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Utilitarianism and similar moral theories often tell us to evaluate an action based on its expected consequences. Usually, this is assumed to be equivalent to the mathematical expectation of some function or other. Isn't this quite a specific probabilistic assumption to be making about the consequences of an action? What would utilitarians do if they had to make a choice over actions where the consequences depended on a random variable with no measure?

The standard ("expected consequences") idea is indeed to compare conduct options in terms of their expected pay-off. Conduct options with a certain, known outcome are valued by the utility of this outcome. Conduct options with several possible outcomes are by the probability-weighted mean utility of these outcomes (this is a sum of products, with each product being the utility of an outcome multiplied by the probability of this outcome). Now the question you raise concerns conduct options with possible oucomes whose utility and/or probability is unknown. This is often discussed under the label "decision-making under uncertainty" (as opposed to "decision-making under risk"). Generally authors advise caution. One rule reflecting this advice is the Maximin Rule: When the probabilities of outcomes associated with some conduct option are unknown, then assume that choosing this option will certainly result in the worst outcome it can result in. In other words, choose the conduct option whose worst outcome is...

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