Every time I have heard utilitarianism discussed, it is generally assumed that utility should be averaged. While this sounds reasonable, the reasoning isn't particularly strong.

  1. What justifications are there for using an (arithmetical) average?
  2. Are there any alternate suggestions for combining individual utility function?

Harsanyi's theorem is often used as a justification of utilitarianism and basically involves averaging of individual utilities.

Other aggregation procedures don't seem applicable. Geometric averaging of individual utilities would be an odd thing to do, for instance. I can't quite give you the reason why it would be odd, but I have an instinct that it would do weird things like massively favour the best off or the worst off, or something like that.

There's a lot of work on judgement aggregation that involves using procedures different from arithmetic averaging, but I don't know whether one could apply it to aggregating utilities...

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  • Harsanyi's theorem assumes that individuals only care about expected utility. Might an individual prefer a guaranteed utility of 1 to a 50% utility of 0 and and 50% utility of 2? – Casebash Jun 16 '11 at 10:58
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    @Casebash No. An agent's attitude to risk is built in to the definition of utility. It might be that an agent prefers $1 for sure versus $2 with probability .5, but that just means she gets more utility from $1 for sure... Risk can have a disutility. This is an important and often overlooked point when discussing expected utility. Any good book on decision theory should explain this point. – Seamus Jun 16 '11 at 11:20
  • @Seamus: Is it necessarily always possible to define utility to have this property? – Casebash Jun 16 '11 at 11:27
  • @Casebash Representation theorems show that, given a profile of an agent's preferences, they can be modelled as an expected utility maximiser. As long as your preferences satisfy some (more or less) reasonable properties (like being transitive) then there is a probability function and utility function such that your choices maximise expected utility with respect to those. We're getting a bit beyond the remit of the original question now and into foundations of decision theory/microeconomics... – Seamus Jun 16 '11 at 11:36
  • @Seamus: Thanks. Do you have a link or know the name of the theorem? – Casebash Jun 16 '11 at 11:42

If we start, as utilitarians do, from the idea that everyone is of equal moral importance, we do need a method of aggregating individual utilities that treats each person's utility outcome for a given action as having equal importance. The simplest mathematical function that achieves this is taking the arithmetical mean. While other procedures are available (for instance, taking the mean of the cubes of utility), the arithmetical mean as simplest has a default presumption in its favour.

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  • As a self-identified utilitarian, I strongly disagree with the idea that everyone is of equal moral importance. This is actually a core component in applying utilitarianism to different species. – eclipz905 May 1 '18 at 19:48

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