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Designer Path Independent Choice Functions

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This paper provides a new characterization result for path independent choice functions (PICF) on finite domains and uses that characterization as the basis of an algorithm for the construction of all PICFs on a finite set of alternatives, V, designed by an a priori given set I of initial choices as well as the determination of whether the initial set I is consistent with path independence. The characterization result identifies two properties of a partition of the Boolean algebra as necessary and sufficient for a choice function C to be a PICF: (i): For every subset A of V the set arc(A) = {B: C (B) = C(A)} is an interval in the Boolean algebra 2v. (ii): If A/B is an interval in the Boolean algebra such that C(A) = C(B) and if M/N is an upper transpose of A/B then C(M) = C(N). The algorithm proceeds by expanding on the implications of these two properties.

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  • Mark Johnson & Richard Dean, "undated". "Designer Path Independent Choice Functions," Working Papers 2145927, Department of Economics, W. P. Carey School of Business, Arizona State University.
    • Handle: RePEc:asu:wpaper:2145927
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    1. Johnson Mark R., 1995. "Ideal Structures of Path Independent Choice Functions," Journal of Economic Theory, Elsevier, vol. 65(2), pages 468-504, April.
    2. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
    3. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    4. Johnson, Mark R. & Dean, Richard A., 2001. "Locally complete path independent choice functions and their lattices," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 53-87, July.
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