[EM] How to find the voters' honest preferences

[Forest Simmons]

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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