# [EM] An interesting scenario (spoilers, utility)

Kevin Venzke stepjak at yahoo.fr
Wed Feb 29 17:32:26 PST 2012

```Hi Jameson,

De : Jameson Quinn <jameson.quinn at gmail.com>
>À : Kevin Venzke <stepjak at yahoo.fr>
>Cc : election-methods <election-methods at electorama.com>
>Envoyé le : Mercredi 29 février 2012 15h35
>Objet : Re: [EM] An interesting scenario (spoilers, utility)
>
>
>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.
>
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>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.
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>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 B>C>A voters are at 0.2.

I think the unintuitive explanation is that A wins often enough to concern these voters. The math for the settings
used doesn't allow two A blocs to ever beat four C blocs. But the scenario has great difficulty stabilizing compared
to under the other methods, and voters occasionally make errors that allow A and B to win sometimes.

This may prevent the scenario from saying much about Approval, but it probably couldn't say that much about it
anyway.

What I think is interesting is the glimpse at what it might look like if you get to sacrifice something in exchange
for greater utility. I feel very torn as to whether this outcome is "good," whether perhaps it's bad but creates
desirable candidate incentives (i.e. cater to the median better), or whether it does the opposite (don't run if you
won't win), or whether the scenario is so unattractive that voters wouldn't put up with it. Etc.

>
>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.
>
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>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 about B>C.
>
I think in real life, A wouldn't be able to win, so that they would have to vote for B in order to affect the race. I
don't think it would depend on what the B>C voters plan to do, though those voters certainly wouldn't vote for
C if A has no chance.

Kevin
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