Rob Brown wrote: > What I suggest is that, prior to tabulating, each Range ballot be > processed into an Approval ballot. But, it should be done taking into > account optimum strategy, with knowledge of how others are voting. You > could call this a "Nash equilibrium seeking" system, as it keeps > adjusting Approval ballots (that is, picking the cutoff point) until a > state is reached where no voter can improve his or her own strategy > given that all other people's strategy stays fixed. (in reality it is > not the voter that is modifying their strategy, it is the formula that > converts the voter's range ballot into an approval ballot, which can be > considered to be operating as an "agent" of the voter) . . . > So the ballot is adjusted, giving only A a yes. The formula would > simply be that all candidate's that are preferred to the leader are > given a yes, and all that are less preferred are given a no. The leader > is given a yes if he is preferred to the second place candidate, > otherwise a no.
You have rediscovered Lorrie Cranor's Declared-Strategy Voting in batch mode using Approval and my "strategy A". Some of my current doctoral research is concerned with investigating DSV using different systems (plurality, Approval, Borda, etc.) and strategies like the above. Please see http://lorrie.cranor.org/dsv.html for Cranor's dissertation on DSV. Unfortunately, DSV in batch mode using Approval and strategy A won't always find a Condorcet winner. Consider the following 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 Reasonably assuming a 50 cutoff for each voter in the first round, B will lead in the first "poll". After cutoffs are adjusted, A will lead, then C will lead next. Then B will lead again and the cycle repeats. D, the Condorcet winner, will never lead, even though the only potential equilibrium (still assuming strategy A for all voters) results in a D win. -- 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
