Steph has already been well-answered, and so I'll limit myself to a few brief comments on his letter: First, this is what I, and all of us, mean by CW: Candidate C is CW if and only if, for every candidate Z who isn't candidate C, the number of voters who prefer C to Z is greater than the number of voters who prefer Z to C. [end of definition] Note that "prefer" refers to sincere preferences, not to votes. Steph wrote: 1) Why is it that important that "truncation won't steal the election from a majority-supported CW"? I reply: How about majuority rule? A majority indicate that they prefer X to Y, so shall we elect Y, if there is no beatpath of stronger majority defeats contradicting that defeat? For judging majority rule violations, I suggest that the most useful definition is something similar to Markus' Beatpath GMC, something that says: Majority rule is violated if we elect a candidate who has a majority defeat that isn't the weakest defeat in a cycle. That could be called Qualitative or Comparative Beatpath GMC (CBGMC). CBGMC is a criterion that is failed by methods that can violate majority rule as defined in the previous paragraph. It's ok that Plurality passes BGMC & CBGMC, because it's accepted that Plurality doesn't violate expressed majority wishes. CBGMC is a special case of Steve Eppley's BC. It's ok that Plurality passes BC, because BC isn't used for comparing method merits, but is only used for determining compliances with other criteria: A rank method that meets BC also meets SFC, GSFC, WDSC, & SDSC. I once defined GMC, saying that a we should never elect a candidate who has a majority defeat if there's a candidate who doesn't. Beatpath GMC improved on that, because it's reasonable that a defeat loses some validity if it's part of a cycle of similar defeats. I prefer CBGMC, because a defeat is more fairly nullified by a beatpath that's stronger than the defeat. In that way, the criterion only lets one candidate win in a Smith set cycle of majority defeats. A good definition of majority rule is important, considering how much the term is used, and how many people consider it an important standard. Also, I use that term in my definitions of offensive & defensive strategy. Defensive strategy is voting that doesn't express all of the voter's sincere preferences and is intended to protect the win of a CW, or enforce majority rule. Offensive strategy is voting that doesn't expres all of the voter's sincere preferences and is intended to take victory from a CW, or elect someone in violation of majority rule. Steph continued: For me if you change a set of ballots S1 into a new set S2 by truncating some ballots, it is quite possible and normal to obtain a different winner: we have different ballots! Why would I preserve a CW of S1 as a winner if he is no more a CW of S2? I reply: He's still CW. Truncation doesn't change who's CW. CW is about sincere preferences, not votes. Nor does it change the fact that a majority of all the voters have indicated on their ballot that they prefer one candidate to another. Steph continued: I do not think it is your goal since this is not guaranteed to preserve the winner if there is no CW. [...] 4) Thus, isn't the expression of sincere preferences aimed to by using winning-votes dependent on having a CW and voters having no sincerely truncated ranking preferences from the start? I reply: SFC, GSFC, WDSC, & SDSC don't depend on any assumption that voters have preferences among all the candidates. Check the critia's wording. As for your claim that the guarantees don't apply when there's no CW, you've forgotten about GSFC: If no one falsifies a preference, and if X is a member of the sincere Smith set, and Y is not, and if a majority of all the voters prefer X to Y, and vote sincerely, then Y shouldn't win. [end of GSFC definition] GSFC applies whether or not there's a CW. The WV methods pass that criterion and have that guarantee. The margins methods don't. Steph continued: Since both conditions have no guarantee, I think winning votes only offer a partial incentive toward sincere votes, and thus another criteria representing optimal fairness (relative margins) should be considered. I reply: WV methods offer absolute guarantees, such as SFC, GSFC, WDSC, & SDSC. Margins methods have situations in which all of the Nash equlibria are ones in which defensive order-reversal is used. Steph doesn't think truncation will happen, but it will be common in rank-ballotings. It happened in all the rank-ballotings that I conducted or participated in. In one instance, a voter indicated strategic intent verbally when he voted. Mike Ossipoff _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
