 To extend the theory of rationality to circumstances involving  risk  (where the objects of choice are lotteries with known probabilities) and uncertainty (where agents do not know the probabilities or even all the possible outcomes of their choices) requires further principles of rationality, as well as controversial technical simplifications. Subjective Bayesians suppose that individuals in circumstances of uncertainty have well-defined subjective probabilities (degrees of belief) over all the payoffs and thus that the objects of choice can be modeled as lotteries, just as in circumstances involving risk, though with subjective probabilities in place of objective probabilities. See the entries on  Bayes’ theorem  and  Bayesian epistemology.  The most important of the axioms needed for the theory of rational choice under conditions of risk and uncertainty is the independence condition. It says roughly that the preferences of rational agent between two lotteries that differ in only one outcome should match their preferences between the differing outcomes. Although initially plausible, the independence condition is very controversial. See Allais and Hagen (1979) and McClennen (1983, 1990).