Rubinstein2005-page141

Rubinstein2005-page141 - October 21, 2005 12:18 master...

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October 21, 2005 12:18 master Sheet number 139 Page number 123 Social Choice 123 Problem 3. ( Easy ) Assume that the set of alternatives, X , is the interval [ 0, 1 ] and that each individual’s preference is single-peaked , i.e., for each i there is an alternative a i such that if a i b > c or c > b a i , then b ± i c . a. Provide an interpretation of single-peaked preferences. b. Show that for any odd n , if we restrict the domain of preferences to single-peaked preferences, then the majority rule induces a “well- behaved” SWF. Problem 4. ( Moderately difficult. Based on Kasher and Rubinstein 1997. ) Who is an economist? Departments of economics are often sharply divided over this question. Investigate the approach according to which the deter- mination of who is an economist is treated as an aggregation of the views held by department members on this question. Let N ={ 1, ... , n } be a group of individuals ( n 3). Each i N “sub- mits” a set E i
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