Rubinstein2005-page55 - h The decision maker orders all...

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October 21, 2005 12:18 master Sheet number 53 Page number 37 Problem Set 3 Problem 1. ( Easy ) Discuss the compatibility of the following “procedural elements” with the “rational man” paradigm: a. The decision maker has in mind a ranking of all alternatives and chooses the alternative that is the worst according to this ranking. b. The decision maker chooses an alternative with the intention that another person will suffer the most. c. The decision maker asks his two children to rank the alternatives and then chooses the alternative that is the best “on average.” d. The decision maker has an ideal point in mind and chooses the alter- native that is closest to the ideal point. e. The decision maker looks for the alternative that appears most often in the choice set. f. The decision maker always selects the Frst alternative that comes to his attention. g. The decision maker searches for someone he knows who will choose an action that is feasible for him.
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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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