Rubinstein2005-page43

Rubinstein2005-page43 - October 21, 2005 12:18 master Sheet...

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October 21, 2005 12:18 master Sheet number 41 Page number 25 Choice 25 Let X ={ x 1 , ... , x N } be the set of all universities in the scope of the student’s imagination. A choice problem A is interpreted as the set of universities to which he has been admitted. The fact that the student was admitted to some subset of universities does not imply his admission outcome for other universities. Therefore, D contains the 2 N 1 nonempty subsets of X . But if, for example, the univer- sities are listed according to difFculty in being admitted ( x 1 being the most difFcult) and if the fact that the student is admitted to x k means that he is admitted to all less prestigious universities, that is, to all x l with l > k , then D will consist of the N sets A 1 , ... , A N where A k ={ x k , ... , x N } . Given a context ( X , D ) ,a choice function C assigns to each set A D a unique element of A with the interpretation that C ( A ) is the chosen element from the set A . Our understanding is that a decision maker behaving in accor-
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.

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