A welfarist critique of social choice theory
| Author | Aki Lehtinen |
| Published date | 01 July 2011 |
| Date | 01 July 2011 |
| DOI | http://doi.org/10.1177/0951629811411753 |
| Subject Matter | Articles |
Article
A welfarist critique of social
choice theory
Journal of Theoretical Politics
23(3) 359–381
©The Author(s) 2011
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DOI:10.1177/0951629811411753
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Aki Lehtinen
University of Helsinki, Finland
Abstract
This paper reconsiders the discussion on ordinal utilities versus preference intensities in voting
theory. It is shown by way of an example that arguments concerning observability and risk-
attitudes that have been presented in favour of Arrow’s Independence of Irrelevant Alternatives
(IIA), and against utilitarian evaluation, fail due to strategic voting. The failure of these two argu-
ments is then used to justify utilitarian evaluation of outcomes in voting. Given a utilitarian
viewpoint, it is then argued that strategy-proofness is not normatively acceptable. Social choice
theory is criticised not just by showing that some of its most important conditions are not nor-
matively acceptable, but also by showing that the very idea of imposing condition on social choice
function under the assumption of sincere behaviour does not make much sense because satisfying
a condition does not quarantee that a voting rule actually has the properties that the condition
confers to it under sincere behaviour. IIA, the binary intensity IIA, and monotonicity are used as
illustrations of this phenomenon.
Keywords
IIA; preference intensity; strategic voting; strategy-proofness; utilitarian winner
1. Introduction
Arrow’s theorem and the Gibbard–Satterthwaite theorem are commonly taken to be
the most fundamental results in areas of social choice theory that deal with voting. In
this paper, I argue that these theorems have very little normative relevance because the
conditions upon which they are based are not normatively acceptable.
The normative and descriptive relevance of preference intensities and the normative
validity of Kenneth Arrow’s Independence of Irrelevant Alternatives (IIA) have been
Corresponding author:
Aki Lehtinen, Department of Political and Economic Studies, practical philosophy unit, PO Box 24, 00014
University of Helsinki, Finland
Email: aki.lehtinen@helsinki.fi
360 Journal of Theoretical Politics 23(3)
under debate for decades in the context of social choice theory. IIA can be defined as
follows. Let C(S) denote a choice made by society in voting from a set of alternatives
S⊂X.Letpand pdenote profiles of individual preferences: passigns a preference
ordering ifor each voter i∈I:p=(1,2, ..., N). Let p|Ydenote the restriction
of the profile pto the subset Yof X.LetC(,S) denote the social choice from profile
pon S.
Independence of Irrelevant Alternatives: For all x,y∈Sand all individuals,
p|S=p
|S→C(,S)=C(,S). (1)
In other words, if the two profiles pand prank each pair of alternatives in the same
way, then the social choice should be the same.
Preference intensities are taken into account in various models of strategic voting
that describe the behaviour of voters under uncertainty.1At the same time, however,
the use of a utilitarian welfare function in evaluating voting rules is rare. I will take
it as given that intensities of preference are intrinsically relevant for evaluating voting
outcomes normatively. I believe that voting theorists, including Arrow (1987), agree with
this judgment, and I will thus not attempt to justify it. The reason for this discrepancy
between positive and normative approaches is thus that Arrow and others have presented
arguments for why one should not use the utilitarian welfare function.
Traditional criticisms of preference intensities can be formulated in terms of two
arguments for IIA. The observability argument states that since it is possible to observe
preference orderings, but not preference intensities or interpersonal comparisons of utili-
ties, allowable information must be restricted to preferences for pairs of alternatives, and
this is what IIA does. The epistemological-moral argument against preference intensities
and for IIA states that von Neumann–Morgenstern (vNM) utilities should not be used in
social-welfare judgements because they ‘reflect only individuals’ attitudes towards gam-
bling’ (Arrow, 1951: 9–11).2The idea here is that vNM utilities are not appropriate in
this context because they inevitably incorporate attitudes towards risk.
Although Arrow may not have introduced IIA in order to preclude strategic voting,3
this seems to be the most important consideration for those who continue to think that
IIA is normatively acceptable. The basis for such views derives either from intuitive
considerations (Plott, 1976; Vickrey, 1960) or from various proofs that link IIA and
strategy-proofness in some way.4The strategic-voting argument thus states that strategic
voting is to be avoided, and a voting procedure that satisfies IIA precludes it.5
I will respond to these points as follows. I will show with a simple example of strate-
gic voting under amendment agendas that if Arrow’s assumption that voters are sincere is
dropped, none of the properties that are commonly attributed to social choice functions6
that satisfy IIA are actually found in the actual voting procedure that the social choice
function was supposed to represent: if there is strategic voting, third alternatives affect
the choice between a pair, and preference intensities as well as attitudes towards risk
affect the outcome.
I will thus not attempt to show that preference intensities are observable, or that we
have particularly precise information on interpersonal comparisons. I will rather establish
that observability cannot be used as an argument against preference intensities in evalu-
ating voting rules. As an argument for IIA, the epistemological-moral argument suffers
from a similar shortcoming: voting choices reflect attitudes towards risk also under voting
rules that satisfy IIA. Whereas this fact shows that the requirement of not taking attitudes
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