[EM] Experimental data on chicken dilemma (post 1 of N: Forsythe 1996)

[Jameson Quinn]

Forsythe [1] conducted elections with a simple divided majority scenario,
using money to induce preferences. Faction sizes were 4,4, and 6; each
subject was in 3 successive groups and 8 elections in each group. There
were 96 elections for each of 3 methods: Plurality, Approval, and Borda.
(48 without polls, and 48 with polls). They were mostly interested in
confirming Duverger's law and didn't really analyze things in terms of the
chicken dilemma under Approval.

They publish their data in a singularly useless format, but here's what I
see in the tables for approval:
without polls:
minority wins: 5/48
minority in 2-way tie: 7/48
minority in 3-way tie: 2/48
Total minority expected wins: 19% (was 26% for approval)

with polls:
MiW: 2/48
Mi2T: 10/48
Mi3T: 0
TMiEW: 30% (17% for approval)

Probability of bullet voting by a divided majority member after an election
where the minority candidate led: 37%; after the minority candidate
trailed: 53%
After polls, those numbers were 51% and 65%.
Those numbers should be below 50% if the minority candidate is to safely
lose (ie, what Ossipoff calls SFR).

What I read from the above is that if you were to scale these elections up
to large numbers of voters, and maintained the perfect balance between the
wings of the divided majority, the chicken dilemma would happen a
significant but not overwhelming portion of the time. Large numbers make
cooperation more difficult if anything.

I've found several other papers which have some useful data of this kind
and I'll talk about them here as I can.

Jameson

[1] Forsythe, Robert, Thomas Rietz, Roger Myerson, and Robert Weber. “An
Experimental Study of Voting Rules and Polls in Three-candidate Elections.”
*International Journal of Game Theory* 25, no. 3 (1996): 355–383.
doi:10.1007/BF02425262.
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