# Utilitarianism with and without expected utility

*MPRA Paper No. 90125*(2016)

**Abstract**

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single 'individual preorder'. The individual preorder then uniquely determines a social preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi's utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a 'local expected utility' condition popular in non-expected utility theory, then the social preorder has a 'local expected total utility' representation. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.

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MCCUWA

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Archival date: 2017-08-20

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References found in this work BETA

Weighing Goods: Equality, Uncertainty and Time.Broome, John

Risk and Rationality.Buchak, Lara

Reasons and Persons.Margolis, Joseph

Reasoning About Uncertainty.Halpern, Joseph Y.

Weighing Lives.Hausman, Daniel M.

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Citations of this work BETA

An Intrapersonal Addition Paradox.Nebel, Jacob M.

The Priority View.McCarthy, David

Probability in Ethics.McCarthy, David

Representation of Strongly Independent Preorders by Sets of Scalar-Valued Functions.McCarthy, David; Mikkola, Kalle & Thomas, Teruji

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