Unformatted text preview: x 2 ” x and x ” x for all x ∈ X 1 . By completeness, any alternative in X 1 other than x 2 is either preferred to x 2 or less preferred. So, let us deﬁne X 2 = { x ∈ X 1 : x ” x 2 } and X 2 = { x ∈ X 2 : x „ x 2 } . Note that X 1 ⊂ X 2 by transitivity. Step 3 : Pick any x 3 ∈ X 2 . It follows from transitivity that x 3 ” x for all x ∈ X 2 , because x 3 ” x 2 and x 2 ” x for all x ∈ X 2 . By completeness, deﬁne X 3 and X 3 . Transitivity implies X 2 ⊂ X 3 ... . . . Step n : Since there is a ﬁnite number of alternatives, the process must end at some point. The alternative in X n is the mostpreferred alternative (without further assumptions, there may be many). 1...
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This note was uploaded on 11/07/2010 for the course ECO 33358 taught by Professor Mathevet during the Fall '10 term at University of Texas.
 Fall '10
 Mathevet

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