# [Election-Methods] A utility simulation for a certain scenario

Kevin Venzke stepjak at yahoo.fr
Sat Dec 15 22:11:28 PST 2007

```Hello,

I was interested in the earlier question of when one should truncate under
various methods, so I wrote a little simulation.

The scenario is that we are trying to maximize the expectation of the
faction supporting candidate A. To them, A is worth 100, C is worth 0, and
B is worth something in-between. The A faction can either vote A
(bullet-vote), A>B, or B>A (compromise strategy). The C faction will vote
either C or C>B.

I wrote the scenario so that the three factions are randomly sized, but
none is allowed to make up a majority, and the B faction is the smallest.
The B faction is divided into three groups of random size that vote B>A, B,
or B>C respectively.

So, here are the recommendations I found for the A faction:

If B is worth only 10 and C voters will bullet vote:
WV and margins: vote A>B
Approval: vote A
IRV and FPP: vote A or A>B, no difference

If B is worth 10 and C voters will vote C>B:
same as above, except:
Margins: vote A

If B is worth 50 (halfway between A and C's values), no matter what C
faction does:
WV and margins: vote A>B
Approval: vote A
IRV and FPP: vote A or A>B, no difference

If B is worth 80, and C voters will bullet vote:
WV and margins: vote A>B
Approval: vote AB
IRV and FPP: vote B>A

If B is worth 80, and C voters will vote C>B:
same as above, except:
Approval: vote A

The most interesting difference was between WV and margins in the case that
B is only worth 10.

If the C voters will bullet vote, under WV the A voters have expectation 50
if they bullet vote also. By voting A>B, they boost their expectation to
55. Under margins the boost is from 50 to 75! Adding the B preference is
unusually likely to cause A to be elected. In 24% of these expectation 75
elections, more voters rank C and don't rank A, than rank A at all, but A
still wins.

If the C voters vote C>B, then under WV the choice is between expectation 5
(bullet voting) and 10 (ranking B). Under margins the choice is between 14
and 10. If A voters don't vote for B, margins may still elect A. It's not
very likely, but B is such a poor compromise choice that it's worth it.

Note that under WV, the optimal strategy doesn't depend on estimating what
the C voters will do.

I plan to tinker with the scenario tomorrow and see if I can find anything
else of interest.

Kevin Venzke

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