[EM] Most Tolerable or Better
This is a three slot method. The two non-blank choices are tolerable and better. Elect the alternative that is marked tolerable or better on the greatest number of ballots. If there is a tie, then elect the tied alternative that is marked better on the greatest number of ballots. If a tie persists after this step, then break it by random ballot. This method should be understood as a good faith attempt to minimize the number of voters that have to live with an outcome that is intolerable for them, so that other preference considerations are secondary. Of course, a statistically confident, determined majority of 51% can still force its will on the rest of the voters by bullet voting instead of admitting that some other alternatives would be tolerable; this method is not a fool proof solution of tyranny of the majority. You might consider this as a cross-walk version of Approval, because most of the time there won't be a tie to be broken, just like most of the time pushing the walk button is just for psychological benefit; it doesn't make the light change any faster. Beyond the psychological value the tolerable versus better distinction can reveal valuable information after the election. But there is also a more important (but subtle) benefit of having a separate tie breaker level; from an instrumental point of view, your vote has only symbolic value anyway when there is no chance of a tie. Voting power is defined as the probability that your vote will be pivotal in the outcome. It is pivotal precisely when it either makes or breaks a tie. If a tie is made or broken by one vote, then everybody who voted is glad that they did (unless their vote broke the tie in an unintended direction as it could under a non-monotonic method). Otherwise, most people recognize that no individual vote, including theirs, made any difference other than symbolic, for example as a mandate for the winner or show of support for a loser. The best case would be when there are two or more alternatives that are tolerable (or better) to everybody, which is not out of the question in situations where the voters are sufficiently like minded. In that case the tie breaker chooses from among these consensus candidates. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Further SODA refinement
Problem: Near-clones A1 and A2 have both put each other at the top of their delegation order. Their totals, combined, constitute a majority, but either one alone would be beaten by B. Both insist that the other one delegate, threatening to refuse to delegate. It's a game of chicken, and the more symmetrical the situation is, the more likely that negotiations fail. Even if they succeed, the winner may simply be whichever is more intransigent, not a good result. Solution: When choosing whether to delegate, candidates do so not simultaneously but sequentially, in order from most delegable ballots to least delegable ballots. This means that candidates with fewer delegable votes are unable to make ultimatums to candidates with more delegable votes. Three sub-scenarios: Assume all votes are delegable (for simplicity). Assume WLOG that A1 is the one with more votes. Note that if this is a 1-dimensional ideological spectrum, that is likely to mean that A2 is the squeezed Condorcet winner. Scenario 1: B prefers A1. B does not delegate, hoping that A1 and A2 will be unable to negotiate. A1 does not delegate, as an ultimatum to A2. A2 is strategically forced to delegate if they don't want B to win. Scenario 2: B prefers A2. B delegates to A2, knowing that otherwise the equilibrium is an A1 win. A1 and A2 do not delegate. A2 wins. Especially if the voters are ideologically divided, we can assume that A2 was the CW. Scenario 3: B prefers neither, or marginally prefers A2 but decides not to delegate (hoping for a win). Results are the same as scenario 1. This is perhaps a good center-squeeze scenario. That is, if there's an approximate 1-dimensional spectrum, chances are that A2 is the centrist candidate and thus the ideological CW. However, B's choice not to delegate to A2 reflects on A2's quality. Perhaps SODA, here, has avoided a mushy middle win which a Condorcet system would have fallen into. Note: If B adopts a worse is better attitude, trying to elect the one of A1 or A2 who will be a weaker opponent in the next election, then they probably can. However, they must do so openly, so hopefully voters will see through whatever they use as a rationalization and punish them for their selfish actions. It is essentially impossible for a good voting system to do any more than that to avoid such anti-patriotic behavior. Note: I got essentially no responses to my last message refining SODA (where I suggested a 5% minimum cutoff to be able to actively delegate votes, with votes below that delegated automatically). Is that just because nobody had anything to add, or are people not interested in discussing this system? If it's the latter, I'd love to know why not. JQ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Most Tolerable or Better
On Jun 29, 2011, at 3:52 PM, fsimm...@pcc.edu wrote: This is a three slot method. The two non-blank choices are tolerable and better. Elect the alternative that is marked tolerable or better on the greatest number of ballots. If there is a tie, then elect the tied alternative that is marked better on the greatest number of ballots. this seems to me to be a sorta backward-working Bucklin. if you replace blank with 3rd-choice, tolerable with 2nd-choice, and better with 1st-choice, it's a basic ranked ballot like for IRV or Condorcet or Borda or Bucklin. it's a lot like Bucklin except Bucklin looks first at only the 1st-choice rankings (and a tie is far less likely than a non-majority, which is what Bucklin uses to trigger looking at the second-round count of 1st and 2nd rankings). it's not Bucklin, but it reminds me of Bucklin. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] SODA in a de-facto two-party system
Having considered these issues, there are two refinements I'd make to SODA: - If, after voting, one candidate has an absolute majority OR is the only possible winner, they win immediately. Sure, I can think an argument for why SODA should elect someone who's not the initial majority winner. But I don't relish the thought of having to make that argument, either with a politician or with a regular voter. And in reality, a majority winner is the correct winner in more than 95% of the cases, so let's just save the time and admit that immediately. - If, after voting, one candidate has fewer than 5% of the votes, their votes are automatically delegated to the first candidate on their preference list who has more than 5% (if any). The receiving candidate may delegate them in turn, only if the result thereby obtained or encouraged is consistent with the preference order of the original candidate. (That means that if minor A's order is B,C,D,E,F, and D is the first one of those with more than 5%, and D's order is C,F,X, E,..., then D may delegate these votes to C, or to C and F if F is already leading E by a greater margin than the number of votes in question, or to C, F, and E if D is delegating their own votes to X as well.) This appears to be a bigger compromise of principle than the above. But consider the kingmaker case: in a basically 50/50 split, some tiny party has the balance of votes, and manages to extract concessions far bigger than their base of support justifies, just in order to [not] delegate those votes. I think that's unjust, and this rule would prevent it. I think that 5% is a good cutoff here; that's tens of millions of voters, and enough to deserve a voice. It shouldn't be too high, because this rule is effectively taking power away from voters; that's only justified if the faction is so small that the power is not legitimate, and so it's better to err a bit on the small side if anything. But under 5% - that is, under 10% of the winning coalition - doesn't deserve kingmaker power. JQ I like it! Don't be impatient; some of us don't have time to read these things every day. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Most Tolerable or Better
Yes, you can think of it as upside down MCA, which is a three slot version of Bucklin. - Original Message - From: robert bristow-johnson On Jun 29, 2011, at 3:52 PM, fsimm...@pcc.edu wrote: This is a three slot method. The two non-blank choices are tolerable and better. Elect the alternative that is marked tolerable or better on the greatest number of ballots. If there is a tie, then elect the tied alternative that is marked better on the greatest number of ballots. this seems to me to be a sorta backward-working Bucklin. if you replace blank with 3rd-choice, tolerable with 2nd-choice, and better with 1st-choice, it's a basic ranked ballot like for IRV or Condorcet or Borda or Bucklin. it's a lot like Bucklin except Bucklin looks first at only the 1st-choice rankings (and a tie is far less likely than a non-majority, which is what Bucklin uses to trigger looking at the second-round count of 1st and 2nd rankings). it's not Bucklin, but it reminds me of Bucklin. -- 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] Most Tolerable or Better
What about strategy for Most Tolerable of Better? In ordinary Approval, the strategy S that maximizes the probability of being pivotal (in the desired direction) is to approve alternative X if and only if X is less likely to be tied with an alternative that you prefer over X than it is with an alternative that you like less than X. When most of the winning probability is concentrated in only two alternatives, this strategy reduces to Rob LeGrand's strategy A: put your approval cutoff adjacent to the alternative most likely to win on the side of the alternative with the next greatest winning probability. Suppose that there are two lesser evils X and Y running about even in winning probability with the candidate Z that you detest the most (anybody but Z). Do you approve both lesser evils X and Y, or just the one X that that you have a slight preference for? Under ordinary approval, this is a difficult question, since the probabilities involved are apt to be pretty rough estimates, and it may be that your preferred compromise X is just short of the necessary support to beat Z. [If you use the strategy S that maximizes the probability of being pivotal (in the desired direction), then you approve Y if and only if Z has a greater probability of winning than X. But these two probabilities are not precisely known.] Under Most Tolerable or Better you can mark X and Y as better and tolerable, respectively, while leaving Z at the default bottom. This maximizes the chance that Z will not win, and contributes to X over Y in the not too unlikely case that X and Y end up with the same tolerable or better score ahead of Z. You might say that these ties are too unlikely to matter, but where there is no tie or near tie, your ballot cannot be pivotal anyway. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet Jury Theorem
my premise, poorly articulated, but my premise nonetheless is that an adaptive voting method that takes into account voters' previous behavior may be able to outperform OMOV in the long run on average. P=NP is only meant to evoke the relevant properties of objective truth i.e. that it is true or false and that people don't know for certain what it is. It is also meant to illustrate how people are NOT Condorcet jurors themselves. We are NOT objective truth with some noise thrown in. In fact, even in the P=NP problem, we would only distrust putting it to a public vote because we have so much additional information about the problem. In retrospect, using it as an example was a mistake. A system of the ilk I am proposing doesn't know anything about the content of the issues, simply what different people believe. Nevertheless, I believe that we can simulate a Condorcet jury by weighting people differently based on past behavior. This would make the resulting voting methods adaptive rather than memory-less. The current methods that I believe have been proposed thus far are all memory-less. The result of the n+1st election can't depend on the nth election, indeed the results of any elections are independent of the order in which they are conducted. However, I would argue that this ignores important information that we have in real life. We know something about the structure of non-randomness in people's opinions and can account for it. Assuming people are honest, I believe it is possible for an adaptive voting method to outperform methods that enforce OMOV for the very limited goal I set forward in my first post… to attempt to determine the truth of propositions, not to make any type of normative decision. I'm pretty sure that P = NP? is a question for which the average person of the public's chance of getting the answer right is much lower than 50%. So we don't ask the public (and if we had to, the jury theorem says we should ask just a single person instead of averaging opinions). Similar arguments have been made against democracy in general, even back to the ancient Greek times, to the effect that statecraft is a skill and the public isn't skilled. The jury theorem still works: you don't need to assume people being wrong in non-random ways for the theorem to tell you it's not a good idea to predict P = NP by vote. You absolutely do need people to be wrong in non-random ways. If p.5 for people, but we were still Condorcet Jurors, you would ask as many people as possible and then negate the answer. That clearly doesn't work; therefore, we are not Condorcet Jurors. I'm not claiming that jury theorem doesn't work or is inapplicable, far from it. I'm claiming that if we have more information on voters and their past behavior, we should be able to devise an algorithm that will outperform OMOV.* *assuming honest voters. I don't want to have to worry about strategic voters yet. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Most Tolerable or Better
On Jun 29, 2011, at 3:52 PM, fsimm...@pcc.edu wrote: This is a three slot method. The two non-blank choices are tolerable and better. Elect the alternative that is marked tolerable or better on the greatest number of ballots. If there is a tie, then elect the tied alternative that is marked better on the greatest number of ballots. What if we changed if there is a tie to if there is a statistical tie? In other words if the difference in the number of tolerable or better votes for alternatives A and B is not statistically significant, then it is treated as a tie, and the distinction between tolerable and better kicks in. You could make it so that the null hypothesis of tied tolerable and better is rejected only five percent of the time (when true). This policy would make the tie breaker level (the better level) come into play more frequently, thus making the game more interesting. Election-Methods mailing list - see http://electorama.com/em for list info
