity) that we can get ranked information from the voters. What difference would a SEC with Random Pair make, with respect to Random Ballot? This sounds interesting, but what exactly do you mean by Random Pair? Pick a randomly chosen pair of candidates and elect the pairwise winner of them? I will think about this... It would lead to a better outcome if the consensus fails, but so also make it more likely that the consensus does fail. Or would it? The reasoning from a given participant's point of view is rather: do I get something *I* would like by refusing to take part in consensus -- not, does *society* get something acceptable. I'm not sure I know what you mean here. Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Jobst Heitzig wrote: Hello Kristofer, you wrote: You could probably devise a whole class of SEC-type methods. They would go: if there is a consensus (defined in some fashion), then it wins - otherwise, a nondeterministic strategy-free method is used to pick the winner. The advantage of yours is that it uses only Plurality ballots. The hard point is, I think, to define what actually a potential consensus option is. And here the idea was to say everything unanimously preferred to some benchmark outcome qualifies as potential consensus. The benchmark then cannot be any feasible option but must be a lottery of some options, otherwise the supporters of the single option would block the consensus. But which lottery you take as a benchmark could be discussed. I chose the Random Ballot lottery since it seems the most fair one and has all nice properties (strategy-freeness, proportional allocation of power). I suppose the nondeterministic method would have to be bad enough to provide incentive to pick the right consensus, yet it shouldn't be so bad as to undermine the process itself if the voters really can't reach a consensus. Although I can hardly imagine real-world situations in which no consensus option can be found (maybe be combining different decisions into one, or using some kind of compensation scheme if necessary). That might be true for a consensus in general, but I was referring to the SEC method, where all it takes is for a single voter to submit a different consensus ballot than the rest. Assume (for the sake of simplicity) that we can get ranked information from the voters. What difference would a SEC with Random Pair make, with respect to Random Ballot? This sounds interesting, but what exactly do you mean by Random Pair? Pick a randomly chosen pair of candidates and elect the pairwise winner of them? I will think about this... Yes. The CW now has a greater chance to win - but note that it's not given that the CW will win, because if he's not picked as one of the pair candidates, he doesn't come into play at all. It would lead to a better outcome if the consensus fails, but so also make it more likely that the consensus does fail. Or would it? The reasoning from a given participant's point of view is rather: do I get something *I* would like by refusing to take part in consensus -- not, does *society* get something acceptable. I'm not sure I know what you mean here. Well, I was thinking that the SEC method provides an incentive for people to reach a common consensus because the alternative, which is the random ballot, isn't very good. Any (random or deterministic) method that favors some group would lead to that group having less of an incentive to participate in the consensus process because they know they'll get something they'll like. Therefore, I at first thought that even though Random Pair would provide a result more people would be happy with, it would make the voters less interested in actually finding a consensus because the alternative isn't so bad anymore. However, then I realized that any given voter, if he's at the point where he doesn't care about the consensus option, will not be deterred from such a line of thinking because the alternative is suboptimal for society, only if it is suboptimal in his point of view. That means that you could replace Random Ballot with Random Pair as long as the fairness (what you call proportional allocation of power) remains intact, because if the improvement in result lifts all the groups equally, there's no more incentive for some group to cheat with respect to any other. There's also another way of looking at it, which I just saw now: my first idea was that you can't move to a lottery that gives consistently good results because that will diminish people's interest in determining a consensus. But if the lottery is both fair and provides good results, then who cares? The consensus option will only come into play if the people can explicitly agree on a choice that's better than the expected value of the lottery. If figuring out a consensus is worth it (much better than the lottery, relatively speaking), then people will care, otherwise they won't. Thus improving the lottery part of the method will improve the method in general - it'll make up the amount it no longer encourages people to determine the consensus, by just giving better results. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
On Tue, Nov 10, 2009 at 8:11 PM, Jobst Heitzig heitzi...@web.de wrote: Hello Kristofer, Assume (for the sake of simplicity) that we can get ranked information from the voters. What difference would a SEC with Random Pair make, with respect to Random Ballot? This sounds interesting, but what exactly do you mean by Random Pair? Pick a randomly chosen pair of candidates and elect the pairwise winner of them? I will think about this... Presumably, it means that the voter submits 2 ballots, a ranking and a nomination for the 2nd round? Clearly, your rankings should be honest, as it is only looked at once the 2 candidates have been decided. However, your nomination would have to be made tactically. It would require that the voter decide the probability of the candidate they nominate winning. If you nominate the condorcet winner, then the odds of your candidate winning the second round is 100%, as no other candidate can possibly beat him.. However, if you nominate an extremist, then your nomination is almost certain to fail, as he will lose to virtually any other candidate. If the voter distribution is symmetric (and voter utility is symmetric) around a central point, then the nominated candidate who is closest to the centre will win. If each voter nominates their favourite, then you best strategy is to nominate the the candidate which maximises f(distance)*utility f(distance) is the fraction of the nominations that nominate candidates further away than that distance from the centre. f(0) is automatically 1 and f(most extremist candidate's distance) is automatically 0. Also, f(d) is a monotonic decreasing function. Thus, when considering 2 candidates of near equal utility, you should nominate the candidate nearest the centre. However, if all voters do that, then most of the nominations will start to be clustered near the centre. This means that the voters should nominate candidates even closer to the centre. I.e. if f(d) = 0.1, then you would have to prefer that candidate at least 10 times better than the condorcet winner in order to nominate him. I think the effect could very easily end up being that the condorcet winner normally wins. It could also be implemented in 2 formal rounds. In the first round, each voter votes for 1 candidate. 2 candidates are picked at random, using random ballot. Those 2 candidates then proceed to the run off. This might even make people accept random ballot. The problem that a candidate with 1% support could get to be President is eliminated. (Unless it happens twice in 1 election.) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Raph Frank wrote: On Tue, Nov 10, 2009 at 8:11 PM, Jobst Heitzig heitzi...@web.de wrote: Hello Kristofer, Assume (for the sake of simplicity) that we can get ranked information from the voters. What difference would a SEC with Random Pair make, with respect to Random Ballot? This sounds interesting, but what exactly do you mean by Random Pair? Pick a randomly chosen pair of candidates and elect the pairwise winner of them? I will think about this... Presumably, it means that the voter submits 2 ballots, a ranking and a nomination for the 2nd round? In the context of SEC, it would be: Voter submits two ballots - one is ranked and the other is a Plurality ballot. Call the first the fallback ballot, and the second the consensus ballot. If everybody (or some very high percentage, e.g. 99%) votes for the same consensus ballot, it wins. Otherwise, construct a Condorcet matrix based on the fallback ballots. Pick two candidates at random and the one that pairwise beats the other, wins. To my knowledge, Random Pair is strategy-free. It might also be proportional, but I'm not sure about that (partly because I'm not sure how you'd define proportional for ranked ballots). You seem to be suggesting a more Condorcet way of doing the consensus balloting. A possible option would be to look at how e.g. Debian handles supermajority issues. On the other hand, grafting Condorcet onto the consensus option would make the actual consensus more opaque, and one may in any case argue: if you have a consensus, there's an agreement and so you don't need a complex method to determine what the consensus actually is. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
On Tue, Nov 10, 2009 at 10:52 PM, Kristofer Munsterhjelm km-el...@broadpark.no wrote: In the context of SEC, it would be: Voter submits two ballots - one is ranked and the other is a Plurality ballot. Call the first the fallback ballot, and the second the consensus ballot. If everybody (or some very high percentage, e.g. 99%) votes for the same consensus ballot, it wins. Otherwise, construct a Condorcet matrix based on the fallback ballots. Pick two candidates at random and the one that pairwise beats the other, wins. How do you pick the random candidates? For that to be clone independent, there would actually need to be 3 ballots: - consensus ballot If more than X% of the ballots pick the same candidate, then that candidate wins. - nomination ballot - fallback ranking 2 nomination ballots are picked to decide the candidate and the pairwise winner according to the rankings wins. However, as I said in my last post, the nomination ballot isn't strategy free. To my knowledge, Random Pair is strategy-free. It might also be proportional, but I'm not sure about that (partly because I'm not sure how you'd define proportional for ranked ballots). The problem is picking the 2 candidates. If 2 are picked at random, then the method isn't clone independent. Also, it favours the condorcet winner, so may suffer from tyranny of the majority. However, if you had a divided society, then both ethnic groups would still have some say. For example, if the split was 55% (A) and 45 (B), and each ethnic group only voted for their own candidate, then the results would be 2 A's: 30% = ethnic group A wins A+B: 50% = ethnic group A wins (as they are the majority) 2 B's: 20% = ethnic group B wins Thus group B gets some power, but not proportional power. However, once the society starts working better, it would seamlessly transition to a near condorcet method. Also, in a divided society condorcet voting might reduce the issue directly. In both cases, there would be an incentive for politicians from ethnic group A to try to get support from voters in ethnic group B. OTOH, a random election method may not be the best plan in a society where corruption is a problem. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Warren Smith wrote: It seems to me that approval and range voting eliminate most of the strategic opportunity in single winner elections and the marginal improvement of other methods is fairly small. Can anyone point me to analysis, preferably at a layman level, that contradicts or supports this assertion? Or, in succinct terms, what are the strategic flaws in approval or range voting? Thanks, Matthew Welland --well... there is the whole rangevoting.org website... my more-recent papers at math.temple.edu/~wds/homepage/works.html discuss range voting including some ways it is provably better than every rank-order voting system for either honest or strategic voters... --but those are not exactly succinct... OK Let me try: 1. Range for 100% honest voters behaves better than IRV, Borda, Condorcet and it is pretty intuitively clear why -- strength of preference info used, not discarded. There is, of course, the flipside of that property. If one wants a voting method where the majority wins, then Range won't work, simply because a minority of strong opinions can outweigh a majority of weak ones. You might argue that that is no bug at all (strong opinions *should* outweigh weak ones), but for those for which Majority compliance is a must-have, it should be mentioned - particularly since that is supposed to be one aspect of the fairness of traditional democracy. In that sense, moving to Range (and perhaps Approval - depends on how you interpret it) is a more radical proposal than, for instance, moving to Condorcet (which passes Majority). (And now I wonder which election method that passes Majority has the least Bayesian regret.) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Dear Kristofer, both Approval Voting and Range Voting *are* majoritarian: A majority can always get their will and suppress the minority by simply bullet-voting. So, a more interesting version of your question could be: Which *democratic* method (that does not allow any sub-group to suppress the rest) has (usually or on average or in the worst case) the least Bayesian Regret. I conjecture that at least when the nomination of additional options is allowed, the method SEC described recently is a hot candidate for this award, since it seems that SEC will lead to the election of the option at the *mean* (instead of the median) voter position, and I guess that in most spacial utility models the mean position is in many senses better and will in particular have less Bayesian Regret than the median position. (Recall that in a one-dimensional spacial model where additional options can be nominated, all majoritarian methods likely lead to median positions being realized and are thus basically all equivalent.) Yours, Jobst -Ursprüngliche Nachricht- Von: Kristofer Munsterhjelm km-el...@broadpark.no Gesendet: 08.11.09 10:23:11 An: Warren Smith warren@gmail.com CC: election-methods election-meth...@electorama.com Betreff: Re: [EM] Anyone got a good analysis on limitations of approval and range voting? Warren Smith wrote: It seems to me that approval and range voting eliminate most of the strategic opportunity in single winner elections and the marginal improvement of other methods is fairly small. Can anyone point me to analysis, preferably at a layman level, that contradicts or supports this assertion? Or, in succinct terms, what are the strategic flaws in approval or range voting? Thanks, Matthew Welland --well... there is the whole rangevoting.org website... my more-recent papers at math.temple.edu/~wds/homepage/works.html discuss range voting including some ways it is provably better than every rank-order voting system for either honest or strategic voters... --but those are not exactly succinct... OK Let me try: 1. Range for 100% honest voters behaves better than IRV, Borda, Condorcet and it is pretty intuitively clear why -- strength of preference info used, not discarded. There is, of course, the flipside of that property. If one wants a voting method where the majority wins, then Range won't work, simply because a minority of strong opinions can outweigh a majority of weak ones. You might argue that that is no bug at all (strong opinions *should* outweigh weak ones), but for those for which Majority compliance is a must-have, it should be mentioned - particularly since that is supposed to be one aspect of the fairness of traditional democracy. In that sense, moving to Range (and perhaps Approval - depends on how you interpret it) is a more radical proposal than, for instance, moving to Condorcet (which passes Majority). (And now I wonder which election method that passes Majority has the least Bayesian regret.) 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] Anyone got a good analysis on limitations of approval and range voting?
On Nov 7, 2009, at 3:12 PM, Matthew Welland wrote: It seems to me that approval and range voting eliminate most of the strategic opportunity in single winner elections and the marginal improvement of other methods is fairly small. Can anyone point me to analysis, preferably at a layman level, that contradicts or supports this assertion? Or, in succinct terms, what are the strategic flaws in approval or range voting? this is no published analysis, but it should qualify as layman level. this is why i don't like either approval or range voting in a governmental election. in a sentence: Approval Voting does not collect enough information from voters and Range Voting requires too much. since any of these methods we discuss here really exist for the purpose of dealing with more than two candidates (if there are exactly two candidates no one really disagrees about what to do) let's see if we have to do with multiple candidates. in fact we can use the 2009 mayoral election in Burlington VT as an object lesson. we have Candidate A (we'll call Andy), Candidate B (we'll call Bob), Candidate C (we'll call Curtis, but in Burlington his name was Kurt), and candidate D (we'll call Dan). Approval Voting: so i approve of Andy and Bob, maybe Dan (not likely) and definitely not Kurt (err Curtis, candidate C). but, if the election comes down to Andy vs. Bob, i want to register my preference for Andy. how do i do that? so then i'm thinking (tactically) that the Bob supporters aren't gonna be reciprocating with an approval vote for Andy, so what do i do if i really support Andy, am willing to settle for Bob, but really want Andy. i will agonize over the decision and likely just vote approval for Andy, just like i would in a traditional FPTP election. but then there is no information coming from me that i prefer Bob a helluva lot more than i approve of Curtis. so Approval Voting has not relieved me, as a voter, from the need to consider tactics, if i want my vote to be effective. Range Voting: so i have 100 points that i can distribute among the 4 candidates. well definitely Candidate C (Curtis, really Kurt) gets zero of my points. i might toss Dan 5 points, but i would likely not waste them. so how do i divide my points between Andy and Bob? i like them both, but prefer Andy over Bob, so what do i do? i have to think tactically again. are the Bob supporters gonna be tossing any points to Andy? i can't trust that they will, they will probably just put all of their support for the candidate that they are behind. if i want my vote to compete effectively with theirs, i will end up putting all 100 points behind my candidate Andy. so, if we have any political identification at all, my vote under Range will convey no more information than it would with FPTP. IRV, Condorcet, and Borda, use the simple ranked-order ballot where we say who we support first (candidate A for me), who is our second choice (candidate B), who is our third choice (candidate D for me) and who is our last choice (candidate C for me). so if the election was just between A and B, we know that this voter (me) would vote for A. if the election was just between B and D, we know this voter would vote for B. if the election was between C and D, we know this voter would choose D. of course, for a single voter (not necessarily for the aggregation of votes) there is no circular preference, we know that if the election was between A and D, this voter would vote for A. we know that this voter would vote for B if the election was between B and C. and we know that this voter would vote for A if it were between A and C. from that simple ranked-order ballot, we know how the voter would vote between any selected pair of candidates in the hypothetical two-candidate election between those two. of course IRV, Condorcet, and Borda use different methods to tabulate the votes and select the winner and my opinion is that IRV (asset voting, i might call it commodity voting: your vote is a commodity that you transfer according to your preferences) is a kabuki dance of transferred votes. and there is an *arbitrary* evaluation in the elimination of candidates in the IRV rounds: 2nd- choice votes don't count for shit in deciding who to eliminate (who decided that? 2nd-choice votes are as good as last-choice? under what meaningful and consistent philosophy was that decided?), then when your candidate is eliminated your 2nd-choice vote counts as much as your 1st-choice. i don't like Borda because it has another arbitrary valuation. the difference in score between your 1st and 2nd choice is the same as the difference in score between your 2nd and 3rd choice. but what eternal value is that based on? what if i like my 1st and 2nd choice almost equally, but think my 3rd choice is a piece of crap? (this is what Range
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
On Sat, Nov 7, 2009 at 8:12 PM, Matthew Welland m...@kiatoa.com wrote: It seems to me that approval and range voting eliminate most of the strategic opportunity in single winner elections and the marginal improvement of other methods is fairly small. The recommended strategy in approval is to approve one of the top 2 and also any other candidates who are above your approval threshold. The threshold is not so important, as it is likely that one of the top 2 will win, so that approval is the only one that matters. You should approve all you prefer to the best of the top 2 and should never approve someone you like less than the worst of the top-2. Some possible thresholds - approve all you prefer to the expected winner - approve all you prefer to the expected utility of the election - approve all you prefer to the best of the top 2 - approve all you prefer to the worst of the top 2 I prefer to the first first one as it will results in the condorcet winner winning the election if there are accurate polls. As long as voters know who are the contenders, then approval strategy is pretty easy. Where there are 3 contenders, there is still some issue with regard to handling the middle candidate. The voter would need to make a call about which tie was more likely and also the differences in utility. Also, strategy isn't necessarily a bad thing. The problem with plurality is that it converges on the 2 party system. It is a Nash equilibrium. If you could go through each voter after an election and ask them if they want to change their vote, most of them wouldn't. It would normally just reduce the margin or victory for their favourite of the top-2. However, with approval, you can have a sequence that goes like: A and B are the top 2, but C is the condorcet winning candidate. Voters follow the policy that they will approve one of the top 2 and any candidate they prefer to the expected winner. Since every voter will only vote for one of A and B (since they are the top-2), one of them must end up with less than 50% of the vote. C is the condorcet winner, so he is preferred to whoever is the expected winner by at least half of the voters. Thus the first poll will show something like A: 45 B: 55 C: 51 Thus C will suddenly be one of the top-2. This might take a few polls, but as C gets more press reports, his percentage will increase. Once he is one of the top-2, he cannot be displaced. No matter who is the other one, he will be preferred to that candidate by more than 50%. Also, once he is one of the top 2, any voters who prefer him to all other candidates will suddenly stop approving either of A or B. Thus one of them will drop in popularity. The point is that it isn't strategy that is the problem. It is that strategy results in the voters ending up with the the better of 2 evils. With approval, the result is that a condorcet winner should normally win, so any strategy results in a fair result. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Raph Frank wrote: On Sat, Nov 7, 2009 at 8:12 PM, Matthew Welland m...@kiatoa.com wrote: It seems to me that approval and range voting eliminate most of the strategic opportunity in single winner elections and the marginal improvement of other methods is fairly small. The recommended strategy in approval is to approve one of the top 2 and also any other candidates who are above your approval threshold. That's strategy T. Some times (see Rob LeGrand's dissertation defense slides) a strategy A is better: approve all that you like better than whoever's getting the most Plurality votes, and approve of him as well if you prefer him to the one in second place on the Plurality count. (I think it's a Plurality count. Late here, so vote-getter may refer to Approval votes - I'm not sure.) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
On Sat, Nov 7, 2009 at 10:57 PM, Kristofer Munsterhjelm km-el...@broadpark.no wrote: The recommended strategy in approval is to approve one of the top 2 and also any other candidates who are above your approval threshold. That's strategy T. Some times (see Rob LeGrand's dissertation defense slides) a strategy A is better: approve all that you like better than whoever's getting the most Plurality votes, and approve of him as well if you prefer him to the one in second place on the Plurality count. Strategy A, as you defined it, is almost equivalent to just setting the threshold to the utility of the expected winner. (I think it's a Plurality count. Late here, so vote-getter may refer to Approval votes - I'm not sure.) I don't think that actually matters much. They should be roughly the same. The main point is that the top-2 candidates are the 2 candidates who are most likely to tie, so you should approve one of them and not the other. Election-Methods mailing list - see http://electorama.com/em for list info
