At 12:46 AM 1/26/2007, Dave Ketchum wrote: >My initial reaction to your words: If not about public elections, >then why bother?
It is theoretical work. It has practical applications, *maybe*. Was Arrow's theorem about "public elections." No, it is about elections, period. Public, NGO, private. >Public elections are such an important part of the purpose of this >group that anything that does not apply to them should be labeled accordingly. This group is *full* of highly theoretical work. >Sure seemed like Warren intended it to be inclusive except, to me >his discussion methods do not quite fit. He's presenting a formal proof. He's a mathematician. He's not writing a piece for popular consumption. There is a great deal of such work on this list. Have you been following the apportionment discussions which are mostly between Smith and Ossipoff? It is highly technical and theoretical. The work has practical applications, yes, but it is at another level, the level of theory. >Certainly theory and other types of elections are worthy topics - >provided their applicability is understood. No. Theory is of value entirely on its own. Application of theory to practice is a completely different matter. It actually requires, often, different expertise. It's the difference between science and engineering. Science is generally about research and exploration, engineering is about practical application. Often theory exists for a *very* long time before practical applications are found. Of course, theory of elections has obvious practical application, but it is not obvious that this particular issue does, beyond a certain political point which might be made with it. The fact is that it is not at all difficult to show a major defect in election methods based on pure ranks without consideration of preference strength, and this defect is addressed by Range. That does not, by itself, mean that Range is superior, because Range might suffer from *other* defects. However, some of the criteria by which Range is commonly judged as defective are "contaminated" with the assumption of ranked ballots and "intuition" based on thinking for several centuries only about them. If you have a group of people, and they need to pick from two choices, and slightly more than half of them have a very slight preference for A over B, but the other half would be very unhappy with A, but love B, it is obvious that a group which cares about the maximum satisfaction of *everyone* would pick B. That choice would leave everyone satisfied, choosing A would leave half of the population, so to speak, out in the cold. But the Majority Criterion and the Condorcet Criterion both would require A to win. This is so blinkin' obvious that it is amazing that it has not attracted much attention. Range methods solve this problem. But do they introduce other problems? That is a major question. Range and Approval do not suffer from Favorite Betrayal. It never hurts you to do your best to elect your favorite with these methods. As to what additional votes you cast, that may be subject to some degree of strategy, particularly with coarse Range (and Approval is as coarse as Range could get.) What about ICC? That is a matter currently under debate. It depends quite a bit on definitions. There are Range *strategies* which, if followed in a fixed manner, are vulnerable to ICC. But the method itself is not, not by any reasonable interpretation of the intuition behind ICC. The intuition is that the introduction of a candidate who is identical to another candidate, in the eyes of all voters, should not change the election outcome, that is, if the cloned candidate would lose, so would the clone. And if the cloned candidate would win, then either they will tie (strict clone) or one of them will win (clone error less than resolution of Range method, or with preference strength less than one rank with ranked methods). The alleged vulnerability to clones of Range is based on ballot normalization. The simplest view of normalization is that voters will vote the maximum and minimum ratings, for at least one candidate each, in the election. If voters are rating candidates in comparison with each other, then, the argument goes, they may give a differing rating of one vs. the other. This couldn't happen with a strict clone except as noise. I.e., it is equally likely that this variation would affect one candidate vs another. This is perhaps why probabilities are mentioned in these proofs. But with clones defined according to the usage in ranked elections, they may differ from each other, that is, voters may have preferences between them. If this preference shows up in the Range ratings, even one point of difference with one voter could, under some circumstances, swing the election to or from the clone set. Even though the ranks on all ballots are identical. (A Range ballot is converted to a ranked ballot by ordering the candidates in order of rating. If equal ratings are allowed in the ranked method, then it is that simple. If not, then an obvious method of conversion is to rank the identically-rated candidates randomly. If the probability of A>B coming out of this is equal to the probability of B>A, or similarly with more than two equally rated candidates, then it is fair. It is, in fact, the coin toss at the end if there is a tie, only it is a series of coin tosses, perhaps. So does Range pass ICC or not? The "ranked" definition of clone was written by people who were not considering Range. They were only thinking, I would bet, about ranked methods. They first thought of cloning as identical, I would presume. (and that is the basis of the common-sense definition.) Then, since they were dealing with ranks, and there *could* be variations between the clones, i.e., voter preferences among them, when considering ICC, they loosened the definition to allow the candidates to be other than identical. But, when used with a method that really allows "ranks" finer than the candidate set, it no longer is an appropriate use of the term "clone," which, in general usage, means an *exact* copy. (Range allows ranks up to the smaller of two numbers: the number of candidates, or the resolution of the implementation. So Range has the ICC problem -- if we think of it as a problem -- only because it collects and uses finer data than pure ranked methods. Basically, for a clone to shift a Range outcome, the clone must *not* be identical. In Range, if two candidates are identically *rated* by all voters, then dropping one of them could have no effect on the outcome of the election (unless that candidate was the winner, in which case the victory would necessarily shift to the other candidate -- unless there were more clones. It is utterly obvious that ICC is a purely theoretical criterion, if applied to Range, unless the electorate is very small. However, the thinking is that, if ICC is not satisfied, then a political party could manipulate the outcome by manipulating the number of candidates. There are methods which are seriously vulnerable to this. In particular, methods which award value to a candidate by how many other candidates are defeated by the candidate, are vulnerable. By adding more "defeated" candidates, the outcome can be shifted toward the preferred candidate among the clone set. *This* has practical application. If we look at the practical application with Range, however, Range is a method where the rating of one candidate is not affected by the presence of other candidates. Except when ballots are normalized. If a new candidate is introduced who is either Maximum Worst, or Maximum Best, then the ratings of other candidates would shift, so the thinking goes. In fact, it might not, at least not at the bottom end. Got it now? >>No rerun. One of the assumptions, I think, is that the method is >>deterministic. That is, it *will* choose a winner, but random >>choice is only allowed if there is a tie (or more than one tie). > > >But now we are back to: responding to a tie by chance should assume >equal probability of comparable results. Yes. In fact, I think that may have been explicitly stated. ---- election-methods mailing list - see http://electorama.com/em for list info
