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Rubinstein2005-page86

# Rubinstein2005-page86 - that might be taken into account...

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October 21, 2005 12:18 master Sheet number 84 Page number 68 LECTURE 6 Choice over Budget Sets and the Dual Problem Indirect Preferences As an introduction to the first topic in this lecture, let us go back to the general choice function concept discussed in Lecture 3. Having in mind a preference relation on a set X , the decision maker may want to construct a preference relation over the set D , the domain of his choice function. When assessing a choice problem in D , the decision maker may then ask himself which alternative he would choose if he had to choose from that set. The “rational” decision maker will prefer a set A over a set B if the alternative he intends to choose from A is preferable to that which he intends to choose from B . This leads us to the definition of , the indirect preferences induced from : A B if C ( A ) C ( B ). The definition of indirect preferences ignores some considerations
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Unformatted text preview: that might be taken into account when comparing choice sets. Ex-cluded are considerations such as, “I preFer A − { b } to A even though I intend to choose a in any case since I am aFraid to make a mistake and choose b ” or “I will choose a From A whether b is available or not. However, since I don’t want to have to reject b , I preFer A − { b } to A .” OF course, iF u represents % and the choice Function is well defned, v ( A ) = u ( C ( A )) represents % ∗ . We will reFer to v as the indirect utility function . ±inally, note that sometimes (depending on the set D ) one can reconstruct the choice Function C % ( A ) From the indirect preFerences % ∗ . ±or example, iF a ∈ A and A Â ∗ A − { a } , then C % ( A ) = a ....
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