Raul Miller writes ("Re: Our supermajority requirement has changed !"): > If you approve of two options but like one better than another, you're > not being penalized if the "liked, but not liked as much" option wins > over your favorite. Instead, you're being rewarded -- there weren't > enough votes to get you your favorite, but there were enough to get you > your alternate.
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.) * The chairman is abstaining but when they cast their vote they will agree either with X or Y, with 50% probability each (and neither X or Y know how the chairman will jump). * Each voter chooses between voting Good:OK:FD and Good:FD:OK. (Ie, let's avoid considering strategies involving other ballots.) 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 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. 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.) Ian.