Re: [EM] The worst about each system; Approval Preferential
2010/5/27 Abd ul-Rahman Lomax a...@lomaxdesign.com At 12:31 AM 5/27/2010, Jameson Quinn wrote: As Abd already said, you can avoid the runoff if only one candidate has a majority. Abd's Bucklin proposal tricks many voters into extending more approvals to decrease the chances of a runoff. I should have been more precise. I believe that with Bucklin/Runoff, people will honestly rank more candidates than are approved with approval/runoff. This will help avoid some unnecessary runoffs, which is a good thing. It will also possibly improve the utility of the result for society. However, it is a strategic mistake on their part. Thus, I call it a trick; if they fully understood the situation, they probably would just vote strategically. Being a trick doesn't make it evil; on the contrary, if anything, it helps the social utility. But it does make it unstable; people might see through it, and it would stop working. (If they have a rational degree of doubt in their own judgement of which option is best, and are voting altruistically, and believe that a majority of voters are voting altruistically or have no negative-sum interests at stake, then it's not a mistake, but the first part at least clearly doesn't describe most.) In APV, adding additional preferences (beyond the approval ballot) is not a strategic mistake, which I think makes it more robust. It also still has the same justifications in human psychology. Correct strategy in APV when the two frontrunners are ideologically distinct is to disapprove one and everybody worse, prefer the other and everybody better, and approve everybody in between. If they're near-clones ideologically (ie, near to same value for most people who aren't strong supporters of one of them), then do the same using the third frontrunner and the most-distinct of the first two; that automatically means at least one approval, for the other clonelike frontrunner. Both of these strategies, if widely followed and if the frontrunner determination is common knowledge, never lead to a runoff. Bucklin, very similar to what I'm proposing, was widely used for a time. We know that some voters don't like being restricted to three ranks in RCV. Additional expression, *if voluntary*, is, in my book, a good thing. If voluntary and honest. But one dishonest strategic expression can poison a number of honest expressions. Moreover, even semi-honest strategy creates two classes of voting power - strategic and nonstrategic - which hurts legitimacy. That's why adding levers and knobs to your voting system is dangerous if they can be used strategically with impunity. I believe that the best solution to expressiveness is not a kitchen sink system such as some of Abd's proposals, but a drastically simple system with an official, nonbinding, Range/Condorcet/Bucklin poll attached. Voters rank each candidate as preferred, approved, or unapproved. So you have an explicit disapproved rank? How is this treated compared to a blank? Same as blank. Exists only to prevent accidentally approving when trying to vote against. Tallied together but break-out percentages reported for anyone who cares. If any candidates have a majority ranking them at-least-approved, then the one of those which is most preferred wins outright. Right. With quite possibly bizarre outcomes. No more bizarre than closed primaries, at the very worst. That is, a solid majority coalition might elect its more radical member, not the centrist. Solid majority means that the median voter is a member of that coalition, supporting the radical on that side over all other candidates. Unlike closed primaries, if there's a majority but it's not solid, the centrist from that side is probably elected. Personally, I don't see that as necessarily bad - think of it as a small taste of time-series proportional representation. In other words, a bit of diversity, instead of centrists winning always, could be healthy. ... instead of his 1, 0.75, and 0, it should be 1, 0.5, 0. But that isn't used in this present statement of the method. It's simply Range analysis. This is only for the nonbinding poll. People can set these numbers explicitly, those were just defaults. Actually, the right default value for the approved rank is the average of the value people explicitly write in for that rank. I do suspect that people would be more likely to write in values above 0.5 than below it, so I suspect that number will be closer to 0.75 than to 0.5. If not, then the two candidates which are most preferred against all others (ie, the two Condorcet winners based on these simple ballots, or the two most-preferred in case of a Condorcet tie) proceed to a runoff Utility theory would not suggest his pair. Utility theory suggests the sum of scores candidates. I only suggest including a Condorcet winner because of conflict between utility theory and democratic majority theory. If a result is to be based on greater summed good, the
[EM] SMD,TR fails the Plurality criterion.
Kevin Venzke has come up with an example that shows that my Strong Minimal Defense, Top Ratings (SMD,TR) method fails the Plurality criterion,contrary to what I've claimed. 21: AC 08: BA 23: B 11: C Approval scores: A29, B31, C32 Maximum Approval Opposition scores: A11, B32, C31 Top-Ratings scores: A21, B31, C11. By the rules of SMD,TR B is disqualified because B's MAO score (of 32, C's approval score on ballots that don't approve B) is greater than B's approval score. Then A (as the undisqualified candidate with the highest TR score) wins. But since B has more first-place votes than A has total votes, or in the language of this method B's TR score is greater than A's total approval score, the Plurality criterion says that A can't win. This seems to show that compliance with my Unmanipulable Majority criterion is a bit more expensive than I thought. I still endorse SMD,TR as a good Favourite Betrayal complying method, but with less enthusiasm. (My UM criterion says that if A is a winner and on more than half the ballots is voted above B, it is impossible to make B the winner by altering any ballots on which B is voted above A without raising on them B's ranking or rating.) I was wrong to claim that compliance with Strong Minimal Defense implies compliance with the Plurality criterion. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] SMD,TR fails the Plurality criterion.
My previous message contained a small blunder. The corrected version is below A candidate X's maximum approval oppostion score is the approval score of the most approved candidate only on ballots on which X is not approved. In the example election I mistakenly gave A's MAO score as 11. The definition of SMD,TR: *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023530.html Chris Benham Kevin Venzke has come up with an example that shows that my Strong Minimal Defense, Top Ratings (SMD,TR) method fails the Plurality criterion,contrary to what I've claimed. 21: AC 08: BA 23: B 11: C Approval scores: A29, B31, C32 Maximum Approval Opposition scores: A23, B32, C31 Top-Ratings scores: A21, B31, C11. By the rules of SMD,TR B is disqualified because B's MAO score (of 32, C's approval score on ballots that don't approve B) is greater than B's approval score. Then A (as the undisqualified candidate with the highest TR score) wins. But since B has more first-place votes than A has total votes, or in the language of this method B's TR score is greater than A's total approval score, the Plurality criterion says that A can't win. This seems to show that compliance with my Unmanipulable Majority criterion is a bit more expensive than I thought. I still endorse SMD,TR as a good Favourite Betrayal complying method, but with less enthusiasm. (My UM criterion says that if A is a winner and on more than half the ballots is voted above B, it is impossible to make B the winner by altering any ballots on which B is voted above A without raising on them B's ranking or rating.) I was wrong to claim that compliance with Strong Minimal Defense implies compliance with the Plurality criterion. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] [Condorcet] Re: IRV vs Condorcet
now ask yourself the question whether or not Condorcet satisfies these criteria (assuming a CW exists). Of course it does, because you only included the anti-strategy criteria which it does pass. But what do you call this: Hypothetical true preferences: 39.4: DH=C 30.8: HCD 27.6: CHD 2.5: NOTA H is the condorcet winner. But if just 8% from the C voters instead vote CH=D (or 4% of them vote CDH, if equal rankings aren't allowed), then there is no Condorcet winner, and C could win. (This election actually happened recently in Hawaii, although of course the lower preferences are simplified guesses). My APV proposal does very well on this and other scenarios. Specifically, for this scenario, the pure strategy which is closest to being a trembling-hand equilibrium is the good situation where H wins in one round (Not true of Approval, Bucklin, margins Condorcet, Range; IRV is the only major system I know of which passes this test). And it is monotonic, and, unlike IRV, unilkely to fail to find a centrist Condorcet winner. In fact, I can't think of a single scenario where the pure strategy closest to being trembling-hand equilibrium doesn't give an very-arguably right answer in one round for APV. And I can easily get IRV to give the wrong answer, so APV is the only system I know of which pass this test. JQ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] The worst about each system; Approval Preferential
At 03:14 AM 5/27/2010, Jameson Quinn wrote: 2010/5/27 Abd ul-Rahman Lomax mailto:a...@lomaxdesign.coma...@lomaxdesign.com At 12:31 AM 5/27/2010, Jameson Quinn wrote: As Abd already said, you can avoid the runoff if only one candidate has a majority. Abd's Bucklin proposal tricks many voters into extending more approvals to decrease the chances of a runoff. I should have been more precise. I believe that with Bucklin/Runoff, people will honestly rank more candidates than are approved with approval/runoff. Yes, and there are two reasons. The most common immediate objection to Approval is that it does not allow the expression of preference within the approved class. That can be very important to me as a voter. If I'm a Nader supporter in 2000, I want to, at the same time, make it clear that I prefer Nader, while allowing my vote to count against Bush, i.e., to support Gore. (If I believe Nader's argument about Tweedle-Dum and Tweedle-Dee, I may not care.) While Approval gives me a better option than Plurality, where it is all-or-nothing, it's still unsatisfactory. In addition, there is a minor problem with multiple majorities due to over-eager additional approvals, which then creates pressure to, next election, bullet vote. It seems fairly clear that approval compared to Plurality will not harm results, long-term, but will improve them to a degree, and Approval is a basically no-cost reform, it would normally require only the removal of a line from the election code that requires discarding and not considering overvotes. This applies to approval/runoff as well. If there is no multiple majority, it's moot, though some may be upset if they would have preferred a runoff to the election of their second favorite, whom they additionally approved. They made that approval, presumably, because they wanted to make sure that a different candidate was not elected. So, Bucklin. Bucklin is *similar* to Approval, in practice, but the phased approval it sets up allows the expression of that preference, and it is even possible, with original Duluth Bucklin, to show strong, weak, or preference. I.e., if it happens to be three candidates plus write-in, This will help avoid some unnecessary runoffs, which is a good thing. It will also possibly improve the utility of the result for society. However, it is a strategic mistake on their part. Sure that depends on their preferences and preference strengths. It seems that Mr. Quinn is making some possibly unwarranted assumptions here. Thus, I call it a trick; if they fully understood the situation, they probably would just vote strategically. With this, I vigorously disagree. While it is possible that some voters will misunderstand the situation, with good ballot instructinons and general education, few are likely to truly misunderstand. It is a fact that with high knowledge (hindsight is high knowledge!) and with nearly any voting system, a voter may see a strategic vote to cast that will improve the outcome for the voter. Far more likely, though, is that the voter will see that their vote was moot, that they could have stayed home with no change in outcome. Bucklin is very similar to Approval, and what a strategic vote is in Bucklin, as in Approval, depends on who the frontrunners are and what the preference strengths of the voters are. In Bucklin/runoff, there is an additional factor, the possible desire to avoid a runoff election. Or, to the contrary, the desire to postpone an approval until the runoff. Mr. Quinn seems to assume that if the voter understands the situation, the voter will therefore prefer a runoff to making an additional approval. But I'd want to see voter education on this be very clear: if you would prefer a runoff to the election of a candidate, don't approve the candidate! If you hate runoffs -- some have expressed that opinion here -- then, TANSTAAFL, you rationally will take a chance on making a significant approval. If you prefer runoffs, you will only add additional approvals if you have relatively low preference strength, or, alternatively, prefer a no-hope candidate, and you want to help get your favored frontrunner into the runoff. With some variations I've proposed, you can do both: avoid electing your preferred frontrunner in the primary, but help get that candidate into the runoff (by using an elevated unapproved class assignment, indicating both preference for condorcet analysis, and higher utility.) The basic instructions to the voters are quite simple, as I've outlined them, and runoff complicates Bucklin strategy only a little. Runoff/Bucklin will almost certainly depress approvals to some degree, but what it will depress is holding-my-nose-and-voting for the preferred frontrunner. It will not depress genuine additional approvals with low preference strength between that candidate and the favorite. Straight Bucklin without runoff will force voters who want
[EM] An assortment of recently online Condorcet elections, some with ballot data
I thought people might find these useful/fun to look at. Click on show details to get access to the ballots where available. 12 Modern Philosophers: Which Ones Are Likely to be Read in 100 Years? (13 choices, 413+ voters, ballots available) http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_520bd5632b7ff3cb Who are the most important philosophers of all time? (48 choices, 948 voters, ballots available) http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_5f1c74bf01172b2a What is the best measure of faculty quality? (4 choices, 256+ voters, ballots available) http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_a90355821e6c7fc3 Favorite programming language (40 choices, 134 voters) http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_540fe382529392ba GNU Mailman Logo Contest 2010 (5 choices, 391 voters) http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_17290602feb24023 Cheers, -- Andrew Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] The worst about each system; Approval Preferential
Correct strategy in APV when the two frontrunners are ideologically distinct is to disapprove one and everybody worse, prefer the other and everybody better, and approve everybody in between. Eh? That forces favorite betrayal, doesn't it? No. Correct strategy presumes that a particular goal is correct. What is it, in this case? Presumed here is an assumption that ideology is the issue. I give a more precise and general definition below for the shorthand ideology, which makes your objections moot. Perhaps you should finish a paragraph before writing several in response to the first sentence. If voluntary and honest. But one dishonest strategic expression can poison a number of honest expressions. Moreover, even semi-honest strategy creates two classes of voting power - strategic and nonstrategic - which hurts legitimacy. I would encourage all voters to vote strategically and honestly. In a Bucklin system there is no advantage to dishonesty that is worth the risk. I.e., from a game theory point of view, net zero or negative expected gain. I happen to agree. But some voters might overestimate their capacity to predict behavior, and the fact that they're wrong doesn't stop the harm they do. In my system, where there is never more and almost always significantly less payoff from dishonest strategy, this is less of a danger. Anyway, you didn't respond to my critique of semi-honest strategy. In APV, naive human nature strategy is closer to being the same as optimal strategy, so the difference in voting power is less. This means more legitimacy. This is important: the math hasn't been done, but my intuition here is that the rational strategic Bucklin ballot is a Range ballot with these restrictions: the candidates are divided into two sets, approved and non-approved, and range ratings are best as sincere ratings *within these sets*. I vigorously disagree. The rational strategic Bucklin ballot is, to first approximation, an approval ballot. In some cases (which I don't quite have a handle on) it might be rational to move a single candidate down from maximal to minimal approval, or to add a minimal approval to a single candidate who would not have made the cut under approval. Intermediate approved rankings are never rational if all voters are purely rational, though if there are some honest voters, it may become rational to use intermediate approvals occasionally. Unapproved rankings besides the bottom are used for turkey-raising if at all. That's why adding levers and knobs to your voting system is dangerous if they can be used strategically with impunity. I've seen no cogent example of this. In evaluating strategy, I'd encourage Mr. Quinn and anyone else to *start* with utilities. I do. Voters will bullet vote, commonly. It is a rational and sensible and *sincere* strategy, properly understood. Absolutely true in many, but not all, cases. I'd guess that mostly it's rational and sincere; sometimes it's rational and insincere; and rarely it's irrational and sincere. Mr. Quinn's proposal is indeed simpler, Simpler; and better at harmonizing naive, individually optimal, and socially optimal strategies. Both are important advantages. No more bizarre than closed primaries, at the very worst. One is getting desperate when one justifies a system as being no worse than a bizarre system. A lower bound which is acceptable to most is not desperate. It is not the average performance. That is, a solid majority coalition might elect its more radical member, not the centrist. Solid majority means that the median voter is a member of that coalition, supporting the radical on that side over all other candidates. Unlike closed primaries, if there's a majority but it's not solid, the centrist from that side is probably elected. In the example shown, there was a drastic difference between the winner and loser. And it was an artificially-constructed example, one which both the naive and the correct strategy (which are the same in this case) would tend to discourage from ever happening. The loser was massively approved, the winner only barely. Bare approval in a situation like that is quite likely to be an anomaly. But without having a set of utilities to start with, we cannot judge a scenario outcome, not well, anyway. If the approvals represented sincere approval, the approval winner would *certainly* have been the best. Mr. Quinn is arguing that preferring the most-preferred candidate will, then encourage additional approvals. But then he discards those approvals in this scenario, making them useless. Tell me again, exactly why do we want to encourage people with a strong preference for first preference to add additional approvals? Beyond the natural encouragement of avoiding a runoff -- when strong preference means they'd rather have a runoff? If their preference is strong enough, they are free to not add approvals. But (lightly)
[EM] meditations
My conjectures turned out to be true: Lemma: If range values are limited to k levels, and alternative X beats alternative Y with a margin ratio greater than (k-1)/1, then alternative X has a greater range score than alternative Y. Proof: Without loss in generality assume that the k possible ratings on each ballot are 0, 1, ...(k-1). If there are x ballots on which X is rated above Y for every y ballots on which Y is rated above X, then the least the difference in the respective range scores could be is d = 1*x - (k-1)*y , since the least possible difference in ratings on any single ballot is one, and the greatest possible difference in ratings on any ballot is (k-1). But when the margin ratio x/y is greater than (k-1)/1, the value of d is positive. Therefore X has a greater total range score than Y. Corollary 1. If range values are limited to k levels, then there can be no beat cycle where all of the defeats have margin ratios greater than (k-1)/1. Corollary 2. If range values are limited to k levels, then no beatpath with margin ratio strength greater than (k-1)/1 can be longer than k times the number of ballots, no matter how many alternatives are rated on the ballots. Corollary 3. In the case of ordinal ballots, if no ballot ranks candidates at more than (k-1) levels, then the conclusions of Corollaries 2 and 3 still hold. Corollary 4. If there are only k candidates , then the conclusions of Corollaries 2 and 3 still hold. How can we put this information to good use? Suppose that we are dealing with 3 slot ballots as in MCA, APV, MAFP, etc. It may not be too common for one candidate to have a wv score against another candidate consisting of more than two thirds of the vote. But that is not needed here, only a margin ratio greater than two to one is needed. In other words, if eleven percent of the voters prefer X over Y but only five percent of the voters prefer Y over X, then we have a margin ratio that cannot be sustained indefinitely in a beatpath, and (more to the point) cannot sustain any cycle no matter how long or short. So the losers in all such defeats can be eliminated without fear of eliminating all of the candidates. Doing so would automatically eliminate all of the Pareto dominated candidates, too, and make the method independent from Pareto dominated candidates. Any other ideas on how to put these facts to use? Forest Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Bucklin-like method meeting Favorite Betrayal and Irrelevant Ballots
- Original Message - From: Chris Benham Date: Thursday, May 27, 2010 12:10 pm Subject: Bucklin-like method meeting Favorite Betrayal and Irrelevant Ballots To: EM This is my suggestion as a good Favorite Betrayal complying method, as an alternative to SMD,TR. It uses multi-slot ratings ballots. I suggest 4-slot ballots as adequately expressive, so I'll define that version: *Voters fill out 4-slot ratings ballots, rating each candidate as either Top, Middle1, Middle2 or Bottom. Default rating is Bottom, signifying least preferred and unapproved. Any rating above Bottom is interpreted as Approval. If any candidate/s X has a Top-Ratings score that is higher than any other candidate's approval score on ballots that don't top-rate X, elect the X with the highest TR score. Otherwise, if any candidate/s X has a Top+Middle1 score that is higher than any other candidate's approval score on ballots that don't give X a Top or Middle1 rating, elect the X with the highest Top+Middle1 score. Otherwise, elect the candidate with the highest Approval score.* By comparison with Bucklin I think it just swaps compliance with Later-no-Help for Irrelevant Ballots, a great gain in my view for a method that fails Later- no-Harm. The incentive for voters to truncate and compromise (in other words not use the middle ratings slots) is less strong. 40: AB 35: B 25: C Here (like SMD,TR) it elects the Condorcet winner A. Bucklin elects B. 35: A 10: A=B 30: BC 25: C Here (like SMD,TR) it elects B. Bucklin elects C It seems to me that this new method would elect A, since A has the most TR (45 versus 40 for B) and the greatest total of approvals below top is only 30 (by C). . The example is from Kevin Venzke. Electing B demonstrates failure of a criterion I called Possible Approval Winner (and Forest Simmons something like Futile Approval). It says that if the voters all enter an approval threshold in their rankings (always making some approval distinction among the candidates but none among those voted equal) that is as favourable as possible for candidate X without making X the thus indicated approval winner, then X mustn't win. In the example above B can't be more approved than A. 21: AC 08: BA 23: B 11: C Like Bucklin it meets the Plurality criterion. In this example where SMD,TR fails that criterion by electing A, it and Bucklin both elect C. Any comments? Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
