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Social Choice and Welfare
Published in: Social Choice and Welfare 4/2015

13-02-2015

Choosing two finalists and the winner

Authors: Gent Bajraj, Levent Ülkü

Published in: Social Choice and Welfare | Issue 4/2015

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Abstract

We study a class of boundedly rational choice functions which operate as follows. The decision maker uses two criteria in two stages to make a choice. First, she shortlists the top two alternatives, i.e. two finalists, according to one criterion. Next, she chooses the winner in this binary shortlist using the second criterion. The criteria are linear orders that rank the alternatives. Only the winner is observable. We study the behavior exhibited by this choice procedure and provide an axiomatic characterization of it. We leave as an open question the characterization of a generalization to larger shortlists.
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Appendix
Available only for authorised users
Footnotes
1
See, for example, Masatlıoğlu et al. (2012), Lleras et al. (2011), de Clippel and Eliaz (2012) and Dutta and Horan (2013).
 
2
Rubinstein and Salant (2008) study extended choice functions of the form \( c(A,f)\) which allow the choice in a set \(A\) to depend on the frame \(f\). They characterize limited attention using axioms such extended choice functions. Since we are interested in standard choice functions, our axioms and approach are different.
 
3
We will denote the subset relation by \(\subseteq \) and its asymmetric part by \(\subset \).
 
4
See, for example, Moulin (1985) for the proof.
 
5
The proofs of Lemmas 1–5 below are in Appendix 2.
 
Literature
Dutta R, Horan S (2013) Inferring rationales from choice: identification for rational shortlist methods. UQAM working paper
Eliaz K, Richter M, Rubinstein A (2011) Choosing the two finalists. Econ Theor 46:211–219CrossRef
Lleras J, Masatlıoğlu Y, Nakajima D, Özbay E (2011) When more is less: choice by limited consideration. Working paper
Manzini P, Mariotti M (2007) Sequentially rationalizable choice. Am Econ Rev 97(5):1824–1839CrossRef
Masatlıoğlu Y, Nakajima D, Özbay E (2012) Revealed attention. Am Econ Rev 102(5):2183–2205CrossRef
Moulin H (1985) Choice functions over a finite set: a summary. Soc Choice Welf 2:147–160CrossRef
Rubinstein A, Salant Y (2006) A model of choice from lists. Theor Econ 1:3–17
Rubinstein A, Salant Y (2008) (A, f): choice with frames. Rev Econ Stud 75:1287–1296CrossRef
Yıldız K (2012) List rationalizable choice. Working paper
Metadata
Title
Choosing two finalists and the winner
Authors
Gent Bajraj
Levent Ülkü
Publication date
13-02-2015
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 4/2015
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-015-0878-3

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