A Stricter Canon: General Luce Models for Arbitrary Menu Sets

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aut.relation.softwareversion2024/04
dc.contributor.authorRodrigues Neto, Jose
dc.contributor.authorRyan, Matthew
dc.contributor.authorTaylor, James
dc.date.accessioned2024-09-27T02:20:10Z
dc.date.available2024-09-27T02:20:10Z
dc.date.issued2024-03-28
dc.description.abstractThe classical Luce model (Luce, 1959) assumes positivity of random choice: each available alternative is chosen with strictly positive probability. The model is characterised by Luce’s choice axiom. Ahumada and Ulk¨u (2018) and (indepen- ¨ dently) Echenique and Saito (2019) define the general Luce model (GLM), which relaxes the positivity assumption, and show that it is characterised by a cyclical independence (CI) axiom. Cerreia-Vioglio et al. (2021) subsequently proved that the choice axiom characterises an important special case of the GLM in which a rational choice function (i.e., one that may be rationalised by a weak order) first selects the acceptable alternatives from the given menu, with any residual indifference resolved randomly in Luce fashion. The choice axiom is thus revealed as a fundamental “canon of probabilistic rationality”. This result assumes that choice behaviour is specified for all non-empty, finite menus that can be constructed from a given universe, X, of alternatives. We relax this assumption by allowing choice behaviour to be specified for an arbitrary collection of non-empty, finite menus. In this context, we show that the Cerreia-Vioglio et al. (2021) result obtains when the choice axiom is replaced with a mild strengthening of CI. The latter condition implies the choice axiom, thus providing a “stricter canon”.
dc.identifier.citationRodrigues-Neto, J. A., Ryan, M., & Taylor, J. (2024). A stricter canon: General Luce models for arbitrary menu sets. Economics Working Paper Series, No. 2024/04. Auckland University of Technology. https://www.aut.ac.nz/__data/assets/pdf_file/0010/884179/working-paper-2024_04.pdf
dc.identifier.urihttp://hdl.handle.net/10292/18068
dc.publisherAUT Working Papers in Economics
dc.relation.urihttps://www.aut.ac.nz/__data/assets/pdf_file/0010/884179/working-paper-2024_04.pdf
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dc.rights.accessrightsOpenAccess
dc.titleA Stricter Canon: General Luce Models for Arbitrary Menu Sets
dc.typec-40
pubs.elements-id542914
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