[EM] Condorcet question - why not bullet vote

[Kristofer Munsterhjelm]

Peter Zbornik wrote:
> Dear all, dear Markus Schulze,
> 
> I got a second question from one of our members (actually the same guy 
> which asked for the first time):
> If I just bullet vote in a Condorcet election, then I increase the 
> chances of my candidate being elected.
> If I have a second or third option, the chances of my prefered candidate 
> to win is lowered.
> Q: In this case why should any voter not bullet-vote?
> I have some clue on how to answer, but not enough for an exhaustive answer.

I would say that the answer is contingency. Say that your favorite is A, 
and it's uncertain whether B or C is more popular, but you prefer B to 
C. Then, bullet-voting A might give you A instead of B (which would be 
good), but it might also give you C rather than B (which would be bad) 
because you falsely reported that it doesn't matter to you whether B or 
C wins.

A bit more formally, consider this: C is the current CW and B is just 
short of beating him, while A is far behind. If two voters vote A > B = 
C, then nothing happens, but by voting A > B > C, B now beats C and wins.

Also note that voting for additional candidates doesn't harm the outcome 
unless you, by doing so, set up or help others set up a cycle. If X is 
the CW and beats others by a lot of votes, then voting others ahead of X 
doesn't itself do anything harmful; the only potential for harm occurs 
in the domain of the cycle.

Similarly, for the "advanced methods" (Schulze, Ranked Pairs, and so 
on), ranking candidates that end up outside of the Smith set doesn't do 
any harm either, because these methods satisfy Independence of 
Smith-dominated alternatives (also called "local IIA").

To sum all of that up: bullet-voting is like driving straight in a game 
of Chicken. Sure, you might benefit by doing so, but you may also crash 
and get a very bad outcome. In addition, the advanced methods pass 
criteria that both narrow down the situations where sincerity will 
backfire, as well as the degree to which it would do so; an 
ISDA-compliant method must obviously elect from the Smith set in the 
first place, for instance.