Designer path independent choice functions

Mark Johnson (mark.johnson.1@asu.edu) and Richard Dean (rxdean@peoplepc.com)

Economic Theory, 2005, vol. 26, issue 3, 729-740

Abstract: This paper provides 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 algorithm is based on a new characterization result for path independent choice functions (PICF) on finite domains and uses that characterization as the basis of the algorithm. 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 ${\rm arc}(A)={\{}B: C (B)=C(A){\}}$ is an interval in the Boolean algebra 2 V . (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. Copyright Springer-Verlag Berlin/Heidelberg 2005

Keywords: Choice functions; Algebraic structure; Lattice; Lower locally distributive; Path independence; Algorithms; Rationalization; Upper transpose; Upper transpose complete; Interval; Prime interval (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s00199-004-0544-y

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