On Wed, May 26, 2004 at 09:23:53PM +0100, Ian Jackson wrote: > Let us suppose that: > > * There are two voters X and Y, whose real utilities are > Voter X: A=+10 (`Good') Voter Y: B=+10 > B= 0 (`OK') A= 0 > FD= -5 FD= -5 > (Let us neglect the quorum for the moment as I want to have just > two voters to simplify the situation.)
FD should be 0 utility. This doesn't affect things greatly, but helps keep perspective. That makes it: Voter X: A=+15 (`Good') Voter Y: B=+15 B= 5 (`OK') A= 5 FD= 0 FD= 0 > Here are the possible outcomes seen from X: > > Payoffs for X Y votes B:A:FD `cooperate' Y votes B:FD:A `defect' > X cooperates +5 (50% of +10) 0 > X defects +10 -5 This becomes: Payoffs for X Y votes B:A:FD `cooperate' Y votes B:FD:A `defect' X cooperates +10 (avg of 5 and 15) 5 X defects +15 0 The same thing, basically, but all outcomes are positive unless both "defect". If X wants to minimize potential losses (and X has certain knowledge that no other votes will be cast), X should cooperate. If X has no knowledge how Y will vote (but knows for sure that no one else will be voting), the potential payoff for X is equal (7.5 with my numbers, 2.5 with yours) for the "defect" and "don't defect" cases. > Whether X's best strategy is cooperate depends on whether Y > cooperates, and X's outcome is mainly controlled by whether Y > cooperates or not. If X knows that Y is going to defect then X should > cooperate. > > This is a strange and dysfunctional game if what we want is for people > to discuss and vote honestly. I'm not sure I agree. > The alternative voting system, with the word `strictly' removed, works > like this: > > Payoffs for X Y votes B:A:FD `cooperate' Y votes B:FD:A `defect' > X cooperates +5 +5 * > X defects +5 * +5 * > > This is much more sensible. (Entries marked * are ones where the > chairman could choose FD too.) I don't see that removing the word "strictly" has this effect at all. The quorum for committee votes is 2, which means that each option must receive 2 votes preferring it over the default option or it is ignored. Furthermore, 1 is not greater than 1 any more than 1 is strictly greater than 1. So even without quorum, I don't see any benefit for this case. -- Raul