"Irrelevant Ballots Independent Fallback Approval" (IBIFA) is the name I've settled on for the method I proposed in a May 2010 EM post titled "Bucklin-like method meeting Favorite Betrayal and Irrelevant Ballots".
http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html In that post I wrote that it uses multi-slot ratings ballots, and defined the 4-slot version: *Voters fill out 4-slot ratings ballots, rating each candidate as either Top, Middle1, Middle2 >or Bottom. Default rating is Bottom, signifying least preferred and unapproved. > > >Any rating above Bottom is interpreted as Approval. > > >If any candidate/s X has a Top-Ratings score that is higher than any other >candidate's approval >score on ballots that don't top-rate X, elect the X with the highest TR score. > > >Otherwise, if any candidate/s X has a Top+Middle1 score that is higher than >any other candidate's >approval score on ballots that don't give X a Top or Middle1 rating, elect the >X with the highest >Top+Middle1 score. > > >Otherwise, elect the candidate with the highest Approval score.*(Obviously >other slot names are possible, such as 3 2 1 0 or A B C D or Top, High >Middle, Low Middle, Bottom.) The 3-slot version: *Voters fill out 3-slot ratings ballots, rating each candidate as either Top, Middle >or Bottom. Default rating is Bottom, signifying least preferred and unapproved. > >Any rating above Bottom is interpreted as Approval. > >If any candidate/s X has a Top-Ratings score that is higher than any other >candidate's approval >score on ballots that don't top-rate X, elect the X with the highest TR score. > >Otherwise, elect the candidate with the highest Approval score.* > It can also be adapted for use with ranked ballots: *Voters rank the candidates, beginning with those they most prefer. Equal-ranking and truncation are allowed. Ranking above at least one other candidate is interpreted as Approval. The ballots are interpreted as multi-slot ratings ballots thus: An approved candidate ranked below zero other candidates is interpreted as Top-Rated. An approved candidate ranked below one other candidate is interpreted as being in the second-highest ratings slot. An approved candidate ranked below two other candidates is interpreted as being in the third-highest ratings slot (even if this means the second-highest ratings slot is left empty). An approved candidate ranked below three other candidates is interpreted as being in the fourth-highest ratings slot (even if this means that a higher ratings slot is left empty). And so on. Say we label these ratings slot from the top A B C D etc. A candidate X's A score is the number of ballots on which it is A rated. A candidate X's A+B score is the number of ballots on which it is rated A or B. A candidate X's A+B+C score is the number of ballots on which it is rated A or B or C. And so on. If any candidate X has an A score that is greater than any other candidate's approval score on ballots that don't A-rate X, then elect the X with the greatest A score. Otherwise, if any candidate X has an A+B score that is greater than any other candidate's approval score on ballots that don't A-rate of B-rate X, then elect the X with the greatest A+B score. And so on as in the versions that use a fixed number of ratings slots, if necessary electing the most approved candidate.* This is analogous with ER-Bucklin(whole) on ranked ballots: http://wiki.electorama.com/wiki/ER-Bucklin Chris Benham ---- Election-Methods mailing list - see http://electorama.com/em for list info
