[EM] Correction, 0-info strategy

[MIKE OSSIPOFF]

EM list--

When I wrote last night, I forgot that there are 2 ways that
a voter can change the outcome of a pairwise method. I assumed
it would be by reversing the direction of a pair-comparison
(which of course would actually require 2 voters, not 1).
I forgot that 2 same-voting voters could also change the outcome
by changing the outcome of the circular tie solution. That
makes for even more of those equally-likely situations that
must be considered.

So, for each configuration of pairwise defeats, one would
consider each way that one could pick a pairwise defeat to be
the one that that pair of same-voting voters could reverse the
direction of. And also one would consider each way one could
pick 2 pairwise defeats to be the ones whose wv is so close
that that pair of voters could reverse the magnitude comparison
between those two wv numbers. Of course if there are many candidates,
and the method drops defeats, and several defeats could be
dropped before getting a winner, then you could influence
the 1st drop, the 2nd one, or 3rd, etc.

***

With any pairwise method, there are situations where different
people's strategies can influence eachother's strategy calculations.
With Margins & BeatsAll//IRV it's especially difficult to ignore,
because something as innocent & ordinary as truncation can
work like an offensive strategy. I'd be rather doubful about
any strategy calculation for Margins or BeatsAll//IRV that
doesn't treat it as a game-theory problem. Maybe the strategy-
interaction could be reasonably ignored in Condorcet in the
0-info case, and otherwise too, if we assume no one offensively
order-reverses.

Mike Ossipoff

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