Cycle Conditions for “Luce Rationality”
Files
Date
Supervisor
Item type
c-40
Degree name
Journal Title
Journal ISSN
Volume Title
Publisher
AUT Working Papers in Economics
Abstract
We extend and refine conditions for “Luce rationality” (i.e., the existence of a Luce – or logit – model) in the context of stochastic choice. When choice probabilities satisfy positivity, we show that the cyclical independence (CI) condition of Ahumada and Ulk¨u (2018) and Echenique and Saito (2019) is necessary and ¨sufficient for Luce rationality, even if choice is only observed for a restricted set of menus. We then adapt results from the cycles approach (Rodrigues-Neto, 2009) to the common prior problem (Harsanyi, 1967-1968) to refine the CI condition, by reducing the number of cycle equations that need to be checked. A general algorithm is provided to identify a minimal sufficient set of equations (depending on the collection of menus for which choice is observed). Three cases are discussed in detail: (i) when choice is only observed from binary menus, (ii) when all menus contain a common default; and (iii) when all menus contain an element from a common binary default set. Investigation of case (i) leads to a refinement of the famous product rule.Description
Keywords
Source
Rodrigues-Neto, J. A., Ryan, M. J., & Taylor, J. (2024). Cycle conditions for “Luce rationality”. Economics Working Paper Series, No. 2024/03. Auckland University of Technology. https://www.aut.ac.nz/__data/assets/pdf_file/0009/884178/working-paper-2024_03.pdf
DOI
Rights statement
Auckland University of Technology (AUT) encourages public access to AUT information and supports the legal use of copyright material in accordance with the Copyright Act 1994 (the Act) and the Privacy Act 1993. Unless otherwise stated, copyright material contained on this site may be in the intellectual property of AUT, a member of staff or third parties. Any commercial exploitation of this material is expressly prohibited without the written permission of the owner.