Math Problem Statement
Suppose that X is a finite set and the decision maker has in mind two oneto-one numerical functions u and v on X. Interpret the following choice procedures in words, and determine whether they lead to choice rules satisfying the Independence of Irrelevant Alternatives. (a) Fix a number v ∗ . For any choice problem A ⊂ X, let a ∗ be the maximizer of u over A and b ∗ be the maximizer of v over A. The decision maker chooses a ∗ if v(a ∗ ) ≥ v ∗ and she chooses b ∗ otherwise. (b) Fix u ∗ . For any choice problem A, the DM chooses a ∗ maximizing u if u(a ∗ ) ≥ u ∗ , otherwise she chooses b ∗ maximizing v.
Solution
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Math Problem Analysis
Mathematical Concepts
Decision Theory
Utility Functions
Choice Procedures
Independence of Irrelevant Alternatives
Formulas
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Theorems
Independence of Irrelevant Alternatives (IIA)
Suitable Grade Level
Undergraduate/Graduate
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