Required ballot information: ordinal with tentative approval cutoff Count: For each candidate X recursively find the candidate X' that would win if X were to withdraw. On those ballots that rank X ahead of X', approve X. On those ballots that rank X equal to X' approve X only if X is tentatively approved. Elect the candidate with the most approval. That's it. Let's call it "Recursive Approval Strategy DSV," or RASDSV. [For recursive purposes it is important to agree that when there is only one candidate, this method will elect that candidate.] Also note that tentative approval information makes no difference on ballots that completely rank the candidates, as in the following example: 40 A>B>C 35 B>C>A 25 C>A>B Because of the ABCA cycle, the respecive candidates C, A, and B, are the recursive winners when B, C, and A, respectively, are withdrawn. So the approval cutoffs determined by this "Recursive Strategy" method are as follows: 40 A>B>>C 35 B>C>>A 25 C>A>>B The approval winner is B, so this method elects B. Note that a direct recursive implementation of this method will take (N-1)! recursive steps where N is the number of candidates, which means that if there are no computational shortcuts, the computation is NP hard. However, even if that turns out to be the case, the winner could be approximated by truncating the recursion after a few steps of depth, and determining the winners at that level by a more tractable method. For example, decide the depth two winner by random ballot. In the above example, nothing would change, since at depth two there is only one candidate. I hope that this message stimulates some new ideas. I've been in a rut for too long. Forest
<<winmail.dat>>
---- election-methods mailing list - see http://electorama.com/em for list info
