At 01:29 PM 8/16/2007, Diego Renato wrote: We should resist TACTICAL bullet voting for the same reason that many other methods than plurality. Increase the overall satisfaction of the voters.
It's an error. The one most harmed by "tactical" bullet-voting is the voter who votes that way. Some analysts are confused by the fact that it can look like tactical voting is advantageous. However, what it boils down to is like this: You are the last voter. By some process, you know how everyone else voted. There is a tie between two candidates. You approve of both of them. How should you vote? Well, you have a choice. You can vote for both, and thus let, usually, chance determine between them, or you can vote for your favorite. The choice is yours. And, indeed, this is the situation with voting, properly: the choice is yours, as a voter. If a so-called "tactical voter" supposedly approves of two candidates, but only votes for one, we must look at why. Let me suggest why: the voter has a preference, and the preference is strong enough to motivate the voter to bullet-vote. There is a contradiction in the assumptions: weak preference is assumed if we think the voter approves of two, and strong preference in the action of voting. The voter has a reason for voting that way! He wants his favorite to win! And there is *nothing* wrong with this. We suggest that the proper way for each voter to vote is to increase his or her own satisfaction. And then we try to use methods that take this information, and use it to find the winner who will satisfy the most. If the voter conceals relevant satisfaction information, then the method will not know how to satisfy this voter! And it may err, with regard to this one, and thus to the overall satisfaction. We must note, that if this "strategic voter" prevails, and the candidate wins, that candidate must have been also approved by others. We may argue that if the voter had also voted for another candidate, that the winner might have changed, and this might have resulted in more people being satisfied. But it is just as likely, unless the voter has the kind of knowledge described above, that the voter who bullet votes ends up with a candidate that the voter is not satisfied with. When I studied the specific outcomes in a Range 2 election (ratings of 0, 1, 2), what I saw with bullet voting as distinct from so-called sincere voting was the same expected outcome, *but* greater variability. That is, sometimes bullet-voting caused the favorite to win, a desirable outcome for the voter, but sometimes it caused the least-favored to win, because the voter did not also approve of the middle candidate. As I recall, there was one scenario (the study looks at all possible pre-vote scenarios where the voter's vote can affect the outcome) out of 27 where a sincere vote resulted in a worse outcome than bullet voting, and one where it resulted in a better outcome. Looking at approval style votes, in particular bullet voting, there were two scenarios where the voter gained by bullet voting, and two where the voter lost. This was a zero-knowledge election. What has happened is that far too many analysists have not taken a close enough look at the actual scenarios, at what actually happens in voting, but instead they rely on superficial analyses and specific examples that make it look like the strategic voter gains something unjust. But the strategy used only makes sense in certain contexts, and the risks of that strategy, in that context, are not considered by the analyst. From what I've seen, the regret of the strategic voter whose strategy fails is deeper than the regret of the sincere voter who loses some value because of voting sincerely. If you give a candidate some support, but not enough, because you had a favorite you wanted to reserve the full vote for, you may regret it, but you know that you were, at least, sincere, and the result turned out differently simply because others did not agree with you. But if you fail to vote at all for someone you really would prefer to the one who wins, you may kick yourself for a long time..... why didn't I just express what I felt? But if the voter really did express how he felt, if he really *didn't* want to vote for that candidate, then his vote was sincere, it was not a strategic vote. We set up a contradiction when, in Range and Approval, we assume weak preference in a context where the voter indicates a strong one. Suppose you are out with friends, and you are choosing a pizza. (Oh, no, here comes the pizza election again!) Your friends say they prefer Pepperoni, but Mushroom is okay with them. You are the last voter. Suppose you are Jewish, keeping kosher, you can't eat Pepperoni. (I think some Jews will have other problems as well, with food not prepared in a kosher kitchen, but lots of Jews aren't that strict, but they won't eat pork.) You will say so, presumably, you will indicate maximal preference for Mushroom, and you will all have mushroom But suppose you were lying. You really don't keep kosher, it was just an excuse, and you have a slight preference for Mushroom, that's all. And you don't care about the others getting their preference, even if there are two of them and only one of you. You want it for yourself, you are selfish. (You might also want to pretend to be keeping kosher, which is another issue, one which I would call strong preference, it's just not about pizza but about something else.) So you say the same thing. And then the guy at the counter says, oops! We ran out of Mushroom. What about Pepperoni? What I've concluded is that we should generally consider that voters vote sincerely, but that "sincere" is not at all obvious, there are many motives that go into it. Many analysists simply assume certain utility numbers, and then assume that those numbers would translate "sincerely" into votes in some fixed way. It's a drastic oversimplification of the system. It's possible to work with simulations where we have something like known sincere absolute utilities, but there is not only one way to translate these utilities into votes. The best overall results are found, indeed, if everyone votes sincerely, meaning that the way they vote actually expresses how satisfied they would be with each outcome; however, there are lots of reasons why it might not be that simple. Further, to me, majority rule requires, where possible, that the majority consent to anything other than its first preference, explicitly. Single step rules cannot both satisfy the Majority Criterion and social utility maximization; forced to choose, I would choose SU. Since that really is the goal, properly, and the majority would only lose its first preference if it loses little, whereas the minority loses more if it loses its preference. However, it is possible to have the Majority Criterion and the cake as well. We can have SU maximization and then test that the majority accepts the result -- "prefers it" -- over its original preference. The easy way, with Range, is to analyze the ballots for preference, and see if there is any candidate who would beat the Range winner pairwise. If there is, a runoff is held. (It is actually rare, Range usually chooses the Condorcet winner, not to mention the Majority winner, it takes special and unusual circumstances to create majority failure in Range. So, if there is majority failure, it would be even rarer that there is more than one candidate who pairwise beats the Range winner, so, my suggestion is that a runoff take place under two circumstances. If there is a pairwise winner over the Range winner, the pairwise winner faces the Range winner in a runoff. If there are two or more such, and there is a Condorcet winner among them, the Condorcet winner faces the Range winner. In the extraordinarily rare circumstance that there was a Condorcet cycle beating the Range winner, the member of the cycle with the highest Range rating would face the Range winner in the runoff. And the final condition (the above being variations on the pairwise situation) is that there is an Approval cutoff specified in the election, perhaps 50%, and no candidate got 50%, and there is no pairwise victor over the Range winner. In that case, the top two Range winners would face each other. Range with top two, which is simply that, I think, unconditional runoff, has better SU results than pure Range, in the simulations. >I'm not sure I understand the "second round." The expression was a >bit garbled, I suspect. I assume that the "second round" is not an >actual runoff, but a recounting. As written, it would seem manifestly >unfair to the first candidate, the plurality winner of the approval election. > > >It is a runoff. With an actual runoff, we can get very good results, very close to optimal from the SU perspective, in a much simpler fashion. >I'm not well informed about Asset Voting, but in Brazil, where >two-round elections are performed for single-winner elections, there >are negotiations among candidates for influence the support of the >voters during the second round. Frequently voters do not vote for >the supported candidate of their first round favorite. That's correct, and it would be here too. However, this isn't like Asset Voting. What is different with Asset is that you really can vote for the person you most trust, of the whole set of everyone willing to serve at least as an elector. When you are voting in an election, sometimes you will vote for someone you don't really trust, but simply because you think you will get a better outcome, considering what is on the ballot. A vote in standard elections does not tell us much about whether or not the voter trusts the one getting the vote, and that's the issue about voting as recommended. In Asset, because votes are not wasted, a vote *does* indicate trust. Asset gives power to the candidate, power either to be elected or to choose, according to the votes they receive, who will be elected. So the issue is trust, far more than party, platform, etc. The latter will be important, but pale in comparison to trust. Now, consider this: if you are actually elected, what you are going to do, a lot, is to delegate authority. As a legislator, you will hire staff, you choose them, and they actually do much of the work, including research. Choose badly, you will perform poorly as a legislator. I'd suggest that a good legislator should be able to choose well. And, thus, if the legislator is *not* elected, that same person should *still* be able to choose well. If I would not trust someone to merely choose a winner, why would I trust that person *as the winner*, for that person is not only going to be elected with my vote, they will then vote on many matters with impact. It really is the same issue, confused for us by the fact that we are accustomed to not having any significant freedom in choosing those who supposedly represent us. I'm claiming that if I can't *choose* my representative, I'm not represented, period. Asset allows me to choose my representative *to the election*, who might also be a candidate, or who might not, might just be someone willing to be a public voter. It might even be me, I might vote for myself, and then I participate in the negotiations to create winners. With only one vote, I might not get a lot of attention, so I will probably seek others with views similar to mine and cooperate with them. In short, I might name a proxy, and so Asset Voting readily becomes, informally, Delegable Proxy. ---- Election-Methods mailing list - see http://electorama.com/em for list info
