[EM] Condorcet question - why not bullet vote?

[Chris Benham]

Peter,

If I just bullet vote in a Condorcet election, then I increase the chances
of my candidate being elected.

Bullet voting in an election using a method that complies with the Condorcet criterion does I suppose
somewhat increase the chance of your candidate being the Condorcet winner.

But all Condorcet methods fail Later-no-Help, and in some this effect is sufficiently strong for the method
to have a "random fill" incentive.  That means that if you know nothing about how other voters will vote
you are probabilistically better off by strictly ranking all your least preferred candidates.

46: A>B
44: B
10: C

Here A is the CW, but if the 44B voters change to B>C then Schulze(Winning Votes) elects B.

Schulze (WV) also has a zero-info. equal-rank at the top incentive. So say you know nothing about
how other voters will vote and you have a big gap in your sincere ratings of the candidates, then your
best probabilistic strategy is to rank all the candidates in your preferred group (those above the big
gap in your ratings) equal-top and to strictly rank (randomly if necessarily) all the candidates below
the gap.

Your question seems to come with assumption that the voter doesn't care much who wins if her favourite
doesn't.

Q: In this case why should any voter not bullet-vote?

The voter might be mainly interested in preventing her least preferred candidate from winning. Bullet
voting is then a worse strategy than ranking that hated candidate strictly bottom.

Another Condorcet method is  Smith//Approval(ranking). That interprets ranking versus truncation as
approval and elects the member of the Smith set (the smallest subset S of candidates that pairwise beat
any/all non-S candidates) that has the highest approval score.

(Some advocate the even simpler Condorcet//Approval(ranking) that simply elects the most approved
candidate if there is no single Condorcet winner.)

In the example above the effect of the 44B voters changing to B>C is with those methods to make C
the new winner.

Those methods do have a truncation incentive, so then many voters who are mainly interested in 
getting their strict favourites elected will and should "bullet vote".

What is wrong with that?

Chris Benham



 


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.    My argument starts:  If I vote for a candidate who has >50% of the votes, then it does not matter  if there is a second or third choice.  If my prefered candidate A gets <50%  of the votes, then it makes sense to  support a second choice candidate B.  However if the supporters of B only bullet vote, then maybe B's supporters  get an advantage over A?  ... at this point I realize, that I don't know enough about Condorcet and/or  Schulze to answer the question.    Why is it not rational to
 bullet vote in a Condorcet election if you are  allowed not to rank some candidates?  I guess you have discussed this question a zillion of times, so please  forgive my ignorance.    Maybe you could help me out with this one.    Peter