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\Strength can be weaknessquot;. A three-person committee has to choose a winnerfor a national art prize. After some debate, there are three...
Strength can be weakness". A three-person committee has to choose a winnerfor a national art prize. After some debate, there are three candidates still under consideration:a woman who draws antelope in urban settings, a man who makes rectangularlead boxes, and a woman who sculpts charcoal. Lets call these candidates a, b and c;and call the committee members 1,2 and 3. The preferences of the committee membersare as follows: member 1 prefers a to b and b to c; member 2 prefers c to a and a to b;and member 3 prefers b to c and c to a. The rules of the competition say that, if theydisagree, they should vote (secret ballot, one member one vote) and that, if and only ifthe vote is tied, the winner will be the candidate for whom member 1 voted. Thus, itmight seem that member 1 has an advantage.(a) Consider this voting game. Each voter has three strategies: a, b, or c. For eachvoter, which strategies are weakly or strictly dominated? [Hints. Be especially carefulin the case of voter 1. To answer this question, you do not need to know the exactpayos: any payos will do provided that they are consistent with the preference ordersgiven above. To answer this question, you do not have to write out matrices].(b) Now consider the reduced game in which all weakly and strictly dominatedstrategies have been removed. For each voter, which strategies are now weakly orstrictly dominated? What is the predicted outcome of the vote? Compare this outcometo voter 1's preferences and comment.
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