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 | |||||||||
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| Additional Information: | © 2005 Springer-Verlag. Received: November 5, 2003; revised version: July 20, 2004. | |||||||||
| 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 | |||||||||
| Last Modified: | 16 Nov 2021 18:08 |
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