--- On Fri, 23/1/09, Kristofer Munsterhjelm <km-el...@broadpark.no> wrote:
> Juho Laatu wrote: > > I try to summarize my comments in the > > form of some rough definitions. > > > > A "simple" method requires > > 1) a 'simple' method to convert honest > > preferences into optimal votes > > > > A "zero-info" method requires > > 2) this method may not use info about > > other voters, but still be able to > > convert honest preferences into optimal > > votes > > > > A "non-manipulable" method requires > > 3) it is in everyone's interests to use > > the default method to convert honest > > preferences into optimal votes > > > > (I didn't cover the "if everyone else uses > this method" case.) > > > > These definitions allow also e.g. Approval > > to be categorized as (close to) "simple", > > not "zero-info" and > "non-manipulable". > > > > One more definition to point out one > > weakness of Approval. > > > > A "decidable" method requires > > 1) a method to convert honest preferences into an > unambiguous optimal vote > > > > The point is that the there should be > > no lotteries that may lead also to > > unoptimal votes but the best vote > > should be found in a deterministic way. > > Approval fails this criterion since > > picking the correct number of approved > > candidates is sometimes tricky (when > > there are more than two strong > > candidates). > > Since all ranked methods are vulnerable to strategy, what > constitutes an optimal vote depends on the votes of > everybody else. Thus no such method can be either of the > above I refer to our discussion on the possibility to meet some criteria partially. I think we too often use black and white criteria (or use the criteria in a b&w way). I'd use all four criteria that I listed also as "partially met" criteria. One can thus define an ideal and then check how close each method gets. > , and any simple method (by the definition) must also > be non-manipulable, since to discover the optimal vote > otherwise, you'd have to know the votes of potentially > everybody else. The definitions that I gave are not necessarily good/optimal/useful. One could e.g. remove word "optimal" from the definition of the "non-manipulable" definition. One should maybe have a separate term for optimal vote at the time of voting and optimal vote at the time of counting the votes. One should also have separate terms for a method with a default vote creation method defined and for one without. These correspond to "election method as part of the society" (with default rules of behaviour) and "vote tabulation method" (that doesn't take position on how and where the ballots came from). You are welcome to propose better definitions. I don't have a perfect set available right now. > > The definitions you gave could be used for zero info > strategy. For instance: > > Simple zero-info: The optimal zero-information strategy is > simple to determine. > > Dominant zero-info: If everybody uses zero info strategy, > and the method doesn't output a tie, no single voter > could gain by changing his vote to something else. > > And there's also the usual zero-info strategy > criterion: > > No zero-info strategy: The optimal zero information > strategy is a sincere vote. > > > "No zero-info strategy" implies "simple > zero-info". Dominant zero-info is vaguely similar to > SDSC, though the latter deals with counterstrategies. > Dominant zero-info may also be too strong: consider a > situation where the voters produce a "tie minus one > vote" (where a certain ballot can produce a tie); then, > if the final voter prefers a candidate that would be ranked > lower to one that would be ranked higher, he can construct a > vote that leads to the two being tied. This last note sounds quite a lot like "one-man-one-vote" (=one voter can not change the end result much). I need to think more what kind of useful definition sets we might have, and which ones could be used as an (few ideal targets based) "coordinate system" to describe and classify the methods. That would (in theory) mean few core criteria and their refinements and estimated levels of compliance (instead of just a large set of black and white criteria). I'm not sure if it is possible to achieve anything useful though but one can always try. Juho ---- Election-Methods mailing list - see http://electorama.com/em for list info