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Stochastic rationality and Möbius inverse

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  • BILLOT, Antoine
  • THISSE, Jacques-François

Abstract

Discrete choice theory is very much dominated by the paradigm of the maximization of a random utility, thus implying that the probability of choosing an alternative in a given set is equal to the sum of the probabilities of all the rankings for which this alternative comes first. This property is called stochastic rationality. In turn, the choice probability system is said to be stochastically rationalizable if and only if the Block-Marschak polynomials are all nonnegative. In this paper, we show that the Block-Marschak polynomials can be defined as the probabilities that the decision maker has to delete each alternative from the choice set when the choice probability system is stochastically rationalizable.

Suggested Citation

  • BILLOT, Antoine & THISSE, Jacques-François, 2002. "Stochastic rationality and Möbius inverse," CORE Discussion Papers 2002035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2002035
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    Keywords

    stochastic rationality; Moebius inverse; choice context;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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