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Foundations of spatial preferences

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  • Eguia, Jon X.

Abstract

I provide an axiomatic foundation for the assumption of specific utility functions in a multidimensional spatial model, endogenizing the spatial representation of the set of alternatives. Given a set of objects with multiple attributes, I find simple necessary and sufficient conditions on preferences such that there exists a mapping of the set of objects into a Euclidean space where the utility function of the agent is linear city block, quadratic Euclidean, or more generally, it is the [delta] power of one of Minkowski (1886) metric functions. In a society with multiple agents I characterize the set of preferences that are representable by weighted linear city block utility functions, and I discuss how the result extends to other Minkowski utility functions.

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  • Eguia, Jon X., 2011. "Foundations of spatial preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 200-205, March.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:200-205
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    1. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    2. Greco, Salvatore & Ishizaka, Alessio & Resce, Giuliano & Torrisi, Gianpiero, 2020. "Measuring well-being by a multidimensional spatial model in OECD Better Life Index framework," Socio-Economic Planning Sciences, Elsevier, vol. 70(C).
    3. Martínez-Mora Francisco & Puy M. Socorro, 2012. "Asymmetric Single-peaked Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-26, December.
    4. Gershkov, Alex & Moldovanu, Benny & Shi, Xianwen, 2020. "Monotonic norms and orthogonal issues in multidimensional voting," Journal of Economic Theory, Elsevier, vol. 189(C).
    5. Chambers, Christopher P. & Echenique, Federico, 2020. "Spherical preferences," Journal of Economic Theory, Elsevier, vol. 189(C).
    6. Knoblauch, Vicki, 2010. "Recognizing one-dimensional Euclidean preference profiles," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 1-5, January.
    7. Naveen Durvasula, 2022. "Utility-Based Communication Requirements for Stable Matching in Large Markets," Papers 2212.04024, arXiv.org.
    8. Jiehua Chen & Martin Nollenburg & Sofia Simola & Anais Villedieu & Markus Wallinger, 2022. "Multidimensional Manhattan Preferences," Papers 2201.09691, arXiv.org.

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