Juho: Here's the MinMax(margins) chicken dilemma example that I promised, in which defection by B voters is successful and rewarded::
Sincere preferences: 75: A>B>>C 51: B>A>>C 100: C>>(A=B) Voted rankings: 75: A>B 51: B 100: C Try MinMax(margins) with that example. Note that it's a Dodgson example too. Note also that the B faction is small in comparison to the other factions. Condorcet(wv) reliably rewards defection. SITC reliably thwarts and penalizes defection. Though MinMax(margins) and Dodgson don't reward defection quite as reliably as does wv, (though the example shows that they easily do so), they certainly don't reliably thwart and penalize it either. An additional problem of MinMax(margins) and Dodgson: It is well established and well-discussed on EM that MinMax(margins) has particularly great problem with strategic truncation and offensive burial. Those things, even offensive burial, aren't a problem with SITC, because the only candidate who can benefit from it is the most top-ranked candidate among the unbeaten candidates--or just the most top-ranked candidate if there are no unbeaten candidates. Offensive burial can't make anyone else win. I'll try to answer (only) the parts of this posting that I didn't answer in part 1 of my reply: > I don't think the following four questions that you gave as a response are > ones that I left unanswered, but new questions or new formulations. I'l check > them anyway. > >> 1. What makes you think that MinMax(margins), Dodgson, or Beatpath >> won't have a chicken dilemma? > > I already said that I do believe that basic Condorcet methods are not very > prone to this problem. I >know that you disagree. Maybe you'll find one day a > proof that will convince me. Above, in this reply, I've posted an example in which defection by the B voters is rewarded. The A voters, expecting likely defection by the B voters can co-operate, by ranking B, because at least one faction must co-operate in order to defeat C. But, if they do, they'll lose to B, because they've been had by the B voters. That's the chicken dilemma, and it's fully there, with MinMax(margins) and Dodgson. As for Beatpath, Beatpath's failure was shown in my posting with my old 27,24,49 example. It's easier to show Beatpath failing, having the chicken dilemma. But, as you can see from the example shown above in this post, MinMax(margins) and Dodgson fail quite easily too. >> Must I do that, to show you their >> chicken dilemma? Request it and I will. (I showed an example, in this posting, in which MinMax(margins) has that problem. > > No need since I don't expect that to change my opinions. It could be a wasted > effort. I'm >interested if there is something really convincing, but maybe > better leave this topic this time, with >the assumption that I would not > believe it anyway. If an example of it happening doesn't convince Juho, then nothing will. That's ok. You said: Many Condorcet strategies are difficult to identify, to use, to coordinate, and often they may also backfire. [endquote] Sure. As I said, in Condorcet, even in a u/a election, you won't know what to do. For example, in a u/a election: Approval: Approve the acceptables and none of the unacceptables. Score: Top rate the acceptables and bottom rate the unacceptables. SITC: Top rank the acceptables, and don't rank anyone else. Unimproved Condorcet (Including MinMax(margins), Dodgson, Beatpath, etc.): You still have the same need to top rank the acceptables, and for the same reason. But, with Unimproved Condorcet, that can, as you said, backfire, because top ranking someone (you don't know which one) could cause your last choice to win. In Unimproved Condorcet, you won't know what to do, even in a u/a election. But suppose there is one Democrat, and some Republicans. There are also some progressives whom you prefer to the Democrat. You believe (you've always heard it in the media, which you completely believe) that the Democrat and the Republicans are the only candidates who can win. You feel that the Republican is unacceptable, and that the Democrat is acceptable, and that it is all-important to ensure that the Republican doesn't win. What do you do? Your optimum strategy is to rank the Democrat _alone_ in 1st place. Now, if there are several Democrats, then you have a problem. You then have a dilemma that you wouldn't have in Approval, Score, or SITC. You must try to guess which Democrat(s) to top rank, but you know that one of them (you don't know which) could, by being top-ranked, change the win from a Democrat to a Republican. That's a dilemma that you wouldn't have in Approval, Score, or SITC. >The details have been debated in the EM list. But the specifics of the above-described situation haven't been discussed. u/a elections have been little discussed here, other than by me. Of course yes, unimproved Condorcet's FBC failure is well known and well-discussed at EM. > >> Sometimes you seem to say that you're just speaking in general, about >> most societies, or many societies. Sometimes, though, you make >> assertions about what won't happen here. > > I started with general claims but I commented also the U.S. related stuff > since that seems to be >on your agenda. That's right, you did. You sometimes do, but then, at other times, you insist that you're only speaking generally, about most societies, or about a matter of "maybe". >> 3. What is your best argument to support your belief that Dodgson, >> MinMax(margins) or Beatpath would do better at choosing the ideal >> sincere winner, if voting were sincere, than SITC would do? > > I don't claim that. I left the selection of the sincere winner criterion open. Of course that means that you can't use it. You can only speculate. Of course that's what you've been doing. You said: As already noted, methods that are strongly strategy defence related may not be exactly built to reflect targets that have been set for selecting the winner based on sincere votes. [endquote] You're repeating, again, something that I've answered--the first time you said it, and also in each repetition. Choosing well under sincere voting, and not causing favorite-burial incentive aren't mutually incompatible, because they both result from respecting the voters' preferences, intent and wishes. Aside from that, I don't know if you're aware that you're talking pure speculation, about how (you believe) maybe there could be a problem, unspecified by you. > >> 4. Tell the requirements that describe the ideal sincere winner. > > I repeat, I left the selection of the sincere winner criterion flexible and > open. Thereby, you left yourself with only some pure speculation. > I presented one >example definition that could be used somewhere. I answered about Dodgson and MinMax(margins). > > If you want some more generic comments, I might say that a good ideal sincere > winner definition >is supposed to tell what kind of properties the society > wants the winner to have. It does not care >about strategic vulnerabilities > and does not defend against them. Is that right. Funny, but this society's mass media regularly claim that favorite-burial strategy is needed "So that you won't waste your vote, you must vote pragmatically." Nearly all of the voters obey those instructions. Oh, but that's right: You were only referring to most societies, or many societies. I guess you're talking about how a society _should_ be. This "ideal single-winner definition"--where would it be useful? La La Land? You said "supposed to". Supposed by whom? You? You're vaguely referring to some supposed ideal or standard, without saying whose ideal or standard you think it is. You said: You could want the winner to be a person that is accepted by all, supported by majority, one that has strong support of some major party, one that has wide geographical support, support in all age groups, one that is not hated by any state, or whatever that makes the winner good. Once you know what you want, you can pick a practical election method that elects such a candidate (or is close enough), maybe tries to defend against strategies, is simple enough to use etc. [endquote] Or you could just seek to carry out what the voters themselves choose, instead of your antidemocratic, autocratic Soviet-like social-engineering goals. While you're at it, it would be nice if the voting system doesn't discourage sincere voting, at least not to an easily-avoidable reasonable degree (No favorite-burial incentive. If it's a rank method, no chicken dilemma). >> Certainly SITC is a different method from Dodgson or MinMax(margins). >> It wasn't clear that that's what you meant. But, if that's what you >> meant, then you're right about that. >> >> So what? > > That was part of my basic claim that best winner criteria and methods that > aim at being strategy >proof are different. Your completely unsupported claim about that. You said: You seem to be close to saying that SITC is not only a relatively strategy resistant method but also (close to) your definition of an ideal winner with sincere votes. [endquote] I said that the CW is a widely-accepted notion of the ideal sincere winner. But change that to legitimately-defined CW. But the more your voting system forces drastic departure from sincere voting, the less sincere voting you're going to get. > >> You mean the status against opposition in office of the candidate >> whose largest margin against him, in favor of another candidate, is >> the least. And being the most favorite, having the largest faction, >> doesn't confer any status against opposition in office? :-) > > Yes, the "least additional support/votes required" criterion (as a definition > of good sincere winner) >points in that direction. You're telling us your own personal opinion about what would (maybe) be the ideal sincere winner (in the event of a circular tie). You keep saying it, but that isn't the same as supporting it. I'm not going to keep on repeating my answers to that. I refer you to my previous replies, where I've answered that statement of yours many times--each time, in various ways. You said: I don't know what "most favorite" and "largest faction" exactly mean [endquote] That's funny, because I just finished defining them, in the post to which you're replying. "Most favorite" was a brief wording for "Voted in 1st place by the most people". First place is the most favored place. So I was referring to the candidate most favored with 1st place ranking. The "largest faction"? Maybe I'd better define two words for you: "Faction" and "Largest". A "faction" refers to a set of people (voters in these discussions) who share some preferences or wishes, and co-operate toward achieving what they want. In voting system discussion, we're referring to a faction of voters who have sufficient preferences or goals in common that they support and vote for the same candidate as favorite, or at least for many of the same set of candidates. In particular, in the examples that I've been posting, I made it clear that the A faction prefers candidate A as 1st choice, and that the B faction prefers candidate B as 1st choice, and that the C faction prefers candidate C as 1st choice. That defines the factions, in that usage. Factions defined by whom they most want to elect. "Large". The large-ness of a faction refers to the number of voters in that faction. No, contrary to what you thought, it has nothing to do with the body-size of the individual persons. The "-est" in "Largest": That means "more large than the others." Let me know if you still don't understand what a faction is, or what "largest faction" means. At least I should give you credit for making a statement that isn't a repetition. But you should have checked a dictionary. About the repetition: I'm not going to keep on answering statements that you keep repeating. I've done that enough. More than enough. >1, but I think they are not addressed by the "least additional support/votes >required" criterion. ...required to make the candidate CW. That isn't a criterion. It's the definition of Dodgson. You may personally like Dodgson (though like to mistakenly call it "MinMax(margins)), but merely stating its definition doesn't establish it as the standard by which to evaluate method when there's a natural circular tie under sincere voting. You're only expressing an opinion. You're welcome to your opinion. You haven't told why anyone else should agree. Why should the candidate who could most easily be made into CW by adding (or subtracting, or disregarding, or reversing) the fewest pairwise votes be the ideal sincere winner in a natural circular tie? Because you think so? That isn't enough. When you rank someone in 1st place, or when you rank a set of candidates in 1st place, it's because you want to help them win instead of the ones you didn't rank in 1st place. The candidate who has been so voted by the most people has strong claim to be the rightful winner when there is no one unbeaten, or no one uniquely unbeaten. No, I'm not advocating Plurality--largely because of its strategy problems. But as a Condorcet completion, the favoriteness standard (a short name for what I described in the paragraph before this one) doesn't bring Plurality's problems, and has a valid claim to rightness. Certainly such a candidate, after being elected, has undeniable strong authority against opposition in office But I've said that before too. I'll repeat that I'm not going to keep repeating the answers to your repeated remarks. You said: It is characteristic to Condorcet methods (like Minmax(margins)) that they can sometimes elect compromise candidates that have limited first preference support. [endquote] Don't worry about that. That's for the voters to choose, for themselves. If you don't like a compromise, then I advise you not to support him, even as a compromise. You don't like the alternative? Well, you do have a problem, don't you. But don't blame it on the voting system. There are a number of justifications for electing CWs. They tend to have good social utility. They're the candidate who would be elected in repeated elections, eventually arrived at, when everyone find out eachother's preferences. They're, therefore, the natural strategic choice. Oops, there's that word that you don't like. I only advocate SITC for informational polling. I don't recommend anything other than Approval and Score for official public elections. But, if we had to have a rank method, SITC would be the best choice. If you want to propose some rank method, for any purpose, then I suggest that SITC would be better. I've amply told why. Mike Ossipoff ---- Election-Methods mailing list - see http://electorama.com/em for list info
