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

[Adam Haas Tarr]

>		A buries	A truncates	A sincere
>B buries	C wins	C wins	B wins
>B truncates	C wins	C wins	AB equal
>B sincere	A wins	AB equal	AB equal

Truncation is a dominated strategy (it never beats sincerity).  
So you can basically get rid of Truncation and just look at 
burying vs. sincerity.

There are two Nash equilibrium.  Each involves one side burying, 
and the other side truncating.  In these cases, neither side can 
improve their odds by changing their strategy (one side has 
guaranteed victory, and the other side can only make things 
worse for itself).

Both sides have an incentive to claim they will bury, whether 
they do or not.  Both sides have an incentive to bury, AS LONG 
AS they think the other side will not.

Say you're an A supporter.  I'll denote your utility for A as 
U_a, B as U_b, and C as U_c.  I'll denote the probability that B 
voters will bury as T.  I'll denote your probability of winning 
the sincere contest between A and B as P_a.  Your expected 
return on burying is:

T(U_c) + (1-T)(U_A)

And your expected return on sincerity is:

T(U_b) + (1-T)(P_a*U_a + (1-P_a)U_b)

so, you should bury when the first number is bigger than the 
second.

The ironic effect of this is that, if you really want everyone 
to vote sincerely, the best thing is for everyone to loudly 
proclaim that they are going to bury their second-favorite.  
This way, nobody really has the incentive to bury (assuming they 
do hate C).  If everyone promises to play nice, then you 
actually have an incentive to backstab once you're behind the 
curtain.

--------

Really, once you start talking about complex strategic options 
like this, a lot of the voting theory arguments go out the 
window.  IRV is basically equally vulnerable in this case, I 
think.  The fact that you have to bury in a "more violent" 
fashion is mostly irrelevant to any voter who is willing to 
consider this sort of strategy.

-Adam