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 likely, in the extremity which he shows, but .... you said "worst." Range and Approval are criticized for failing MF when, in fact, they do so to choose a more broadly acceptable winner. That is hardly a bad outcome..... IRV can choose, fairly easily, a winner who is strongly *disliked* by a majority, if I'm correct. (Warren's example is extreme in this, but there are much more likely outcomes; it is basically the well-known center squeeze effect.) > > 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. > >In simulations it seems to be quite a good guess, assuming sincerity. Sure. Particularly when you have many candidates, Condorcet converges on Range in some ways. What happens, I think, is that preference strength becomes more uniform. Range can handle preference strength in a three-candidate election, Condorcet can't, generally. But with a lot of candidates spread across the spectrum, Condorcet effectively *does* consider preference strength, so it is not surprising that it does well. Condorcet is the king of *preference* election criteria. To do better, one must start considering preference strength, which is what Range does. >Also, I can substitute "EUC" for "Condorcet" in that paragraph and >really have the same criticism. No. EUC is *about outcome* and Condorcet is about process. (More accurately, of course, EUC is about "expected* outcome, expected outcomes are summed in Range, across the electorate, providing a measure of total satisfaction. Condorcet doesn't attempt to do this, rather it does something else that we intuit will do it. We intuit that the winner of every pairwise election will satisfy the most people. But, unfortunately, this can be far from true. Range, instead, asks people *how much* they will be satisfied by each possible outcome. It is thus approaching, as closely as possible, the goal of elections. The real question, to me, is not whether or not Range is superior with sincere votes, it obviously is, but what happens when voters, for whatever reason, are *not* sincere. It is quite a different question than "what is the best election method," for the answer to that latter question may depend greatly upon context. If we have a collection of people who value social unity, we wouldn't even consider Condorcet if we know about Range. People who are polarized, who only think about their faction winning, this is more difficult. Warren's work appears to indicate that Range is still as good or better than Condorcet methods. It would certainly be useful if others would confirm this result, or show that it is defective.) > > > > 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.) > >Well, you're replying to yourself here. I didn't say this. Right. But the question does stand. Is MF unlikely to choose a truly bad candidate. *Normally*, no. But under conditions of polarization, critical conditions, it can. That's the point. MF works well *most* of the time. Just not when something better is needed! >I just want to know that you're positing sincerity when you say that >methods which specifically optimize utility fail MF. Yes. Of course. That is, all voters can vote sincerely, utility can be optimized *as they define utility*, and the method will fail MF, and might do so fairly often. In fact, it's possible, I haven't looked at this in detail, that *nearly always* MF is not the socially optimum result, when the election is about something important and controversial. MF is brilliant when the decision is very small and uncomplicated. It is very good when the decision is Yes/No *and* there has been thorough and fair debate, when voters are informed. >But when you posit sincerity it isn't clear that this is an interesting >point. It is hard for me to take this as an argument that MF is not >desirable for real elections. I'm saying that a good election method should work with sincere voters!!! It should *also* work with some segment of voters which aren't sincere, and it should not truly *punish* sincere voters. What this means for me is that a good election method *must* fail MF, at least in the simple-minded definition of MF that can be used for one-step elections. If the majority has an opportunity to change its preference based on accurate information about the state of the whole electorate, that's another matter. If that opportunity is provided, MF can be satisfied *and* SU can be maximized, and I give MF priority *under these conditions.* Why? Precisely because of the measurement problem. If the measure of SU is defective, for some reason, who is to determine that? Essentially, I've been led inexorably to the conclusion that the majority has the right of decision, but that it better make sure it knows what it is doing, because the majority unnecessarily imposing its choice on a minority can be quite destructive of social unity and welfare. You win the election and then your family is wiped out in the civil war that results. Some victory! So a good method will, among other things, function to inform the electorate. Range really provides the necessary information, alone among all the methods. The question of how to analyze that information remains. And the majority has the right to say, "this process didn't work, I smell a rat." No." >[...] > > Yes. However, that is post-facto information. How would I know that I > > will seriously disappoint half of society? *The poll is the > > information.* I have argued again and again that single-step election > > methods are doomed to be inferior to more complex, essentially > > deliberative, process. > >Well, I would argue that public elections actually are multi-step and >complex. Since in public elections there should already have been >polls. > >I believe in this scenario I really would be likely to know that almost >half of the voters will be seriously disappointed by A. Sure. And what we have works as well as it does because this works, *to a degree.* It's context, and, obviously, context can determine how an election method functions. What is good for one context might not be so for another. The multistep process we have in the U.S. for many elections, i.e., party primaries followed by a general election, unfortunately, tends to produce polarization. Of course, the whole U.S. legal system is based on polarization, on contests. Attorneys duke it out before a judge or jury. Problem is, the truth can get lost in the process, the results can depend on the skill of the attorneys or the funds available to each side. If one outcome is profitable for one party, and the other outcome has no single big winner, merely general public benefit, public benefit can get short shrift. Make no mistake about it, election methods are the tip of the iceberg. The real issue is how society is organized, how collections of human beings make decisions about how to communicate and cooperate. > > Here is a way in which a Range method satisfies the Majority > > Criterion: A Range poll is taken and the winner is presented for a > > second vote to the electorate, "Shall the Range Winner be elected?" > > > > If the majority votes Yes, we have, with the overall method, > > satisfied the Majority Criterion. > >What happens if the majority votes No? If it's "elect the range winner >or have a new election" I wouldn't say that satisfies MF. Not quite. In the case mentioned, the electorate has explicitly rejected a candidate. It doesn't matter why. That candidate should be ineligible. The exact ensuring process doesn't have to be stated for our purposes here. It could be to present the next winner in sequence, or to present the Condorcet winner (not so good, in my opinion), or, best, a new Range election, same rules, but without the previous Range winner. When the majority says No, it should mean No. And this method satisfies the *goal* of the Majority Criterion because the Majority has explicitly elected the winner by voting Yes. The Majority, in that case, prefers that winner over the alternative (i.e., someone else). If the method failed because of strategic voting, the majority can simply toss that result out. Unless the results were very close, or, unless there was serious distortion for some reason, such as some kind of last-minute campaigning that was drastically unfair, I think that it would be quite unusual for the Range winner to be dumped. But possible. > > We could also do the same thing by presenting the Range Winner > > together with the best winner by any other method, in which case, the > > question would be a runoff between two candidates. > >I think Range winner vs. MF runoff would at least not fail MF in a >meaningful way. Sure. In this case, the majority would have the explicit opportunity to choose its favorite, and would only choose the Range winner if it decides that this will be better for society. Which is *true* preference, informed preference. The question is whether or not preserving the MF in this way is worth the cost. It's not clear to me. If people are worried about Range failing due to strategic voting, the runoff, where the MF and Range winners differ -- which won't happen very often, I'd predict -- then the MF/Range runoff would make sense. Range fanatics -- we have a few -- might disagree with me. They would claim that the Range winner is the best, period. But they depend too much, I'd say, on perfection of the method, and don't trust the majority sufficiently. Besides, the *real* problem is how the majority becomes an informed majority. We don't have to inform everyone, indeed if only a relatively small number of voters -- well short of a majority -- become well-informed, it would be enough. How can groups of people become informed, which reduces to, how can truth be found amidst the chaff and deliberate deception that is raised up, how can we find information that we can trust? Even more important, how can we find *analysis* that we can trust, because information is not enough if it is buried in the mountain of facts (and lies) that come before us every day? I probably wouldn't raise the question here if I didn't think I had an answer, but what I find really odd is that fundamental questions like this receive so little attention.... ---- election-methods mailing list - see http://electorama.com/em for list info