[EM] Re: serious strategy problem in Condorcet, but not in IRV?

[James Green-Armytage]

Dear election methods fans,

I have noticed one small bright point in this situation which I overlooked
before. Let's think of this as a voting game with multiple rounds, or
perhaps a series of polls leading up to an actual election.

Round one / sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B
 
A wins. B voters have incentive for offensive order reversal.

46: A>B
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 90:10

B wins.

Here is what I neglected before: At this stage, the 5 C>A voters have an
incentive to change their preferences to A>C, resulting in the election of
A, because they favor A over B. 

46: A>B
5: A>C
44: B>C
5: C>B

A:B = 51:49
A:C = 51:49
B:C = 90:10

At this point neither the B>A voters nor the C>B voters (nor of course the
C>A voters) can do anything to get additional gain. So the voting game has
reached a sort of equilibrium, with A, the sincere Condorcet winner, as
the actual winner, cheerfully enough.

Of course, a real situation would not be so tidy and deterministic.
For example, if this was a series of polls leading up to an election.
Sure, the C>A voters switching to A>C would settle the matter. But there
is a possibility that they might prefer to hold on and see what happens
with the chicken game between A>B and B>A voters, hoping that neither will
swerve and C will end up with the victory after all. Another gamble
between risk and reward.

Anyway, this represents a slight improvement for my fairly grim example,
but I will say that the basic problem is still there, and still fairly
unsettling.

James