[EM] A better nonmonotonic rank-count

[MIKE OSSIPOFF]

Markus--

When there's a group that doesn't agree on what voting system to use,
how do you conduct a vote? I suggest the following nonmonotonic
method, which I call "Voter's Choice". Monotonicity is desirable
when it's attainable, but when there isn't agreement on how to vote,
we must take what we can get.

Say we're voting on what voting system to begin using.

Assuming that some of the proposed methods are rank-balloting methods,
voters are invited to rank the proposed methods in order of
preference. If Approval is one of the proposals, then voters are
also invited to vote an Approval ballot, in addition to their
ranking.

We count the ballots by all of the proposed methods. If a voter
didn't vote an Approval ballot, then one can be inferred from his
ranking, as was done in the _Discover_ article: When all we know
about a voter is how he ranks the alternatives, then the 0-info
Approval strategy that maximizes his utility expectation is one that
votes for his favorite half of the alternatives. If someone votes
an Approval ballot but not a ranking, then of course, for rank-method
purposes, that is counted as voting in 1st place all the candidates
for whom he voted on his Approval ballot.

Each voter has one Plurality vote. Your Plurality vote goes to the
winner of the method that you've ranked highest. If you've only
voted an Approval ballot, then you give a Plurality vote to the
winners by all of the methods to which you've given an Approval vote.

The method with the most Plurality votes wins.

The advantage of Voter's Choice is that if you feel that a certain
voting system is the one that would do the best job of picking the
best compromise that you can get, then that's the method that you'd
want to guide where you give your Plurality vote.

Though that procedure is unavoidably nonmonotonic, hopefully the
winning method in that count would be a monotonic method, and that
method would be used in subsequent elections.

Mike Ossipoff



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