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Sometimes when people don't know what the outcome of an event will be, they can at least know the probabilities of each possible outcome. For example, if there are 100 tickets in a fair lottery, then a person can know that the chance of any of them winning is 1%. Making decisions when the probabilities are known is called “decision-making under risk”. These are the sorts of cases where decision rules like maximizing expected utility are most plausible.

But sometimes people not only don't know what the outcome of an event will be, but they don’t even know what the probabilities of each of the possible outcomes are. For example, if a person is trying to predict which country will be the most powerful in the world in 200 years, they might have very little idea about how likely it is to be the US or France or China. Making decisions when the probabilities are not known is called “decision-making under uncertainty” (it is also sometimes called “decision-making under ignorance”).

How should we make decisions when we are uncertain about the probabilities involved? One option is to treat decision-making under uncertainty like decision-making under risk but with low resilience credences, i.e. in the case above, we assign precise probabilities to the US, France, and China being the most powerful countries in 200 years, while having low confidence that those probabilities are correct. This allows us to use standard tools like expected utilities in problems where we are uncertain about probabilities. Alternatively, we can try to make decisions using imprecise credences in these cases (Bradley 2014). Or we can use distinct decision rules in cases that involve uncertainty, such as the “minimax regret” rule (Wikipedia 2016).

Further reading

Bradley, Seamus. 2014. Imprecise probabilities. In Edward Zalta (ed.), Stanford encyclopedia of philosophy.

Peterson, Martin. 2009. An introduction to decision theory. Cambridge: Cambridge University Press, chs. 3-4.

Wikipedia. 2016. Minimax regret.