Designer Path Independent Choice Functions

Mark Johnson () and Richard Dean
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Mark Johnson: W. P. Carey School of Business Department of Economics, http://wpcarey.asu.edu/Directory/stafffaculty.cfm?cobid=2143748
Richard Dean: California Institute of Technology - Department of Mathematics, http://wpcarey.asu.edu/Directory/stafffaculty.cfm?cobid=2145929

Working Papers from Department of Economics, W. P. Carey School of Business, Arizona State University

Abstract: 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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