Yes, in standard game theory everyone would know the exact utility of the B supporters in each outcome.
Here, those utilities are hidden, so there is some incentive for the B supporters to lie and say they are indifferent between A and C. On Mon, Dec 12, 2011 at 4:17 PM, <[email protected]> wrote: > Thanks for checking the details. > > In traditional game theory the rational stratetgies are based on the > assumption of perfect knowledge, so > the A faction would know if the B faction was lying about its real > preferences. Even knowing that the > other faction knew that they were lying they could still threaten to > defect, and even carry out their threat. > There is no absolute way out of that. > > ----- Original Message ----- > From: Andy Jennings > Date: Monday, December 12, 2011 12:40 pm > Subject: Re: [EM] This might be the method we've been looking for: > To: Jameson Quinn > Cc: [email protected], [email protected] > > > You're right. I've drawn out the game theory matrix and the > > honest outcome: > > 49 C > > 27 A>B > > 24 B>A > > is indeed the stable one, with A winning. > > > > So the only way for B to win is for his supporters to say they are > > indifferent between A and C and threaten to bullet vote "B". > > Then the A > > supporters fall for it and vote "A=B" to prevent C from winning. > > B wins. > > > > I wonder if this is sequence of events is likely at all. > > > > ~ Andy > > > > > > > > On Fri, Dec 9, 2011 at 2:31 PM, Jameson Quinn > > wrote: > > > No, the B group has nothing to gain by defecting; all they can > > do is bring > > > about a C win. Honestly, A group doesn't have a lot to gain > > from defecting, > > > either; either they win anyway, or they misread the election > > and they're > > > actually the B's. > > > > > > Jameson > > > > > > 2011/12/9 Andy Jennings > > > > > >> Here’s a method that seems to have the important properties > > that we > > >>> have been worrying about lately: > > >>> > > >>> (1) For each ballot beta, construct two matrices M1 and M2: > > >>> In row X and column Y of matrix M1, enter a one if ballot > > beta rates X > > >>> above Y or if beta gives a top > > >>> rating to X. Otherwise enter a zero. > > >>> IN row X and column y of matrix M2, enter a 1 if y is rated > > strictly>>> above x on beta. Otherwise enter a > > >>> zero. > > >>> > > >>> (2) Sum the matrices M1 and M2 over all ballots beta. > > >>> > > >>> (3) Let M be the difference of these respective sums > > >>> . > > >>> (4) Elect the candidate who has the (algebraically) > > greatest minimum > > >>> row value in matrix M. > > >>> > > >>> Consider the scenario > > >>> 49 C > > >>> 27 A>B > > >>> 24 B>A > > >>> Since there are no equal top ratings, the method elects the same > > >>> candidate A as minmax margins > > >>> would. > > >>> > > >>> In the case > > >>> 49 C > > >>> 27 A>B > > >>> 24 B > > >>> There are no equal top ratings, so the method gives the same > > result as > > >>> minmax margins, namely C wins > > >>> (by the tie breaking rule based on second lowest row value > > between B and > > >>> C). > > >>> > > >>> Now for > > >>> 49 C > > >>> 27 A=B > > >>> 24 B > > >>> In this case B wins, so the A supporters have a way of > > stopping C from > > >>> being elected when they know > > >>> that the B voters really are indifferent between A and C. > > >>> > > >>> The equal top rule for matrix M1 essentially transforms > > minmax into a > > >>> method satisfying the FBC. > > >>> > > >>> Thoughts? > > >>> > > >> > > >> > > >> To me, it doesn't seem like this fully solves our Approval > > Bad Example. > > >> There still seems to be a chicken dilemma. Couldn't you > > also say that the > > >> B voters should equal-top-rank A to stop C from being elected: > > >> 49 C > > >> 27 A > > >> 24 B=A > > >> Then A wins, right? > > >> > > >> But now the A and B groups have a chicken dilemma. They should > > >> equal-top-rank each other to prevent C from winning, but if > > one group > > >> defects and doesn't equal-top-rank the other, then they get > > the outright > > >> win. > > >> > > >> Am I wrong? > > >> > > >> ~ Andy > > >> > > >> > > >> > > >> ---- > > >> Election-Methods mailing list - see http://electorama.com/em > > for list > > >> info > > >> > > >> > > > > > >
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