The following method makes use of two ballots for each voter. The first ballot is a three slot ballot with allowed ratings of 0, 1, and 2. The second ballot is an ordinal preference ballot that allows equal rankings and truncations as options.
The three slot ballot is used to select two finalists: one of them is the candidate rated at two on the greatest number of ballots. The other one is the candidate rated zero on the fewest ballots. The runoff between them is decided by the voters' pairwise preferences as expressed on the three slot ballots (when these finalists are not rated equally thereon), or (otherwise) on the ordinal ballots when the three slot ballot makes no distinction between them. [Giving priority to the three slot pairwise preference over the ordinal ballot preferences is necessary to remove the burial incentive.] Note that there is no strategic advantage for insincere rankings on the ordinal ballots. Questions. (1) What are some near optimal strategies for voters to convert their complete cardinal ratings into three slot ratings in this context? (2) We have a "sincere approval" method of converting cardinal ratings into two slot ballots. What is the analogous "sincere three slot" method? [Sincere approval works by topping off the upper ratings with the lower ratings; think of the ratings as full or partially full cups of rating fluid next to each candidate's name. If you rate a candidate at 35%, then that candidate's cup is 35% full of rating fluid. Empty all of the rating fluid into one big pitcher and use it to completely fill as many cups as possible from highest rated candidate down. Approve the candidates that end up with full cups. This is called "sincere approval" because generically (and statistically) the total approval (over all voters) for each candidate turns out to be the same as the total rating would have been.] Thanks, Forest
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