Rob Brown wrote: > 1) start with a much lower cutoff. Say 10 or 20. Or, if the ballots > are simply ranked, start by giving a "yes" to all but the bottom-most > candidates.
No, the same B->A->C->B cycle obtains given the votes A B C D 33: 100 70 30 0 16: 10 100 70 0 17: 0 70 30 100 34: 30 0 70 100 > 2) use an average of all previous totals to determine strategy > each round. You have rediscovered Forest Simmons's cumulative batch mode for DSV: Instead of compiling a fresh poll for each round, the current votes are added to a cumulative poll. For the above example, D does in fact break the cycle and emerge as the leader and eventual winner, but it takes more than 170 rounds. Unfortunately, even Approval DSV in cumulative batch mode using strategy A will cycle forever when there is a strong top cycle. > I'm still thinking the results will converge, if not on a true > equilibrium. What do you mean by "a true equilibrium"? A strong Nash equilibrium? > Unfortunately this stuff is too tedious to work out by hand, so I'd > have to write something to test it. I've written my own software to simulate DSV with all of these tweaks. Let me know if there's another test election you'd like me to try. > However, looking at the case you gave, I almost want to say that D > shouldn't win, even though he's the condorcet winner (since he is > clearly a very polarizing candidate, with half loving him and half > hating him). I agree that D seems to be a polarizing candidate, but no other candidate can be elected at an equilibrium. Any voting system that doesn't elect D will be prone to manipulation. For example, say a voting system elects C for the above example. Then the factions of 17 and 34 voters would be motivated to bullet-vote for D. It's a strange voting system that wouldn't then elect D. -- Rob LeGrand, psephologist [EMAIL PROTECTED] Citizens for Approval Voting http://www.approvalvoting.org/ __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ---- election-methods mailing list - see http://electorama.com/em for list info