Crudely put, utilitarianism is the thesis that one world is better than another if it contains greater total welfare. In the classical version associated with Bentham and Mill, the idea does not seem to have much going for it. Indeed, it has been the target of endless philosophical criticism. But utilitarianism received a major boost in 1955 in a seminal work by John Harsanyi, a Nobel Prize winning economist.
Harsanyi (1955) showed that utilitarianism can be derived from expected utility theory plus a plausible Pareto principle. The Pareto principle says that if one situation is better for some people than another, and at least as good for everyone, then it is better overall. Expected utility theory is the standard theory of rational choice under conditions of risk, so Harsanyi’s theorem seems to put utilitarianism on solid foundations.
However, Harsanyi’s use of expected utility theory commits him to three controversial assumptions about welfare comparisons:
- All goods are comparable.
- No goods are infinitely better than others.
- A specific treatment of welfare comparisons involving risk.
These are, respectively, consequences of the completeness, continuity, and independence axioms of expected utility.
When interpersonal welfare comparisons are allowed, all three expected utility axioms can be abandoned. Nevertheless, when one situation is better than another is still completely determined by three simple and plausible axioms for aggregation along with basic facts about individual welfare comparisons, even when the population can vary. See this post for further discussion.
Without interpersonal comparisons, we can drop the completeness and continuity axioms, but still obtain a major generalization of Harsanyi’s most fundamental theorem, even when the population is infinite.
This account of utilitarianism rests on remarkably weak and plausible premises. Contrary to a criticism frequently made by contractualists, for example, utilitarianism can allow that welfare is a plural notion whose components may be difficult to compare precisely.
Work in progress extends our treatment of uncertainty.
McCarthy, D., Mikkola, K., Thomas, T., Utilitarianism with and without expected utility. MPRA Paper No. 90125 (2018).Online Article | PDF | Abstract
McCarthy, D., Mikkola, K., Thomas, T., Aggregation for general populations without continuity or completeness. MPRA Paper No. 80820 (2017).Online Article | PDF | Abstract
We generalize Harsanyi’s social aggregation theorem. We allow the population to be infinite, and merely assume that individual and social preferences are given by strongly independent preorders on a convex set of arbitrary dimension. Thus we assume neither completeness nor any form of continuity. Under Pareto indifference, the conclusion of Harsanyi’s theorem nevertheless holds almost entirely unchanged when utility values are taken to be vectors in a product of lexicographic function spaces. The addition of weak or strong Pareto has essentially the same implications in the general case as it does in Harsanyi’s original setting.