[EM] An interesting scenario (spoilers, utility)

[Kevin Venzke]

Hello,

I have been adding some code to help investigate cases where Approval
shows greater "perception of spoiler" than, say, IRV. To make the 
scenarios easier to visualize I just allocated six voting factions 
proportionately along 1D, positions ranging from -1 to 1.
 
I found an interesting case with the candidate positions:
.939, 0.333, -.06  (call them A, B, C)
 
Approval showed perception of spoiler as 27%, whereas IRV, TTR, and FPP
showed none. So I checked to see if it was consistent and what was 
happening.
 
With six blocs the scenario looks roughly like this (with the pipe
indicating the location of average utility for the bloc):
~3 C>B | A
~1 B>C | A
~1 B>A | C
~1 A | B>C
 
Under IRV, all votes were sincere. Under FPP and TTR, the lone A bloc
was compromising and voting for B. The result was that the sincere CW
(either C or B) was always winning and no one perceived spoilers.
 
Under Approval, the C>B voters bullet-voted, the two B blocs voted for
their top two candidates, and the A bloc bullet-voted.
 
(A much rarer outcome had the B>C faction bullet-voting, with the B>A
and A factions voting for both A and B, giving the same result as the
other three methods. I think it's clear that this outcome was rarer
because the B>C voters are happier with settling for C than the A 
voters are with settling for B.)
 
The result of this is that Approval was only electing the sincere CW
half the time. Instead of alternating between C and B winning, C won by
far the most often. B or A won rarely (and, I'd say, largely thanks
to the AI confusion that results from one candidate winning most of
the time).
 
Note that C is easily the closest candidate to the median. Even when 
B has a majority win over C, B is still not likely to be the utility 
maximizer. Approval's success rate at electing the utility maximizer 
was thus nearly perfect (instead of 50%).
 
I'm not sure what I think of this personally. I'm sure this scenario
isn't any kind of general rule for Approval, but suppose that it was?
Would it be a viable trade-off, to elect the utility maximizer more
often, in exchange for more complaints about spoiled elections?
 
Kevin Venzke