Consider a committee of Ann, Bob, and Carol that is choosing between three alter

Question

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?

4. Consider a committee of Ann, Bob, and Carol that is choosing between three alternatives, {, y, Player i's preferences are represented by the ordering Suppose the three player's preferences are: Each player has couplete and trasitive strict 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?

Explanation / Answer

a)No, M is not complete and transitive.

In economic preference, we say that a relation is complete if and only if for all A,B we have A>B or B<A or both. So consider A,B,C such that A>B and B>C . Then the relation is not complete since we do not have explicit relationship.

b) No, the committe preference can not be represented by a utility function.

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