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Consider a committee of Ann, Bob, and Carol that is choosing between three alternatives, {x, y, z}. Player i's preferences are represented by the...
Consider a committee of Ann, Bob, and Carol that is choosing between three alternatives, {x, y, z}. Player i’s preferences are represented by the ordering i . Suppose the three player’s preferences are: x A y A z. y B z B x. z C x C y. Each player has complete and transitive strict preference. Suppose the committee decides to operate on the basis of majority-rule: the committee strictly prefers alternative a to alternative b if a strict majority prefer alternative a to b. Let M be the committee’s preference. Based on the preferences of the committee members,
(a) Is M complete and transitive?
(b) Can you represent committee preferences by a utility function?
