robert bristow-johnson wrote:
because *both* the winning votes is tied and the margins is tied. what
else is there?
i wonder if it would be better to first rank each pair according to
Margins and then, in the case of tie of Margins, Winning Votes are used
to break the tie to determine which pair result has priority over the
other.
for some reason, i like Margins because it is the product of the percent
spread (which indicates how decisive a defeat is) times the number of
voters participating (which indicates how important the pair election
is). that product is a natural measure for how important and decisive a
pairwise defeat is. Winning Votes, all by itself, should not be the
sole (or primary in the present case) decider. what if there is a lot
of voters, but the pair-election is close (say a defeat by 1 vote)?
it's not a decisive defeat, but Winning Votes would say it is. i think
Margins is more salient than Winning Votes.
Note, though, that methods that do Margins first may violate the
Plurality criterion. In other words, it may be the case that, in a
Margins election, a candidate wins when some other candidate has more
first place votes than the winner has any-place votes.
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