Dear Adam! You wrote: > imagine many of the CBA voters have strategically upranked A (with some of > them approving A as well) in order to create a cycle. Here is the "concrete > example": > > 10% C>>B>A (the "honest" ones) > 23% C>>A>B > 18% C>A>>B > 12% B>C>>A > 12% B>>A>C > 17% A>B>>C > 10% A>>B>C
Hm. This adds up to 102%, but I guess from what you wrote next that the first 10% are meant to be just 8%. I will assume so here. > B>C 41% approval I suppose this means the B>C defeat is considered to have strength 41% since this is B's approval. > C>A 61% approval > A>B 45% approval OK. In DMC, C wins. That is, the C voters have sucessively buried B. But the last 10% A-voters can prevent this by approving of B also. This means that it seems wise to approve the Condorcet winner and all above her in order to assure a good compromise, right? But you suggest not this easy countermeasure but a more difficult one: > Now, imagine you are in the 17% A>B>>C faction, and you are aware of the > situation. The only way you can prevent C from winning is by insincerely > disapproving of A. > > 10% C>>B>A > 23% C>>A>B > 18% C>A>>B > 12% B>C>>A > 24% B>>A>C (including 12% insincerely disapproving of A) > 5% A>B>>C (the "honest" ones) > 10% A>>B>C > > Now A's approval (33%) is lower than B's (41%), which allows B to win the > election. It is true that they can perform this, but it is false that this is the only strategy for the A-voters to prevent the C-voters from manipulating the election by burying. In fact, it is far more natural for the A-voters to just approve B which effectively protects B from losing. You could answer that this requires that some of the last 10% approve B but that they perhaps won't do so since they don't care which of their non-approved candidates B,C wins. But then you assume that the actual sincere preferences are rather like this: 49% C>>B>A 12% B>C>>A 12% B>>A>C 17% A>B>>C 10% A>>B=C In this situation, C is the *sincere* Condorcet winner and no strategizing by the C voters is necessary. > There is a rather large set of situations where this can occur. I > constructed this one to be what I saw as a plausible situation where > insincere order-reversal and disapproval was clearly a superior strategy. Superior to just approving B as I suggest? Why do you think so? > In winning votes, the ABC faction can simply equal-rank. So you suggest winning votes was better since it provides for a counterstrategy which requires *insincere* rankings. But in DMC the counterstrategy I specifyed above involves only sincere rankings, so I guess this rather shows that DMC is better in this situation. Yours, Jobst ______________________________________________________________________ XXL-Speicher, PC-Virenschutz, Spartarife & mehr: Nur im WEB.DE Club! Jetzt gratis testen! http://freemail.web.de/home/landingpad/?mc=021130 ---- Election-methods mailing list - see http://electorama.com/em for list info