Rubinstein2005-page46

Rubinstein2005-page46 - 12:18 28 master Sheet number 44...

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October 21, 2005 12:18 master Sheet number 44 Page number 28 28 Lecture Three Proof: Define by x y if x = C ( { x , y } ) . Let us first verify that the relation is a preference relation. Completeness : Follows from the fact that C ( { x , y } ) is always well defined. Transitivity : If x y and y z , then C ( { x , y } ) = x and C ( { y , z } ) = y . If C ( { x , z } ) = x then C ( { x , z } ) = z . By and C ( { x , z } ) = z , C ( { x , y , z } ) = x . By and C ( { x , y } ) = x , C ( { x , y , z } ) = y , and by and C ( { y , z } ) = y , C ( { x , y , z } ) = z . A contradiction to C ( { x , y , z } ) ∈ { x , y , z } . We still have to show that C ( B ) = C ( B ) . Assume that C ( B ) = x and C ( B ) = x . That is, there is y B so that y x . By definition of , this means C ( { x , y } ) = y , contradicting . What Is an Alternative Some of the cases where rationality is violated can be attributed to the incorrect specification of the space of alternatives. Consider the following example taken from Luce and Raiffa (1957): A diner in a restaurant chooses chicken from the menu { steak tartare , chicken } but chooses steak tartare from the menu { steak tartare , chicken , frog legs } .
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