Dear Folks! The following comment of Juho's made me think about the concepts of "best canidate" and "Social Ordering" again.
Juho Laatu wrote: > If the "god" that elects the best winner would be one > individual, then we could expect him to give a linear order to the > candidates. And in this case it looks natural that candidates outside > the Smith set must be lower than candidates in the Smith set. And it > looks natural that after this decision all that there is left is to > break the loops in the Smith set and make also their order linear. But > as we know, group opinions may contain natural cycles and one can not > say that they are wrong and should be corrected. For this reason I find > methods that try to e.g. evaluate each candidate separately more natural > than ones that try to force the group preferences into some linearly > ordered preferences. Let us look a bit deeper at the notion of "best candidate": First of all, the principal aim of a single winner election method is to find a single winner (that's trivial). Intuitively, one is tempted to say this should be "the best" candidate. But this implicitly assumes that there *is* a "best" candidate. We know of course that most often one can easily find two measures which do not agree on which candidate is "best", so we're left with deciding which measure is most important. But what if no measure is "most" important but each is important in some sense or other? Then perhaps there is a most important sense in which measures can be important... etc... Some methods focus on one measure, for example Plurality (direct support), Approval Voting (approval score), Copeland (number of pairwise defeats), MinMax (strength of strongest defeat), Beatpath (strength of beatpaths), Kemeny (using some measure of fit between a social order and the pairwise defeats), ignoring all other measures. Other methods consider more than one measure, for example DMC (approval score and pairwise defeats) or DFC (approval score, pairwise defeats, and direct support). My claim is that the latter are much safer against arguments of using the wrong measure when there is no agreement upon which measure is most important. So, I suggest not to claim your favourite method finds "the best" candidate, as so many of us frequently do. Rather, one should say that the favourite method elects a "very good candidate as measured by <whatever>" and then explain why those measures are considered important! DFC, for example, is my current favourite since it elects a very good candidate as measured by direct support, approval score, and pairwise defeats, and I find this combination of measures most satisfying since they correspond to the three most basic complementary forms of preference information: 1. Individual direct support, answering the "global" question of which candidate I would personally elect if I could decide. 2. Approval, answering the "local" question of whether I find a particular candidate acceptable or not. 3. Pairwise preferences, answering the elementary comparison question of which candidate I would personally elect if only these particular two were feasible. Now, what about "social orderings"? Why should anybody want such a thing or assume that such a thing should exist? The implicit assumption behind a social ordering is not only that there is a "best" candidate, but that there is even a "second best", "third best", and so on. Why the hell should that be the case when there is not even a clear notion of "best"? Of course, a social ordering can be useful in some situations, for example when it is not clear beforehand which of the options are actually feasible, like when deciding upon the movie to watch without knowing which movies might be sold out. But in an election, there is no such uncertainty, and in the unlikely case in which the winner becomes unavailable between the election and the time of taking office, one would rather hold a new election than put the "2nd best" candidate in office... Another use of social orderings could be for information purposes: Which candidates were "close to winning"? But such questions can easily be answered independently after the actual election, for example by reporting how many voters would have had to vote differently to get the particular candidate. But there is no reason why the latter measure should be involved in *finding* the winner in the first place. Likewise, one can report after the election on the strongest beatpaths from the winner to all other cnadidates, without any need to consider beatpaths for finding the winner. Actually, I think one should report as much and as diverse information as possible to justify the winner once s/he is determined, no matter whether that information was used in finding the winner. Finally, there is an important criterion by Steve, "immunity from 2nd place complaints", which seems to indicate that a social ordering was needed. But that criterion only states that when we remove the original winner and apply the method *again* after striking out that candidate from all ballots, then the new winner should not be one who defeats the original one pairwise. This is a useful criterion, but it has nothing to do with social orderings, at least in my opinion. So, I suggest we should drop the idea of "social ordering" altogether and never mention it to anyone, especially not when arguing in favour of some single winner election method, because it is absolutely misleading. Yours, Jobst ---- Election-methods mailing list - see http://electorama.com/em for list info
