Choice via grouping procedures

• Date: 01 March 2018
• Author: Jun Matsuki,Koichi Tadenuma
• Published date: 01 March 2018
• DOI: http://doi.org/10.1111/ijet.12144

doi: 10.1111/ijet.12144

Choice via grouping procedures

Jun Matsuki∗and Koichi Tadenuma†

In this paper,we consider a natural procedure of decision-making, the grouping choice methods,

which leads to a kind of bounded rational choice. In this procedurea decision-maker first divides

the set of available alternatives into some groups and in each groupshe chooses the best element

(winner) for her preference relation. Then, among the winners in the first round, she selects

the best one as her final choice. We characterize grouping choice methods in three different

ways. First, we show that a choice function is a grouping choice method if and only if it is a

rational shortlist method (Manzini and Mariotti 2007) in which the first rationale is transitive.

Second, grouping choice methods are axiomatically characterized by means of a new axiom

called elimination, in addition to two well-known axioms, expansion and weak WARP(Manzini

and Mariotti 2007). Third, grouping choice methods are also characterized by a weak versionof

path independence.

Key wor ds grouping of alternatives, preference, bounded rationality

JEL classification D01

Accepted 20 August2017

1 Introduction

The construction of models to explain (seemingly) irrational choices of individuals or societies has

recently been one of the central themes in economic theory. In this paper, we consider a natural

procedure of decision-making, called “grouping choice methods,” which leads to a kind of bounded

rational choice. In this procedure,a decision-maker (DM) first divides the set of available alternatives

into some groups, and in eachg roupshe chooses the best element (w inner) for her preferencerelation.

Then, among the winners in the first round, she selects the best one as her final choice.

Such choice behaviors are often observed in real life. For example, suppose that a family would

like to buy a house. Three houses {x,y, z}are available, of which xand yare located in town A, and

zin town B. They first choose the best house in each town, and then make a final choice from the

“winners” in the first round. Suppose that they prefer xto y,yto z, and zto x.1Now, when yand z

are available, each of them is the only house in each town. Hence, they choose yfrom {y,z}because

∗Konica Minolta Japan,Tokyo, Japan.

†Hitotsubashi University,Kunitachi, Tokyo,Japan. Email: koichi.tadenuma@r.hit-u.ac.jp

We are grateful to Sean Horan for his detailed comments, which improved a part of the proof of the main results in

this paper. Wealso benefited from helpful comments from Paola Manzini and Marco Mariotti, and participants at the

Workshopon Bounded Rationality in Choice held at the University of St. Andrews. Thanks are also due to an anonymous

referee for useful comments. Financial support from the Ministry of Education, Culture,Spor ts, Science and Technology,

Japan, through the Grant-in-Aid for Scientific Research (B) No.24330062 is gratefully acknowledged.

1Note that a family’spreference relation may become cyclic because it is a collective preference relation (if they decide by

majority voting, for instance).

International Journal of Economic Theory 14 (2018) 71–84 © IAET 71

International Journal of Economic Theory