Concave Rationalization with an Ideal Point: An Afriat Theorem and an Application to Survey Design
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918433625473024 |
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| author | Seror, Avner |
| author_facet | Seror, Avner |
| contents | This paper develops an Afriat-type characterization of concave rationalization with an unknown ideal point. We show that a system of Afriat inequalities - where the unknown peak enters as a virtual observation with the highest utility - is necessary and sufficient for the existence of a continuous concave utility with an ideal point that rationalizes choices from linear budget sets anchored at different corners of the choice space. A stronger characterization adds the requirement that supergradients at observed choices point coordinatewise toward the peak, a necessary condition for single-peaked rationalizability. The resulting peak-oriented Afriat system provides the basis for a Houtman--Maks consistency index that measures the largest fraction of observations jointly rationalizable with a common ideal point. This characterization provides the theoretical foundation for the Priced Survey Methodology (PSM), in which respondents complete the same survey under different linear constraints. A parametric single-peaked specification then sharpens identification into estimates of ideal answers and importance weights. We apply the PSM to study political preferences in a sample of French respondents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03876 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Concave Rationalization with an Ideal Point: An Afriat Theorem and an Application to Survey Design Seror, Avner Theoretical Economics This paper develops an Afriat-type characterization of concave rationalization with an unknown ideal point. We show that a system of Afriat inequalities - where the unknown peak enters as a virtual observation with the highest utility - is necessary and sufficient for the existence of a continuous concave utility with an ideal point that rationalizes choices from linear budget sets anchored at different corners of the choice space. A stronger characterization adds the requirement that supergradients at observed choices point coordinatewise toward the peak, a necessary condition for single-peaked rationalizability. The resulting peak-oriented Afriat system provides the basis for a Houtman--Maks consistency index that measures the largest fraction of observations jointly rationalizable with a common ideal point. This characterization provides the theoretical foundation for the Priced Survey Methodology (PSM), in which respondents complete the same survey under different linear constraints. A parametric single-peaked specification then sharpens identification into estimates of ideal answers and importance weights. We apply the PSM to study political preferences in a sample of French respondents. |
| title | Concave Rationalization with an Ideal Point: An Afriat Theorem and an Application to Survey Design |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2401.03876 |