At 07:01 PM 8/19/2007, Peter Barath wrote: >Which means that the concept of "two candidates with the best chances" >depends not solely on the candidates themselves but theoretically >possibly on the voting method too!
Yes. Of course. But I don't think that voting method results in a different estimation of who is in the top two or three, which is all that is relevant in nearly all real-world situations. Let's leave out the California gubernatorial recall.... >In your example with 47 percent firm Bush supporters the voters >were very wrong in supposing that he is a harmless candidate. >In reality, in this case the strategic votes would be identical >to the honest ones. > >However, I think your example did point to a widely ignored fact: >that the ugly dilemma of the Plurality vote: "how will other >voters vote?" does exist in Approval, even if it's smaller It's not widely ignored. The question of how to vote in Approval is certainly not as simple as "Which candidates do you approve of?" However, it is quite a reasonable way to vote in Approval to, quite simply, answer the question sincerely, for yourself, and vote for those candidates. It is not necessarily strategically optimal. But what is the penalty for failure? One suboptimal vote is not much to worry about! >So it's plausible to mix Approval. Absolutely, this does not follow from what was stated. For one thing, "Approval" is absolutely the simplest, cheapest reform on the table. Simply Count all the Votes. Few among us consider Approval the best method, though there are, in fact, some experts who do. It's a respectable position. However, there is no doubt but that Count All the Votes -- the name "Approval" greatly confuses the issue -- is a vast improvement for no cost. Sure, when you have a third party candidate who approaches parity with the big two, i.e., there are more than two frontrunners, strategic issues arise again. However, they do not bite as badly. And they bite even less in Range. The choice becomes more difficult in Approval merely because the method is so black and white, so ... binary. > My favourite (at this moment) >is a preference ranking with an approval cutoff. For me it's >interesting enough that it can be used in two ways: Well, I've been suggesting the reverse: Approval with preference indication. >1. If there is a Condorcet-winner she/he/it wins. If there is > not, the Approval winner wins. 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. Secondly, if you *do* think that the Condorcet winner is the best, if one exists, one would think that, if there is a cycle, that the winner should come from a candidate who is a member of the cycle, and not be an Approval winner, who would have been beaten by any member of the cycle. So if you really want to go this way, you use approval level to determine which member of the cycle wins. And I don't know what this is called, but it is certainly a known method. However, consider the reverse, and, while we are at it, we might as well use a Range ballot. Range ballots need be no more complicated than ranked ballots, but they provide more information. You can do preference analysis on Range ballots, but not range analysis on Ranked ballots. It is already established practice in many places, when there is no majority preference shown in the election, to hold a runoff. What is generally done is that the runoff is between the top two. And, of course, this is just like IRV, except better. And more of a nuisance, hence the idea of combining the runoff with the first election.... But my point, really, is that certain conditions trigger a runoff. Now, Range is the only method on the table that considers true preference strength. Some Condorcet methods use a presumed measure of preference strength, but there is no reliability to it at all. In any case, in simulations, Range outperforms nearly all other methods in optimizing overall voter satisfaction with the result; it essentially does this by using *expressed* expected satisfaction! Some claim that this makes it vulnerable to "strategic voting," but the term is actually misapplied to Range, in part because there is no fixed algorithm for converting sincere preferences and internal absolute utilities to specific Range votes. Essentially, what I've come to, is a Range vote is a *vote*, i.e., an action, not a sentiment. And the simulations show that even if voters "strategize" to their heart's content, Range still outperforms other methods. *On average*. You can always come up with specific scenarios that will make it appear otherwise, but what I find fascinating is that, so far, all such scenarios I have seen depend on contradictory assumptions. A voter has a weak preference, i.e., does not care much which of two candidates wins, but votes a strong preference, supposedly to make his favorite win. I.e., votes as if he cares. Why would he do that if he does not care? He *does* care, he wants his favorite to win! There is absolutely nothing wrong with that. What I would like to see, in Range, is that voters vote to optimize their own expectations. If that means voting Approval style, fine! However, from what I've seen in my own limited work, it appears that the presence of even a few voters casting intermediate votes improves the expected outcome for *everyone*. Now, Range Voting does *not* always fully optimize overall satisfaction, for various reasons. It is *not* perfect, for a number of reasons. For one thing, there is no reasonable way for voters to vote absolute utilities. (Someone might prove me wrong, someday; for example, if voters' votes are bids, where they have to pay if they get what they want, we might assume that the votes will be reasonably accurate ... this would, in fact, be tax reform as well as election reform; I'm certainly not taking on this project at this time!) Instead, what we expect most voters to vote is normalized utilities, normalized to the candidate set. This distorts absolute satisfaction, equating what might be a weak preference range for one voter with what might be a strong preference range for another. In any case, one of the situations that can happen with Range is that the preference of a majority fails to win. This is sometimes used as an argument against Range, but it is actually a strength, that such a situation is possible, because once you look at preference strength and its implications, it is obvious that an ideal method would not satisfy the Majority Criterion. However, there is one aspect to the MC which is very important: it resembles the principle of majority rule. It is *not* majority rule, because, quite simply, the majority may sometimes decide -- by majority vote -- to choose other than its own first preference. However, a single-stage election method, where the information is gathered that might lead a majority to make a choice like that, cannot clearly allow this. Technically, a majority could, on the ballot, consent to the winner being the Range winner, but that is an a priori consent, which is problematic. "But I didn't realize that it would be ...." It is not full, clear consent, and the consent of a majority is a basic principle of democracy. Hence my proposals: first of all, a range ballot. We really should start using range ballots, even if we only analyze them, to determine winners, as ranked ballots. I.e., take a set of ranks and allow overvoting at any rank, and undervoting in others. Even if the election is, say, a Condorcet method, it them becomes possible, particularly if the voters understand what is going on, to analyze them to study the effect of Range. But as an actual method, use such a ballot, determine the Range winner, and then consider if any candidates beat the Range winner in preference analysis. If so, hold a runoff. In most cases, the Range winner will be unbeaten, but it is the exceptions that are interesting. (Range, like Approval, usually finds the Condorcet winner if there is one). If the Range winner is beaten, it would be rare that there are two who so beat the Range winner, so I'm not going to, at the moment, go into how to resolve this, whom to include in the runoff. But I do not consider it a difficult problem, and it has very little effect on strategic considerations, because we can expect it to be a very rare consequence. Suddenly, we have Range being MC compliant, as to the overall method! And it really is only an application of existing practice, modified to meet the somewhat new circumstance of something other than top-two plurality. >2. Calculate the two candidates with the most Approval points > and the pairwise winner of them wins. > >Peter Barath > >____________________________________________________________________ >Tavaszig, most minden féláron! ADSL Internet már 1 745 Ft/hó -tól. >Keresse ajánlatunkat a http://www.freestart.hu oldalon! >---- >Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
