Rubinstein2005-page56 - 12:18 38 master Sheet number 54...

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October 21, 2005 12:18 master Sheet number 54 Page number 38 38 Lecture Three Problem 3. ( Easy ) Check whether the following two choice functions satisfy WA: C ( A ) ={ x A | the number of y X for which V ( x ) V ( y ) is at least | X | / 2 } , and if the set is empty then C ( A ) = A . D ( A ) ={ x A | the number of y A for which V ( x ) V ( y ) is at least | A | / 2 } . Problem 4. ( Moderately difficult ) Consider the following choice procedure. A decision maker has a strict ordering ± over the set X and he assigns to each x X a natural number class ( x ) interpreted as the “class” of x . Given a choice problem A he chooses the element in A that is the best among those elements in A , that belong to the “most popular” class in A (that is, the class that appears in A most often). If there is more than one most popular class, he picks the best element from the members of A that belong to a most popular class with the highest class number. a. Is the procedure consistent with the “rational man” paradigm?
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