[EM] Majority winner set

[MIKE OSSIPOFF]

Markus defined Beatpath GMC as follows:


    "X >> Y" means that an absolute majority of the voters
    strictly prefers candidate X to candidate Y.
    "There is a majority beat path from X to Y" means that
    (1) X >> Y or
    (2) there is a set of candidates C[1],...,C[n] with
        X >> C[1] >> ... >> C[n] >> Y.

    If there is a majority beat path from candidate A to
    candidate B and no majority beat path from candidate B
    to candidate A, then candidate B must not be elected.

I reply:

It seems to me that no method can meet that criterion. Say, for instance,
that the method is BeatpathWinner, defined in terms of actual voted
preferences. Maybe the voter believe that they have a situation where
they need defensives truncation, and so they don't vote all of the
preferences that they feel. (It's also possible that some voters
merely might not have time to rank all of the candidates, or don't
feel like expressing preferences for disliked candidates over more
disliked ones--there are some voters who might feel that way).

Then those people's preferences won't translate into actual voted
preferences on the BeatpathWinner ballots. BeatpathWinner is defined
in terms of voted preferences rather than felt preferences, and
your criterion is defined in terms of felt preferences. You told me
that a criterion shouldn't be defined in that way. Of course you
could specify that if some voters have certain sincere preferences and
vote sincerely, then a certain result must happen. In that way your
criterion would be meetable, without being met by Plurality, as it
would be if you merely defined it in terms of voted preferences.


Mike Ossipoff


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