# Utilitarianism, Welfare, and Information

McCarthy, D., Mikkola, K., Thomas, T., Utilitarianism with and without expected utility. *Journal of Mathematical Economics*, forthcoming.

A common criticism of **utilitarianism** is that it makes strong assumptions about **welfare comparisons**. It assumes that we can measure welfare precisely. But to many people, that assumption is very implausible. They think that welfare is made up of many different kinds of goods which are difficult to compare.

Moreover, many people think that social welfare comparisons should reflect the social consensus about individual welfare comparisons. But the social consensus about individual welfare comparisons might fall a long way short of a full agreement. This is one of the objections that defenders of **contractualism** make against utilitarianism. For example, Rawls (1982) gives an especially clear statement of this criticism.

Our paper explains how utilitarianism can respond. This post will also connect this topic with **uncertainty**.

#### Harsanyi’s utilitarianism

Criticisms of utilitarianism, including those made famous by Rawls, are too often directed at old fashioned versions of the view. But this particular criticism applies to the sophisticated version presented in the 1955 **utilitarian theorem** of John Harsanyi.

Harsanyi’s theorem is stated for circumstances involving **risk**. In other words, he assumes that probabilities are objective or universally agreed. He made some simple and apparently plausible assumptions. He then showed that these assumptions imply that individual welfare comparisons uniquely determine social welfare comparisons.

Harsanyi’s assumptions are mostly taken from **expected utility theory** (EUT). This is the best known and developed theory for rational decision making under conditions of risk. But this is where the criticism recurs. Expected utility theory contains three basic axioms: completeness, continuity, and independence. But in Harsanyi’s framework, this means the following.

- Completeness implies that all goods are comparable.
- Continuity implies that no goods are infinitely more valuable than others.
- Independence implies a precise way of making welfare comparisons under risk.

#### Information and uncertainty

The following is another features of Harsanyi’s framework.

- The use of risk means that the theorem only applies when probabilities are objective or agreed.

Amartya Sen taught us to think about different ethical theories in terms of how much **information** they need in order to function. Both classical utilitarianism and Harsanyi’s utilitarianism require a lot of precise information about welfare comparisons. But in only applying to risk, Harsanyi’s utilitarianism requires a lot of information about **uncertainty**. But in real-world situations, we often face uncertainty without having any idea about what the probabilities are.

In Sen’s terms, we can summarize 1 to 4 as follows. Harsanyi’s utilitarianism demands a very high, and perhaps unattainable, amount of information. It is not a theory which we can use in most of the situations where we need ethics.

#### A utilitarian solution

Our main result manages to avoid all of these difficulties. We present three simple and plausible axioms. These are much weaker than Harsanyi’s axioms, but they still preserve the utilitarian flavor of his approach. Moreover, our axioms still imply that individual welfare comparisons **uniquely determine** social welfare comparisons.

In addition, we do not assume any of the expected utility axioms. In fact, they are all allowed to fail. This means that our approach is much more flexible than Harsanyi’s in the welfare comparisons it handle.

- Our result can accept that some goods are incomparable.
- It allows some goods to be infinitely more valuable than others.
- It has room for a wide range of welfare comparisons involving risk.

- Our approach allows for wide range of ways of representing uncertainty.

In my view, this means that standard criticism of utilitarianism we started with is off-target. But I would not put this by saying that utilitarianism is right and contractualism is wrong. We could also say that the result allows utilitarianism to move closer to contractualism.

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