At 04:58 PM 8/20/2007, Peter Barath wrote: > >Sure. That's been proposed many times. However, > >it's not a very good method. First of all, it is > >blatantly obvious, if you care to look, that the > >Condorcet winner is sometimes *not* the best > >winner, by far. > >I guess this is an unjust blame because this thing >affect all voting methods.
No. It *particularly* affects ranked methods, because ranked methods obscure preference strength. While there may be methods which promote the expression of absolute utilities in the votes (one possibility is mentioned below by Mr. Barath), if we set these aside, even Range methods may fail to accurately aggregate utilities because of normalization, resolution, or, yes, issues of strategy. Assuming that the Condorcet winner in an election is, unconditionally, the best winner, is blatantly an error, because it is easy to construct scenarios where reasonable people will agree that a different winner is better, and deliberative process would be almost certain to choose that winner. Election methods are shortcuts, which reduce what may be considered impossibly tedious or complex deliberative process to a matter of counting and analyzing ballots, but it is practically inherent that the shortcut introduces flaws; this does indeed affect Range as well as ranked methods. But not as badly, not *nearly* as badly. Most analysts here comment that, with "sincere voters," Range is the best method; they then, often, go on to claim that, however, because of the issue of strategic voting, Range is impractical or dangerous or whatever. Yet I have never seen a scenario which actually shows this, and, at the same time, shows votes that make any sense, that real voters would be at all likely to cast. The basis of the claim is often that voters will essentially disable themselves by voting weak votes against smart strategic voters who vote strong votes. However, if I vote a weak vote, it means that my preference is weak, and I have little ground to complain if, therefore, someone who expresses strong preference prevails. I allowed that by my vote. And, I claim, we should take the votes as writ. In any case, I find the question interesting, "What is the ideal method with sincere voters?" It is obvious that Condorcet methods *fail* rather badly with sincere voters, when they trip over the matter of preference strength. In a ranked method, where A>B>C is expressed, no information at all is provided about preference strength. If we assume that A>>B>>C is impossible, an assumption that Range generally makes (you only have one vote to express, so you cannot express full vote strength in the AB pair and at the same time full vote strength in the BC pair), we can look at the three rough possibilities: A>>B>C, A>B>C, A>B>>C, plus a ranked method that does not allow equal ranking may also have, as actual preferences of the voter, A=B>>C, and A>>B=C. (I'm neglecting the weak A=B>C and A>B=C; in the language of Range, I'm normalizing.) Those votes are really quite different in meaning and value. I may be able to discern a preference and therefore express it in a ranked method, but this preference may be insignificant compared to the preference I have for both these candidates as compared to all the others. Yet any ranked method will treat this maximally weak preference -- it may actually be no preference if the method forces ranking and does not allow equal ranking -- as quite the same as a life-or-death, full vote preference. Blatantly, this causes, under some conditions, poor results. The Condorcet Criterion sounds good, it would seem obvious that a proper election winner, if the election allows full ranking, should not lose the pairwise contest with any other candidate, i.e., if the election were immediately held, at the outset, only between these two, vote for one, we would think that the ideal winner would not lose. But that is only true if we neglect preference strength. In real elections, the effect I'm talking about is more rare than we might expect because if, in fact, voters have a weak preference, they might not even bother to vote, depending on who the frontrunners are. > Even in a two-candidate >contest where every considerable method becomes >Plurality, it's possible that the minority has >stronger preference, so the winner is not the >social optimum. In public elections under present conditions, absolutely, no method will choose the true SU winner unless somehow absolute utilities are expressed. It does happen, sometimes, and sometimes we forget that election methods are general and public elections are not the only application. Further, in some public elections, the context is *not* the highly competitive, polarized situation we commonly think of with regard to elections. Normalization with two candidates only obscures the preference strength, causing all preferences to become equal. However, it is a serious error to apply this fact to elections with more than two; as the number of candidates increases and the range of candidates becomes broader, normalization has less and less impact, and votes will tend more toward becoming a relatively accurate expression of utilities. Note that the common characterization of bullet voting as "strategic" and "not sincere" is, arguably, an error. Bullet voting in Range can be sincere; what is overlooked is that there is no defined sincere mapping of internal utilities to Range Votes. We use simulated internal utilities and map them to Range Votes with various assumptions, but it is not at all a clear matter to term a mapping of some finite preference to a vote equality as "insincere." We would never term, in plurality, a vote as "insincere" because it ranks more than one candidate bottom equal; in this case it would be forced by the method. But what if the method were Approval? Obviously, with Approval one must equal rank somewhere. In Range, though, I have defined "truncation" to refer to the process whereby an internal utility scale is mapped to the Range Vote scale such that some finite spread in the internal utilities, a subset of the full possible utilities, is mapped to the Range Votes, and some of the candidates are thus off-scale. Or even all of them are off-scale, and are thus rated either top or bottom. Even if there are preferences between them. Quite simply, there is no defined "sincere" rating for a candidate. We often talk about Range strategy, i.e., about methods of mapping utilities or expected satisfaction to Range Votes. Suppose a voter were to think of the absolute best possible candidate as 100%, I call this the Messiah vote. And the absolute worst, 0%, I call the Antichrist vote. (I use these terms not to propose some religious meaning, only as references to an extreme polarity. I once did this and someone objected that perhaps someone doesn't like the Messiah. That is a contradiction, because in this context, "Messiah" only means the absolute best possible candidate under any conditions.) In a sense, this scale is the same for all voters. I call it the "first normalization," though, because it is not really the same, we are assuming that all people have the same complete range of preference, or, more accurately, we want to treat their voting as if they do. These are still not absolute utilities, but we may choose to treat them as such. (And this is what the simulators do, they assume a commensurable internal scale. This is *not* the Range Votes, necessarily, but if voters simply vote these full-scale utilities, Range does the best possible job of maximizing overall voter satisfaction. it will choose the right pizza, if any method can.) Take those same utilities and use them to rank candidates, and you often get the same result, but also you can get a worse result. It happens. But we do not expect people to vote absolute utilities, and those are the ones that would be most deserving of the term "fully sincere votes." Obviously, in most elections, the range of candidates present in the election is not that full range, we do not have both the Messiah and the Antichrist running, except for a very small minority of mentally ill voters. (or that terminally rare election where they actually are running, which we will neglect. If that is the election, we have more to worry about than election methods!) If I vote these fully sincere utilities in a real election, then, I will be casting a weak vote. Indeed, if it were Range 100, I might be voting max 51 and min 49, casting, really, only 1/50th of a vote. Or something like that, maybe more, maybe less, but never the full Range. But if someone comes to me and says, we have these three choices, I *don't* think of the full range of possible candidates. Rather, first, and most easily, I rank them. And I can readily discern variations in preference strength. I can thus construct a set of ratings without even looking at the Antichrist and Messiah. I would choose my favorite and max rate. I would choose my least favorite and min rate. And the other, where would I put the other? It might seem that somewhere in the middle would be "sincere," unless I could discern no difference between the middle one and the ones at the ends. But consider this. I mentioned that someone came to me and asked me to choose among three. In most elections, the *real* choice is between two. So what do I do? I do just what was described above. I normalize to the set of *real* candidates. So I max rate the favored frontrunner and min rate the least-favored. And where the others go is, to me, fairly inconsequential *unless* my favorite is among the others. In any case, my vote would probably be to rate the others in the middle unless they were better than the max frontrunner or worse than the min frontrunner. Or equal to them. This is a different mapping, but really quite the same principle as the first mapping where the best of all candidates fixes the top end of the scale, and the worst fixes the bottom end. Instead of that mapping, the best frontrunner and worst frontrunner are used. All of these are sincere, in the ordinary meaning. Generally, equal ranking when there is some preference between the candidates is *not* insincere. I would not call it "fully sincere" either, since some preference strength is concealed in the process. In any case, I see utterly no harm in voters choosing how to vote. In Range, I would treat their votes as sincere expressions of their preferences. For example, there are three candidates. As to performance in office, a voter considers A to be the best, C to be the worst, and B is right in the middle. And then there is D, who is almost as good as A, in the view of the voter. The voter votes, in high-res Range, A and D max, B midrange, and C min. Is this a sincere vote? Well, trick question. The voter is D's mother. She is not going to vote against D, period. Indeed, this gives her a strong preference for D. Does this mean that her sincere vote would be D max and all the rest min? Maybe. It's up to the voter. We see scenarios where supposedly a voter has "sincere preferences" of A=B, nearly, but bullet votes for A (there are other candidates as well, of lower preference), and supposedly this is "strategic," which is a term which conceals the motive and true preferences. A voter votes "strategically" because the voter hopes to gain value by doing so. We *want* voters to use the system to maximize value! If the voter has sufficient preference for A to cause the voter to bullet vote for A, this is a contradiction with the assumption that the preference is weak. The voter wants the favorite to win! Range is not vulnerable to Favorite Betrayal, unless one makes the strange condition that the Favorite is betrayed by voting the Favorite equal with another. The application of the term "strategic voting," and the approbation that accompanies it, is problematic when applied to equal ranking or rating. More properly, and more offensive, is preference reversal, which Range never rewards. Essentially, there is no strategic voting pattern which is not a monotonic mapping of the internal utilities to the Range Vote, but it is possible that what I called the "magnification" is different for different parts of the scale. And it is possible that there is truncation, such that the extremes are collapsed, which is equivalent to a compressed expression of utilities. >(The only defense against this is the money voting, the >Clarke-tax, which is - I think - treated also a little >unjustly. At least the theoretical honor should be given >for showing the possibility of strategy-freeness. >And who knows, one day it can be proven even practical >in some circumstances.) This, of course, contradicts what was said at first, but no problem.... "Strategy-free" is, in my view, not a proper goal, unless it means that the method is free of incentive for preference reversal. That is laudable. Generally, Condorcet methods are not strategy-free by this definition, though certainly it is possible that strategic voting could be difficult to pull off. ---- Election-Methods mailing list - see http://electorama.com/em for list info
