[EM] Arrow's Theorem - The Return (again)

[Alex Small]

John B. Hodges said:
> Alex's example above shows the possibility of a "spoiler effect",  i.e.
> in a two-person race between A and B, A wins, but adding C to  the race
> gives the victory to B. Those who vote for C give the
> election to their last choice, so if they understood the situation in
> advance, they would abstain from voting for their first choice.


No.  There is never a disincentive to abstain from approving your first
choice if you use approval voting.  Those who voted for C decided NOT to
approve their second choice as well.  Maybe they had inadequate polling
data and didn't realize what would happen if they abstained.  Maybe they
wanted to punish A for not being good enough.  That is their right, and I
will not criticize people who withhold votes from candidates whom they
find to be unworthy.

I normally think of the spoiler effect as happening when the addition of a
new candidate changes the outcome without the new candidate winning, and
all voters voting sincerely.  In that case, any system that flunks IIA has
the potential for a spoiler effect.  However, it's much less severe in
approval because well-informed voters can make sure there is no
"spoiling."  It's only if they follow sincere but uninformed information
that they get "spoilage."

I'm going to post more on this in the next few weeks.  I'm examining Nash
equilibria in 3-way Approval races.  I'm looking at situations where
everybody approves one of the top 2, so that we simulate what's likely to
happen in response to polls.  Interesting things can happen when there's
no CW.  More on that in a few weeks.



Alex