Hi James, --- James Green-Armytage <[EMAIL PROTECTED]> a écrit : > James: > >> Okay then, how do you define majority rule? The question I'm interested > >> in is not whether we can invent an interesting new concept; the question > >> is what is the most appropriate criterion to be identified as "majority > >> rule". When we say that a given method is a majority rule method, what > >> should we mean by this? > > Kevin: > >I think the most intuitive is Steve Eppley's criterion that Markus quoted. > >When v(i,j)>50% and there is no beatpath of strength >50% from J to I, > >then > >J mustn't win. Basically, when more than half prefer I to J, in the > >"normal" > >case you mustn't elect J. > > We disagree about whether "majority" should refer to the a majority of > ballots cast, or a majority of ballots that express a preference between a > given pair of candidates. If you remove the >50% stipulation from your > definition above, you are left with what? The Schwartz set? Anyway, > something close to the Smith set, right?
Right, you're left with "when I beats J and J has no beatpath I, then J can't win." > Kevin: > >If this criterion is too strong (although I doubt you think so), then I'd > >suggest Minimal Defense: When a majority rank X>Y and Y over no one, then > >Y mustn't win. > > Sounds like a useful criterion, but it strikes me as being a bit too > specific to be regarded as the technical definition of majority rule. It > seems like there are plenty of scenarios where one could fairly say that > majority rule has not been satisfied although the above criterion has not > been violated. Here is a weaker quick test: If for some A and B, v[a,b]>50%, and there is no pair of candidates C and D (where C is not A) for whom v[c,d]>50%, then B must not win. IRV still fails this. > Kevin: > >But what you write above doesn't seem true. Choosing just anyone from the > >Smith set can "unnecessarily overrule" defeats, unless I don't understand > >what you mean by "unnecessarily." > > I don’t know whether you understand what I mean or not. I mean that if > there is a CW, there is no need to overrule any defeats in order to choose > a winner. If there is a majority rule cycle, then it is necessary to > overrule at least one defeat, but it is not necessary to overrule a defeat > outside of the Schwartz set (= Smith set in large electorates). Hence, > choosing a candidate outside of the Smith set always involves > unnecessarily overruling a pairwise defeat. If you disagree, please state > your reasoning in more detail. Well, I believe the >50% interpretation is useful. So given that, and the following two elections: 49 A 24 B 27 C>B 9 A>B 5 B 8 C In my mind it's a majority rule violation (and a complete waste of an election) to elect A in the first scenario, but nothing near that to elect B in the second scenario. Neither the Smith set, nor the set of candidates I consider electable according to majority rule, is a subset of the other. > Kevin: > >IRV guarantees majority rule by a solid coalition. But in general I don't > >consider it to be a "majority rule method." > > Nor do I, really. Or perhaps I consider it a majority rule method in a > “weaker” sense than a Smith-efficient method. Here are some key criteria > that I consider to be indicative of the “majoritarian-ness” of a given > method: > (1) Mutual majority criterion, > (2) Condorcet criterion > (3) Condorcet loser criterion > (4) Smith criterion > IRV only meets (1) and (3). Beatpath, ranked pairs, and river meet all > 4. > Minimax only meets (2). Approval and plurality meet none of the above. > Borda, I believe, only meets (3). I've criticized before that this list lacks a criterion dealing with majority (my sense) pairwise wins. The CDTT methods I like only meet (1), but I consider them more majoritarian than e.g. Margins. > Kevin: > >I don't agree that we should use Smith as the reason, since Smith is too > >weak to satisfy "majority rule" in the >50% sense. > > We disagree on the importance of the >50% of cast ballots definition. I consider it a fundamental component of IRV's badness that it can't see >50% opinions. If you don't insist on that kind of capability, I wonder if you won't end up with a method just as poor. > Kevin: > >In my mind the problem is IRV's failure of Minimal Defense slash SDSC: > >In a race primarily between A and B, even when a majority prefer A to B, > >they can "confuse" the method into electing B just by ranking weaker > >candidates above A. > > Wouldn’t they have to rank the weaker candidate above B as well? > Otherwise, the insincere ranking wouldn’t have an impact until B was > already eliminated. I’m not saying that IRV passes minimal defense, I’m > just saying that what you’re talking about sounds like the push-over > strategy, which I suggest is relatively hard to use in practice (low > reward/risk ratio). No, not push-over. I could have been clearer. When I say "they" can confuse the method, I mean that the A>B voters can *unintentionally* confuse the method. It's just a compromising problem. IRV and FPP both have it. > Kevin: > >I agree that MMC is *far* too "broad," but in some cases I think Condorcet > >is too narrow: > >9 A>B > >5 B > >8 C > >I don't agree that a method "fails majority rule" if it elects B here. > > A is a Condorcet winner. A 9-5 majority (a majority as I define it, not > as you define it) prefers A to B, and a 9-8 majority prefers A to C. Hence > I assert that electing A is the only way to satisfy majority rule (as I > define it). I wouldn't feel too bad insisting on Condorcet if it were more compatible with Later-no-harm. Kevin Venzke __________________________________________________________________ Découvrez le nouveau Yahoo! Mail : 250 Mo d'espace de stockage pour vos mails ! Créez votre Yahoo! Mail sur http://fr.mail.yahoo.com/ ---- Election-methods mailing list - see http://electorama.com/em for list info