[EM] Does IRV pass strategic condorcet?

[Jameson Quinn]

If there is a majority Condorcet winner, any voting system that passes the
majority criterion will elect that candidate in a unique strong Nash
equilibrium. But the standard version of chicken dilemma involves a
non-majority Condorcet winner:
40: X
35: Y>Z
25: Z>Y

Y is the CW, but the victory over Z is non-majority, only 35 to 25, because
the X voters are indifferent.

In that case, and (I believe but haven't proven) all other cases with a CW,
rated systems like Approval, Score or (Graduated?) Majority Judgment still
have a strong Nash equilibrium for the CW: Y voters top-rate only Y, while
Z voters top-rate both Y and Z. The problem is that this is no longer
unique; there's another strong Nash equilibrium where Y voters bullet and Z
voters compromise, and if both groups shoot for the equilibrium they
prefer, the result is a non-equilibrium where the Condorcet loser Z wins.

(SODA mostly solves this problem by forcing candidate X to pre-declare a
preference between Y and Z; but that's not the point of this message.)

My question for the list is: can anyone prove, or give a counterexample
for, the proposition that, in IRV, there always  strong Nash equilibrium in
which the CW wins? My suspicion is that it's not true, and I'll be looking
at scenarios myself to see if I can prove it either way, but I thought I'd
open up this interesting puzzle to the list as well.

(This message was inspired by comments on the wikipedia talk page for
Voting system.)

Jameson
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