2011/7/7 <[email protected]> > > > ----- Original Message ----- > From: Andy Jennings > > > > > > Of course, with too many factions, the optimal strategy > > computation would > > > be intractable. > > > > > > > With twenty candidates, there are about a million different > > possible subsets > > to consider. Seems like it could be tractable. > > Building the tree and finding the order of play is tractable,
That may be so, but I still don't understand what algorithm you're proposing. > but computing the optimal strategy is > intractable. > Suppose there are twenty candidates, then each candidate has 19 choices of > where to put her approval > cutoff in her ranking of the candidates. That makes 19^20 possibilities. > Precisely one of these will be > optimal for the given order of play. So Jameson is right; it is better to > not compute the optimal strategy > automatically; just let the candidates play the chess game the best they > can. > > However, when it gets down to the last five players, there will be only > 19^5 possibilities left, and these > could be done automatically in order to completely remove the temptation > for a potential "kingmaker" to > throw the election for some personal gain. > Actually, if you assume only the top five vote-getters are "viable" - generally justified from the outset in real elections - then there are only 5^19 possibilities, and some good chess-playing algorithms could prune that tree to tractability. But the reason I said we should let the candidates do it rather than computing wasn't computability; it was to prevent pre-election strategy (principally burial) for candidates. JQ
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