A dual approach to nonparametric characterization for random utility models
| Autor: | Koida, Nobuo, Shirai, Koji |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 \'a la Kitamura and Stoye, we construct a matrix $\Xi$ 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 $\pi$, is consistent with a RUM, if and only if $\Xi\pi \geq \mathbb{1}$, where the RHS is the vector of $1$'s. In addition to providing a concise quantifier-free characterization, especially when $\pi$ is inconsistent with RUMs, the vector $\Xi\pi$ 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 Chv\'atal rank of polytopes and the duality theorem in linear programming play key roles to obtain these results. Comment: In this revision: typos in the preceding version has been fixed, and other changes are made mainly for readability. A reference is added. Results are unchanged |
| Databáze: | arXiv |
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