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
Full text is not posted in this repository. Consult Related URLs below.
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20200325-130629354
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: |
| |||||||||
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 |
Repository Staff Only: item control page