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The Repeated Insertion Model for Rankings: Missing Link between Two Subset Choice Models

Published online by Cambridge University Press:  01 January 2025

Jean-Paul Doignon ,
Aleksandar Pekeč  and
Michel Regenwetter
Jean-Paul Doignon
Affiliation:
Université Libre De Bruxelles
Aleksandar Pekeč
Affiliation:
Duke University
Michel Regenwetter*
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Michel Regenwetter, Department of Psychology, University of Illinois, 603 E. Daniel St., Champaign, IL 61820. E-mail: [email protected]
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Abstract

Several probabilistic models for subset choice have been proposed in the literature, for example, to explain approval voting data. We show that Marley et al.'s latent scale model is subsumed by Falmagne and Regenwetter's size-independent model, in the sense that every choice probability distribution generated by the former can also be explained by the latter. Our proof relies on the construction of a probabilistic ranking model which we label the “repeated insertion model.” This model is a special case of Marden's orthogonal contrast model class and, in turn, includes the classical Mallows φ-model as a special case. We explore its basic properties as well as its relationship to Fligner and Verducci's multistage ranking model.

Keywords

Approval votingprobabilistic choice modelsprobabilistic ranking modelssubset choice
Type
Theory And Methods
Information
Psychometrika , Volume 69 , Issue 1 , March 2004 , pp. 33 - 54
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

The authors are grateful to the National Science Foundation for grants SES98-18756 to Regenwetter and Pekeč, and SBR97-30076 to Regenwetter. This collaborative research was carried out in the context of the conference Random Utility 2000 held at Duke University and sponsored by NSF, the Fuqua School of Business and the Center for International Business Education and Research. We thank the editor and four referees for helpful suggestions and we are grateful to Prof. J. I. Marden for providing useful information on contrast models. We thank Moon-Ho Ho for programming and running the data analyses.

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