Self-selective social choice functions

Semih Koray,Arkadii Slinko

doi:10.1007/s00355-007-0276-6

Abstract

It is not uncommon that a society facing a choice problem has also to choose the choice rule itself. In such situations, when information about voters’ preferences is complete, the voters’ preferences on alternatives induce voters’ preferences over the set of available voting rules. Such a setting immediately gives rise to a natural question concerning consistency between these two levels of choice. If a choice rule employed to resolve the society’s original choice problem does not choose itself, when it is also used for choosing the choice rule, then this phenomenon can be regarded as inconsistency of this choice rule as it rejects itself according to its own rationale. Koray (Econometrica 68: 981–995, 2000) proved that the only neutral, unanimous universally self-selective social choice functions are the dictatorial ones. Here we introduce to our society a constitution, which rules out inefficient social choice rules. When inefficient social choice rules become unavailable for comparison, the property of self-selectivity becomes more interesting and we show that some non-trivial self-selective social choice functions do exist. Under certain assumptions on the constitution we describe all of them.

Highlights

It is not uncommon that a society facing a choice problem has to choose the choice rule itself
The main result of this paper presented in a theorem below states that π antidictatorships are effectively the only non-trivial examples of self-selective social choice functions (SCFs) if we restrict the set of rival SCFs to selections of π
In this paper the authors have made the first attempt to find a framework in which non-dictatorial self-selective SCFs may exist

Summary

Introduction

It is not uncommon that a society facing a choice problem has to choose the choice rule itself. Allowing social choice rules to be multi-valued does not lead to any new interesting examples and one ends up with a rediscovery of the Condorcet rule as the maximal neutral and self-selective social choice rule (Koray 1998) These theorems showed that the concept of self-selectivity was made too strong to be useful. An alternative approach to the “choosing how to choose” problem is pursued by Houy (2003, 2006) He assumes that individuals do not pay attention to immediate consequences of the choice but form their preferences on the basis of the intrinsic values of the rules alone: for example some voters might have ethical objections to dictatorship despite the benefit that it can bring to them personally. A preliminary versions of this paper was published as a working paper of CIREQ (Koray and Slinko 2006)

Basic notions and examples

Self-selectivity and resistance to cloning

The main theorem

Proof of Theorem 2

Findings

Conclusion and further research