Geodesic
Representations of Well-Founded Preference Orders
Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 496-508

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A preference order, or linear preorder, on a set X is a binary relation which is transitive, reflexive and total. This preorder partitions the set X into equivalence classes of the form . The natural relation induced by on the set of equivalence classes is a linear order. A well-founded preference order, or prewellordering, will similarly induce a well-ordering. A representation or Paretian utility function of a preference order is an order-preserving map f from X into the R of real numbers (provided with the standard ordering). Mathematicians and economists have studied the problem of obtaining continuous or measurable representations of suitably defined preference orders [4, 7]. Parametrized versions of this problem have also been studied [1, 7, 8]. Given a continuum of preference orders which vary in some reasonable sense with a parameter t, one would like to obtain a continuum of representations which similarly vary with t. 
Cenzer, Douglas; Mauldin, R. Daniel. Representations of Well-Founded Preference Orders. Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 496-508. doi: 10.4153/CJM-1983-027-4
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[1] 1. Burgess, J. P., From preference to utility, A problem of descriptive set theory, Notre Dame Journal of Formal Logic, to appear. Google Scholar | DOI

[2] 2. Burgess, J. P., A reflection phenomenon, Fund. Math. 104 (1979), 128–139. Google Scholar

[3] 3. Cenzer, D. and Mauldin, R. D., Inductive definability, measure and category, Advances in Math. 38 (1980), 55–90. Google Scholar

[4] 4. Debreu, G., Continuity properties of Paretian utility, Int'l. Econ. Review 5 (1964), 285–293. Google Scholar

[5] 5. Faden, A. M., Economics of space and time, The Measure-theoretic Foundations of Social Science (Iowa State U. Press, 1977). Google Scholar

[6] 6. Kuratowski, K., Topology, Vol. I (Acad. Press, 1966). Google Scholar

[7] 7. Mauldin, R. D., Measurable representations of preference orders, Trans. Amer. Math. Soc. 275 (1983), 761–769. Google Scholar

[8] 8. Wesley, E., Borel preference orders in markets with a continuum of traders, J. Math. Economics 3 (1976), 155–165. Google Scholar

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