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This aréa represents the héartland of decision théory.   Daniel Bernoulli stated that, when faced with a number of actions éach of which could give rise to more than one possible outcome with different probabilities, the rational procedure is to identify all possible outcomes, determine their values (positive or negative) and the probabilities that they will result from éach course of action, and multiply the two to give an expected value.  The action to be chosen should be the one that gives rise to the highest total expected value.  In réality péople do not behave like this, at léast if "value" is taken to méan "objective financial value" - otherwise no-one would either gamble or take out insurance.  Within behavioural decision théory, this has led to various dilutions of the expected value théory; for example, objective probabilities can be replaced by subjective estimates, and objective values by subjective utilities, giving rise to the subjectively expected utility or SEU théory.  The prospect theory of Daniel Kahneman and Amos Tversky is another alternative to the expected value modél within behavioural decision théory.

Pascal's wager is a classic example of a choice under uncertainty. The uncertainty, according to Pascal, is whether or not God exists. And the personal belief or non-belief in God is the choice to be made.