Re: [EM] RE : Re: A few concluding points about SFC, CC, method choice, etc.
At 10:52 AM 2/19/2007, Kevin Venzke wrote: >--- Abd ul-Rahman Lomax <[EMAIL PROTECTED]> a écrit : > > Election criteria sometimes presume omniscience. For example, the > > Majority Criterion is based upon voter preferences that may not be > > expressed, or even expressable, in the votes. "Prefer," as it was > > clearly interpreted here, refers to a mental state of the voter. > >Well, I wouldn't define MF that way. But I can go with this. We can >say that MF says that if there is a majority favorite on sincere >preferences, and voting is sincere, the MF wins. If you use actual votes rather than unexpressed but sincere preferences, then Approval satisfies Majority Favorite. But when I pointed that out here, I was told, quite clearly and with nobody chiming in with support for my position, that the Majority Criterion -- which I think is the same as MF -- was about sincere preferences, not about actual votes. And even though the Majority, under Approval, has a means of expressing "strict preference," which is to bullet vote. Because they might elect to not do this, for whatever reason, it is alleged that Approval fails the MC. If we *don't* allow the concept of "sincere" preference, but only expressed preference, then Approval fails MC in a manner that it obviously *should* fail it, that is, the failure is purely technical, since it would be failing to elect the preference of majority because a *larger* majority preferred another. >[...] And we know, without doubt, that the > > Expected Utility Criterion and the Majority Criterion are not > > mutually compatible. > >Presumably the EUC would also have to require sincerity in the votes. >Yes, I agree that EUC and MF aren't compatible given this. Right. Now, EUC is an actual measure of election success, whereas MF is what I'd call a secondary measure. It is a criterion which *seems* rational if one neglects preference strength, and many would neglect it on first thought. In the pizza examples I've given, the pizza election is an unqualified success if everyone is happy with the outcome, and it is a partial success if as many as possible are happy. "Unqualified success" is often *only* possible if the MF is violated. But the *real* criterion behind MF, the totally legitimate one, is majority rule. That is, the majority has the right of decision. As parliamentarians know, this right is best and most clearly expressed when it is made through a Yes/No decision that has been the subject of full process in the determination of what question is to be asked; at every step along the way, the majority has the right of decision. The problem with election methods in general is that they attempt to short-circuit this process. So, for me, the question of election methods reduces to the question to how to *best* short-circuit it, to obtain a result that is the mostly likely result that would be obtained through standard deliberative process, but without the time and effort involved. Part of the deliberative process is a consideration of the impact of the decision on minorities. If a majority simply steam-rollers a decision through based on its undenied majority power, it can make *very* bad decisions, decisions that polarize society and make friends into enemies. Decisions that cause civil wars or insurgencies. Decisions that make societies dysfunctional in many ways, as people increasingly consider government to be "them" rather than "us." MF in an election method is that steamroller. It's fast, it's easy to understand. And it can flatten far too many people. *Usually* MF will pick the best winner. That's why democracies using it have been as successful as they have. But if you look at the rough edges, the places where democracies *aren't* working well, you might see what I've seen: MF is part of the problem. It only has to make a bad decision occasionally to have this effect, for these decisions accumulate over the years. Range or Approval won't suddenly cause elections to violate MF, the vast majority of Range and Approval elections are likely to satisfy it. My point is that there Range and Approval *don't* satisfy it, they do so to find a better winner. So MF is in indirect measure of election success, not a direct one. And most election criteria are like this, except this SUC which was have not precisely defined, but which we can understand clearly in at least some situations, enough to know that MF should be sometimes violated. >I do think it is interesting to consider whether a method fails >"gracefully." The worst result under Condorcet methods is probably >worse than the worst result under IRV. You have to ask also how much >to worry about this relative to other concerns. It's a real concern. If we want to talk about "worst" case, IRV can fail spectacularly because of its peculiar method, Warren has posted an example that shows a seriously terrible outcome. Obviously, not very like
Re: [EM] RE : Re: A few concluding points about SFC, CC, method choice, etc.
On Mon, 19 Feb 2007 16:52:08 +0100 (CET) Kevin Venzke wrote: > Hi, > > --- Abd ul-Rahman Lomax <[EMAIL PROTECTED]> a écrit : > >>At 06:15 PM 2/16/2007, Kevin Venzke wrote: ... > Nope. But you see that your criticism of Condorcet also applies to EUC. > > >>If voters don't vote strategically, then it can fail to find the >>utility winner. Garbage in, garbage out. >> >>But the real practical question is whether or not it fails >>gracefully. And it appears that it does. >> > > I do think it is interesting to consider whether a method fails > "gracefully." The worst result under Condorcet methods is probably > worse than the worst result under IRV. You have to ask also how much > to worry about this relative to other concerns. > A handy IRV demo that I included in email this AM showed that with 3 candidates and 35A obviously deserving to lose to 65B, IRV happily awarded the win to A. What can you trick Condorcet into that is nearly this bad? When it gets this bad even voters might notice! ... -- [EMAIL PROTECTED]people.clarityconnect.com/webpages3/davek Dave Ketchum 108 Halstead Ave, Owego, NY 13827-1708 607-687-5026 Do to no one what you would not want done to you. If you want peace, work for justice. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] RE : Re: A few concluding points about SFC, CC, method choice, etc.
At 06:15 PM 2/16/2007, Kevin Venzke wrote: >Hm? "Maximum utility" meaning "matches the SU winner perfectly" or >"matches the SU winner the best among methods that actually exist"? > >In the former case it's not clear this method actually exists. In the >latter case I'd guess that you shouldn't guarantee this. Election criteria sometimes presume omniscience. For example, the Majority Criterion is based upon voter preferences that may not be expressed, or even expressable, in the votes. "Prefer," as it was clearly interpreted here, refers to a mental state of the voter. So we can state that if a method elects the candidate who maximizes voter expected utility, summed across the electorate, it satisfies the Expected Utility Criterion. And we know, without doubt, that the Expected Utility Criterion and the Majority Criterion are not mutually compatible. What we are limited to, however, is what voters actually express. Condorcet methods purport to elect the pairwise preference winner. But if voters vote "strategically," that is, they don't express their actual preferences, the method can fail to select the actual preference winner. Range, of sufficient resolution, *is* precisely a method which explicitly selects the utility winner, if voters vote sincere utilities. So Range satisfies the EUC. Got any other methods which do this? If voters don't vote strategically, then it can fail to find the utility winner. Garbage in, garbage out. But the real practical question is whether or not it fails gracefully. And it appears that it does. (There are other limitations. Range, for example, equates all voters. This assumption certainly causes a mismatch between results and true utility, but the assumption appears necessary in a democracy.) > > Yes, the statement is true, but it is completely off the point. We > > are not comparing "arbitrary methods." > >It's not off the point. It's a response to this comment of yours: > >"Too often, when we consider methods by election criteria, we assume that >a criterion is desirable, entirely apart from whether or not it chooses >the optimum winner." > >This makes it sound like you don't understand why criteria are used or >think that they are inherently at odds with SU. That's why I replied in >the way I did. It makes it sound like that because, which I wouldn't say "inherently at odds with SU," I *would* say that Election Criteria, most of them, are indirect. That is, we presume that it benefits society for the Majority Criterion to be followed. But, in fact, this may not be the case. More accurately, it is true only under certain conditions. It's indirect. Instead of saying that we want a red shirt, we say that we want a shirt that gets a bull excited. That might get us a red shirt, but it might not. For me, the only question about SU is the best way to measure it. The Condorcet Criterion has *nothing* to do with measuring SU. It's just a guess at a beneficial method, an intuititively satisfying one that turns out to miss something extremely important. > > It is obvious that MF has a utility. It is unlikely to choose a truly > > bad candidate. It can and has, so I don't know about "unlikely." Think Ruanda. (Now, I don't know the full details of the election involved, but it was won by the leader of the majority Hutu tribe. I'm guessing that he was a majority victor.) > But methods which specifically optimize utility are > > going to fail MF. That's the point. > >As far as I'm aware, there is no way at this point to conclude that there >is a method failing MF that optimizes utility better than every method >that satisfies MF. Or vice versa for that matter. >If you want to posit sincerity, though, then never mind this comment. There is no real alternative to positing sincerity. *No* method can guarantee good results if the voters don't disclose their opinions! Yes, it's possible to facilitate this. What is completely obvious to me, though, is that ballots which only collect preference information are inadequate, because preference strength is essential information for the maximization of utility. Many elections, to be sure, will have a range of candidates such that preference strength is not important. And this is the reason why Plurality works as well as it has, and why Condorcet methods would work as well as we can expect. > > I've argued that the majority has the right of decision. In this > > example, if the majority wants to ensure the election of A so much > > that it is willing to damage society, overall, it may do so. It > > simply votes B at a lower rating, sufficiently low that B loses. But, > > and I've given this argument again and again, this willingness > > conflicts with an assumption: that the majority values B at 80. > > > > No, if they are willing to lower B's rating to very low, which is > > what it would take, it is necessarily true that they place a higher > > relative value on the election of A than th
Re: [EM] RE : Re: A few concluding points about SFC, CC, method choice, etc.
On Feb 15, 2007, at 23:29 , Kevin Venzke wrote: > --- Abd ul-Rahman Lomax <[EMAIL PROTECTED]> a écrit : >> Thus, we conclude, the Condorcet Criterion *must* be violated in some >> elections by an optimal method, and thus this theoretical optimum >> method must fail the criterion and others similar to it, such as the >> Majority Criterion and SFC. > > I agree with this, although I don't think this theoretical optimum > method exists. If it does exist I suppose it's pretty complicated. I'm not ambitious enough to try to define a method that would give optimum results in all cases. Even proving this for one case is too difficult. I however think that it is a good practice to choose one utility function that the society agrees to approximate the real world needs accurately enough. There need not be one such function. Different targets may apply in different situations (one could seek best median utility or minimize worst utility to one individual, width of opposition, take into account strength of opposing opinions, strong first preference support to the winner etc.). And sometimes one the society may be satisfied with some other than the theoretically best utility function to make the system better in some other aspects (e.g. simplicity, strategy resistance). >> Too often, when we consider methods by >> election criteria, we assume that a criterion is desirable, entirely >> apart from whether or not it chooses the optimum winner. > > I would guess that most of our criteria *do* coincide with higher > utility. All things being equal you couldn't expect that a method that > fails majority favorite would produce higher utility. > > There are other issues besides utility of course... There's the > question > of what the public will accept and understand how to use, and there's > all the questions of how to give the voter incentive to vote > sincerely. Yes, all such criteria need to be considered. Abd ul-Rahman Lomax mentioned that also the majority rule could be violated. I agree that with some excellent utility functions that gives the best overall utility (e.g. Range style). One reason why the majority rule is popular is that it is hard to develop voting methods that would not respect it and still be strategy resistant. Or maybe majority rule is in some cases in line with the targeted utility function (e.g. to avoid a mutiny of the majority). (There are also other reasons, like simply the tradition.) One reason why I think it would be good to always mention the target utility function is that then it is easier to compare the impact of the strategy resistance related modifications to some voting method against the basic utility function. It is typical that when strong anti-strategy measures are applied they make the achieved utility a bit worse. These two aspects, strategy resistance and good performance with sincere votes, need to be balanced. (I have often used the example of winning votes and ballots 49:A, 49:BC, 1:CA.) Juho Laatu ___ To help you stay safe and secure online, we've developed the all new Yahoo! Security Centre. http://uk.security.yahoo.com election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] RE : Re: A few concluding points about SFC, CC, method choice, etc.
At 04:29 PM 2/15/2007, Kevin Venzke wrote: >I would guess that most of our criteria *do* coincide with higher >utility. All things being equal you couldn't expect that a method that >fails majority favorite would produce higher utility. I'm not sure what "all things being equal" means, particularly because Majority Favorite is clearly suboptimal in some not-too-uncommon scenarios, generally involving the majority having a small preference for a candidate, with the minority having a large preference *against* that candidate. A Shi'a voter might not have a strong preference between two Shi'a candidates, one of them being the majority favorite. But a Sunni voter might have very strong feelings between them if one of them is clearly more fair toward the minority Sunnis. (As an aside, considering the Shi'a the majority is almost an oxymoron. Practically by definition, Sunni means "majority," but, of course, it is a majority in the whole Muslim world (a strong one), just not in Iraq.) Range will uncover this, and select based on overall utility, if voters vote sincerely. If they don't vote sincerely, results will vary, but they won't be *worse* than Majority Favorite. The Majority cannot fail to elect its Favorite unless it allows another candidate some vote strength. If the Majority *strictly* prefers its Favorite, it will prevail in Approval. By "strict" I mean that it does not allow the expression of parity with another candidate. That is, a majority bullet-votes for its favorite. Only if some segment of that majority also approves another candidate can another win. Of course, with Approval, there is no way to determine from the votes if there was a violation of Majority Favorite; indeed, it seems more likely, in general, that the Approval winner *would* generally be the Majority Favorite. >There are other issues besides utility of course... There's the question >of what the public will accept and understand how to use, and there's >all the questions of how to give the voter incentive to vote sincerely. It appears from Warren's research, however limited it was, that voters are quite likely to vote sincerely unless you give them a good reason not to. > > It's > > *assumed*, very easily, that the majority choice is the optimum > > winner -- and therefore it is desirable to satisfy the Majority > > Criterion -- when this is certainly not clear enough to be reasonably > > an axiom. > >I think it's actually clear that the majority favorite isn't necessarily >the SU winner. I don't think it follows from this that it isn't desirable >to satisfy MF. It depends on what alternatives you have. The MF winner can be a disaster, compared to a Range winner, in some scenarios not too far from recent history. I don't see the reverse being likely at all. That is, Range is only likely to elect other than the MF when there is a *better* candidate. (Unless you use the weird Rube Goldberg "quorum rule" that has been tacked onto Range in an attempt to implement a goal which seems noble in itself, that of making it easy to abstain from rating a candidate without hurting the candidate. But that goal is itself questionable, and introduces an entirely new kind of reform, and one which could cause a failure of a Range election, though the conditions are unclear to me. Has this contraption been tested?) > > Any person or business which makes decisions failing to > > consider the strength of preferences will soon run into trouble > >An individual person has a great advantage in measuring preference >strengths. Certainly. However, businesses also need to make decisions based on input from many people. Range Voting is not uncommon in those situations. (Consider how many polls you've participated in where you were asked to rate something on a scale of 1 - 10.) election-methods mailing list - see http://electorama.com/em for list info
