Author
Listed:
- Jose A. Rodrigues-Neto
(Research School of Economics, Australian National University)
- Matthew Ryan
(Department of Economics and Finance, Auckland University of Technology)
- James Taylor
(Research School of Economics, Australian National University)
Abstract
The 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 Ulku (2018) and (independently) 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".
Suggested Citation
Jose A. Rodrigues-Neto & Matthew Ryan & James Taylor, 2024.
"A stricter canon: general Luce models for arbitrary menu sets,"
Working Papers
2024-04, Auckland University of Technology, Department of Economics.
Handle:
RePEc:aut:wpaper:2024-04
Download full text from publisher
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aut:wpaper:2024-04. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
We have no bibliographic references for this item. You can help adding them by using this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Gail Pacheco (email available below). General contact details of provider: https://edirc.repec.org/data/fbautnz.html .
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.