Hi Jameson,
De : Jameson Quinn <jameson.qu...@gmail.com>
>À : Kevin Venzke <step...@yahoo.fr>
>Cc : election-methods <election-meth...@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.
>
>
>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 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.
>
>
>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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