Cycle conditions for "Luce rationality"

José Rodrigues-Neto, Matthew Ryan () and James Taylor
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Matthew Ryan: Department of Economics and Finance, Auckland University of Technology
James Taylor: Research School of Economics, Australian National University

No 2024-03, Working Papers from Auckland University of Technology, Department of 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 Ulku (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.

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Date: 2024-03
New Economics Papers: this item is included in nep-dcm and nep-mic
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Journal Article: Cycle conditions for “Luce rationality” (2025)
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