Unformatted text preview: isfying the above axioms. e. Are the above three axioms independent? Problem 2. ( Moderately difFcult ) N individuals choose a single object from among a set X . We are interested in functions that aggregate the individuals’ recommendations ( not prefer-ences , just recommendations!) into a social decision (i.e., F : X N → X ). Discuss the following axioms: • Par : If all individuals recommend x ∗ then the society chooses x ∗ . • I : If the same individuals support an alternative x ∈ X in two proFles of recommendations, then x is chosen in one proFle if and only if it chosen in the other. a. Show that if X includes at least three elements, then the only aggre-gation method that satisFes P and I is a dictatorship. b. Show the necessity of the three conditions P , I , and | X | ≥ 3 for this conclusion....
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- Fall '10
- Social welfare function, Social Choice and Individual Values