Economics serving society

Harsanyi’s aggregation theorem with incomplete preferences

Eric Danan, Thibault Gajdos et Jean-Marc Tallon

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Economists often base their recommendations on an aggregate measure of the gains promised by a certain policy. Ideally, the measure should reflect the increased well-being for the society that the policy will bring, but quantifying this social well-being is difficult. In a celebrated article in 1955, John Harsanyi proposed, for an environment in which the result of policies is not deterministic, that the criterion of social well-being (in economists’ language, “social utility”) be the weighted sum of the well-being of all the individuals in it (that is, of individual utility). This utilitarian criterion rests on a principle of quite weak unanimity (if a policy improves the well-being of all individuals, it ought to improve social well-being), while assuming that individuals assess their own well-being by the average utility that the policy in question brings them.
In this article, Eric Danan, Thibault Gajdos and Jean-Marc Tallon generalise this result for situations in which individuals have not necessarily been able to compare all the policy alternatives; we say in such cases that the individual preferences are incomplete. Their research shows that a form of utilitarianism – which we can call “extended utilitarianism” - remains true in this context, as social well-being can be described as the sum of individuals’ well-being. In contrast, the criterion of social well-being does not necessarily classify all policies, which cannot be compared with each other at the social level. The authors also establish that not being able to compare some alternatives at the individual level does not necessarily indicate that it is impossible to compare them at the aggregate level.
Original title of the article : “Harsanyi’s aggregation theorem with incomplete preferences”
Published in : CES Working Papers 2014.02
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