[EM] Approval strategy puzzle

[Richard Moore]

Last night I started playing around with a very simple
example of an approval election and I'd like to put it
to the group as a strategy puzzle:

An approval election is held with three candidates (A, B, C)
and four voters. The first three voters have the following
probabilities of voting various ways:

Voter 1    A (50%) or AB (50%)
Voter 2    B (50%) or BC (50%)
Voter 3    C (50%) or CA (50%)

Assume ties will be broken by a fair and random lottery.

1. As the fourth voter, with utilities A = 100, B = 70, and C = 0,
how should you vote: A or AB?

2. Explain how you arrived at the answer to #1.

3. At what B utility (keeping A and C constant) do your A and
AB votes' strategic values become equal?

 -- Richard