On the choice of most-preferred alternatives
Maximal elements of a binary relation on compact subsets of a metric space define a choice function. Necessary and sufficient conditions are found for: (1) the choice function to have nonempty values and be path independent; (2) the choice function to have nonempty values provided the underlying relation is an interval order. For interval orders and semiorders, the same properties are characterized in terms of representations in a chain.
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- Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
- Mukherji, Anjan, 1977. "The Existence of Choice Functions," Econometrica, Econometric Society, vol. 45(4), pages 889-94, May.
- Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
- Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
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