After talking about that Approval should be DSV, I thought of this
method. It is:
- Voters submit ranked ballots.
- First count as in Plurality. Candidates that are tied at top rank may
either get one point each, or 1/k if there are k tied candidates - I
don't know which would be better.
- Call the Plurality winner "X" and the runner-up "Y".
- Using the Plurality data and the original ballots, count each ballot
as if he voter employed approval strategy A. That is, approve all
candidates ranked ahead of X, and X if he is ranked ahead of Y.
- The candidate with the highest approval score wins.
Would that method be any good? I don't know. It probably wouldn't be
monotone, but it is quite simple. Since it's "instant", it would have
the same problems with regards to ordinary strategic approval as IRV has
with regards to exhaustive runoff.
Finally, being a ranked method, it would be subject to Arrow's theorem.
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