General Pairwise Strategy

[Mike Ossipoff]

The 3-party Copeland strategy that I described a few minutes ago
wouldn't work with more parties. It would become a mess. Most
likely it would be necessary for voters to use the general pairwise
strategy:

For simplicity, putting it as a 3-candidate example, A, B, &
C, with B as the middle compromise, if the C voters feel that
B is Condorcet winner, that C doesn't have a win, & that
A voters might truncate (truncation, as I said, is always
common in rank-balloting), then their general pairwise
strategy is to rank B equal to A in 1st place. lf, however,
they feel that A voters might order-reverse, then the defensive
general pairwise strategy is for C voters to rank B _over_
C, ranking B alone in 1st place--something that would never
be necessary in Condorcet.

B has a general pairwise strategy too, but it's more complicated.
Well, if it's known that A voters, & not C voters, are inclined to
truncate or order-reverse, then B voters can just make sure they
rank C over A, ensuring that there's no way A can beat C, and
therefore no way A voters can profit by truncation or order-reversal.
Of course the intention to use that strategy would be published
before the election.

But if it isn't known that one side isn't inclined to order-reverse
or truncate, then what is B's general pairwise strategy? It's
a probabilistic strategy, which, as I said, is more complicated:

Find out what the polls say about the 1st choice strength of A
& C, and each B voter uses a chance device, so that the result
is that the number of B voters voting each way  among the
extremes, A & C,ÿ is just right so that no one can predict
whether A beats C or C beats A. This would offer some degree
of deterrence against order-reversal or truncation. Hopefully
voters would be disciplined enough to not truncate when they
know that B voters are using that strategy. Good luck.

For instance, say that the best estimate is:

A: 40%
B: 25%
C: 35%

...for 1st choice strength.

Well, if a number of B voters equal to 5% of the total number
of voters vote C in 2nd place, and the rest of the B voters
vote no 2nd chocie, then no one will know whether A will beat
C or vice-versa. So, that means that 1/5 of the B voters should
vote a 2nd choice: C. So if you're a B voter, drop 5 pieces of
paper into a bag, with an "X" marked on one of them. Draw one
out. If it's the one witht he "X", then vote C 2nd. Otherwise
don't vote a 2nd choice.

***

Obviously the defensive general pairwise strategy of the C
voters is much simpler: Just vote B in 1st place (alone
in defense against order-reversal, or with C in defense
against mere truncation).

***

Except in that special 3-party situation I described earlier,
Copeland doesn't offer anything better than the general
pairwise strategy.

***

Mike
 



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