[EM] An interesting scenario (spoilers, utility)

Jameson Quinn jameson.quinn at gmail.com
Wed Feb 29 13:35:28 PST 2012

```This is indeed an interesting scenario. Something is particularly weak
about those B>C preferences. It could be one of two things:

1) Maybe you're using some kind of trimmed or decaying utility function,
where the difference between a candidate who's 2/3 units away and one who's
1 unit away is negligible. Thus, your A voters are like Nader voters; so
far out of the mainstream that the other two candidates appear more similar
than they really are. So they bullet vote, holding out for a tiny chance of
victory. The rest follows; the hapless B>A voters give A a vote, to prevent
the likely C win; the B>C voters thus vote for C to ensure A doesn't win;
and C's win is almost guaranteed.

2) Depending what you mean by "six factions proportionally from -1 to 1",
the B>C>A voters could have tiny B>C preferences. They're either at 0.2 (if
the factions are evenly-spaced points), which puts them .13333 from B and
.26  from C; or they're at 0.16666 (if the factions are the center of
evenly-spaced line segments) which puts them .16666 from B and .22666 from
C, a difference of only 0.06.

In the second case, the B=(>)C>A votes cause the A>B=(>)C votes and not
vice versa. But in either case, the two blocs together form an equilibrium;
neither has much motive to change until the other one does.

I wouldn't be surprised if there is an alternate equilibrium where the A
voters approve B, and a more traditional chicken dilemma ensues.

The funny thing is that this is both a chicken dilemma, and precisely the
opposite of a chicken dilemma, at the same time. A's bullet vote could be
seen as trying to provoke a chicken dilemma between B and C, but since B
voters are not unified on their second choices, the fight ends up being
played out between B voters, not between B and C. Or you could say that C
is trying to cause a chicken dilemma between B and A, and, with the help of
some extremely weak-willed C>B voters, is succeeding brilliantly.

Anyway: in real life, I think that the A voters would be able to see that
if they changed, then the B>C voters would change, and so the A voters
would only continue to bullet vote if they really were largely indifferent

Jameson

2012/2/28 Kevin Venzke <stepjak at yahoo.fr>

> 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
> ----
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>
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