[Election-Methods] A utility simulation for a certain scenario, part 2

[Kevin Venzke]

Hello,

I implemented a couple additional scenarios.

Scenario: Same as the original, except no B voters will vote B>A. They vote
either B or B>C (two randomly-sized blocs then scaled to fit the B
faction's total allotment).

If B is worth only 10, no matter whether C voters vote for B:
WV, margins, IRV, and FPP: vote A>B
Approval: vote A

If B is worth 80, no matter whether C voters vote for B:
WV: vote A>B
Approval: vote AB
Margins, IRV, and FPP: vote B>A

Interesting to look at where exactly it becomes advantageous to use
favorite betrayal. For Margins it seems to be when B is worth at least
about 74. For IRV B needs to be worth only about 19. For FPP B has to be
worth more than 50 (the average of A and C), since A's chances of winning
are still good in this scenario. WV never reaches this point since if the A
faction votes A>B, a C victory is impossible, so there is no reason to
betray A to secure a B victory.


Scenario: The requirement that the B faction be the smallest is dropped.
Instead, the C faction is required to be the largest, and the B voters
won't vote B>C. They only vote B>A or B.

If B is only worth 10, and the C voters bullet vote:
WV and Approval: vote A
Margins and IRV: vote A>B
FPP: vote B>A

If B is worth 10, and the C voters vote C>B:
WV, margins, and IRV: vote A>B
Approval: voting A or AB makes no difference (B will win)
FPP: vote B>A

So here, in contrast to the example in my previous post, under WV one may
want to truncate depending upon what the C faction is predicted to do.

This is essentially the scenario where the A and B factions are allies
against C. WV is more likely to give the election to A or B as long as
there is enough cooperation for one of the candidates to defeat C. It makes
sense for the A faction to defect and hope for votes from B, especially if
B is such a poor compromise. When the factions don't cooperate well (such
as when the candidate who defeats C is defeated in turn by the allied
candidate), margins is more likely to elect C, reducing the expected
benefit of truncating.

If B is worth 80, no matter what the C voters do:
WV and margins: vote A>B
Approval: vote AB
IRV and FPP: vote B>A

That's it for now. I hope it's of some interest.

Kevin Venzke


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