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Unformatted text preview: i , . . . , n ) , is a dictatorship. 3. Another related concept is the following. Let Ch ( 1 , . . . , n ) be a function that assigns a choice function to every proFle of orderings on X . We say that Ch satisFes unanimity if for every ( 1 , . . . , n ) and for any x , y A , if y i x for all i then, x / Ch ( 1 , . . . , n )( A ) . We say that Ch is invariant to the procedure if, for every proFle ( 1 , . . . , n ) and for every choice set A , the following two approaches lead to the same outcome: a. Partition A into two sets A and A 00 . Choose an element from A and an element from A 00 and then choose one element from the two choices. b. Choose an element from the unpartitioned set A . Dutta, Jackson, and Le Breton (2001) show that only dictatorships satisfy both unanimity and invariance to the procedure. Bibliographic Notes Recommended readings : Kreps 1990, chapter 5; Mas-Colell et al. 1995, chapter 21....
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- Fall '10