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Unformatted text preview: h. The decision maker orders all alternatives from left to right and selects the median. Problem 2. ( Moderately difFcult ) Let us say that you have to make a choice from a set A . Does it matter whether (a) you make a choice from the entire set or (b) you Frst partition A into the subsets A 1 and A 2 , then make a selection from each of the sets and Fnally make a choice from the elements you selected from among A 1 and A 2 ? a. ormulate a path independence property. b. Show that the rational decision maker satisFes the property. c. ind examples of choice procedures that do not satisfy this property. d. Show that if a (single-valued) choice function satisFes path indepen-dence, then it is consistent with rationality. e. Assume that C is a (multivalued) choice function satisfying path inde-pendence. Can it be rationalized by a preference relation?...
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- Fall '10