2024/03/07 by Nobuo Koida, Koida, Nobuo, Koji Shirai +1
Decision Sciences · Economics, Econometrics and Finance · #Decision-Making and Behavioral Economics #Econometrics (econ.EM) #Economic and Environmental Valuation #Economics of Agriculture and Food Markets #FOS: Economics and business #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2403.04328
openalex publication_date 2024/03/07 · openalex created_date 2024/03/09 · openalex updated_date 2026/07/28
This paper develops a novel characterization for random utility models (RUM), which turns out to be a dual representation of the characterization by Kitamura and Stoye (2018, ECMA). For a given family of budgets and its "patch" representation á la Kitamura and Stoye, we construct a matrix Ξ of which each row vector indicates the structure of possible revealed preference relations in each subfamily of budgets. Then, it is shown that a stochastic demand system on the patches of budget lines, say π, is consistent with a RUM, if and only if Ξπ≥ \mathbb1, where the RHS is the vector of 1's. In addition to providing a concise quantifier-free characterization, especially when π is inconsistent with RUMs, the vector Ξπ also contains information concerning (1) sub-families of budgets in which cyclical choices must occur with positive probabilities, and (2) the maximal possible weights on rational choice patterns in a population. The notion of Chvátal rank of polytopes and the duality theorem in linear programming play key roles to obtain these results.