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Unformatted text preview: ( x , y ) of distinct elements in X exactly one of the three values x y , y x or I so that for any three different elements x , y and z in X , the following two properties hold: No order effect : f ( x , y ) = f ( y , x ). Transitivity : if f ( x , y ) = x y and f ( y , z ) = y z then f ( x , z ) = x z and if f ( x , y ) = I and f ( y , z ) = I then f ( x , z ) = I . Note again that I , x y , and y x are merely symbols representing verbal answers. Needless to say, the choice of symbols is not an arbitrary one. (Why do I use the notation I and not x y ?) A Discussion of Transitivity The transitivity property is an appealing property of preferences. How would you react if somebody told you he prefers x to y , y to z and z to x ? You would probably feel that his answers are confused. Furthermore, it seems that, when confronted with an intransitivity...
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- Fall '10