# [EM] Approval strategy puzzle

MIKE OSSIPOFF nkklrp at hotmail.com
Thu Mar 1 13:41:49 PST 2001

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

As I was saying, vote only for A, if you're letting them flip coins.

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

For each of the 8 equiprobable ways that those 3 people could all vote,
determine the effect, on the worth to you of the result, of voting for
B, in addition to A. That means considering the instances, among those
8 voting results, where you'd make or break a tie by voting for B.
The worth, to you, of a tie is the average of your ratings for the
tie members. If the sum of the worth of how you'd change the result by
voting for B is positive for all those 8 situtations, vote for B. If
it's negative, then don't. It's negative.

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

Replace the 70 with Ub. Write expressions for how voting for B
changes the worth of the outcome for you in those 8 instances.
Add the expresssions up. Solve for Ub.

Mike Ossipoff

>
>  -- Richard
>
>

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