Q5 "Your strength can be your weakness" A three-person committee has to choose a winner for...

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Q5 Your strength can be your weakness A three-person committee has to choose a winner for a national art prize. After some debate, e are three candidates still under consideration: a woman who draws antelope in urban set- tings, a man who makes rectangular lead boxes, and a woman who sculpts charcoal. Lets call these candidates a, b and e; and call the committee members 1, 2 and 3. The preferences of the nmittee members are as follows: member I prefers a to b and b to c: member 2 prefers c to a and a to b: and member 3 prefers b to cand c to a. The rules of the competition say that, if they disagree, they should vote (secret ballot, one member one vote) and that, if and only if ft vote is tied, the winner will be the candidate for whom member I voted. Thus, it that member 1 has an advantage might seem

(a) Consider this voting game. Each voter has three strategies a, b, or c. For each voter which strategies are weakly or strictly dominated? Hints. Be especially careful in the case of voter 1. To answer this question, you do not need to know the exact payoffs: any payoffs will do provided that they are consistent with the preference orders given 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 dominated strategies have been removed. For each voter, which strategies are now weakly or strictly dominated? What is the predicted outcome of the vote? Compare this outcome to voter Is preferences and comment Hint: When answering this question. it is useful to construct the best responses for each player For player 1, the best response fanction oill look ke WTC For example, if Player and Player & both chose a, then a is the winner no matter what Player 1 does, its best response is to chose anything In contrast, if Player 2 votes for a and Player 3 votes for b, then Player 1 is better off by voting for a (voting for b or c is strictly worse for Player 1)

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Q5 "Your strength can be your weakness" A three-person committee has to choose a winner for...

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