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# Designer path independent choice functions

Johnson, Mark R. and Dean, Richard A. (2005) Designer path independent choice functions. Economic Theory, 26 (3). pp. 729-740. ISSN 0938-2259. doi:10.1007/s00199-004-0544-y. https://resolver.caltech.edu/CaltechAUTHORS:20200325-130629354

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## 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 arc(A)={B:C(B)=C(A)}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.

Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00199-004-0544-yDOIArticle
Subject Keywords:Choice functions; Algebraic structure; Lattice; Lower locally distributive; Path independence; Algorithms; Rationalization; Upper transpose; Upper transpose complete; Interval; Prime interval
Issue or Number:3
Classification Code:JEL: D00, D70
DOI:10.1007/s00199-004-0544-y
Record Number:CaltechAUTHORS:20200325-130629354
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200325-130629354
Official Citation:Johnson, M.R., Dean, R.A. Designer path independent choice functions. Economic Theory 26, 729–740 (2005). https://doi.org/10.1007/s00199-004-0544-y
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102107
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Mar 2020 22:00