[EM] A Proportionally Fair Consensus Lottery for which Sincere Range Ballots are Optimal

[Jobst Heitzig]

Even simpler is this:

Method "Top-3 approval sincere runoff" (T3ASR)
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1. Each voter separately supplies
   a "nomination" approval ballot and a "runoff" range ballot.

2. From all "nomination" ballots, determine
   the options A,B,C with the top-3 approval scores a>b>c.

3. Let p be the proportion of nomination ballots
   which approve of C but not of B.

4. If on at least half of all "runoff" ballots we have a rating
   r(A) > p*r(C) + (1-p)*r(B), then option A wins.

5. Otherwise draw a "nomination" ballot.
   If it approves of C but not of B, C wins, otherwise B wins.

Most of the time, this will elect one of the top-2 approval options, and
only rarely the 3rd placed.

One can then also compute and publish some kind of "index of sincerity"
by comparing the submitted approval and range ballots.

The method is majoritarian, since any majority can rule by bullet voting
on both ballots.

Yours, Jobst