These questions can be answered by writing down some constraints on the preferences that arational agent should have, and then showing that the MEU principle can be derived from theconstraints. Writing down these constraints is a way of defining the semantics of preferences.The idea is that, given some preferences on individual atomic states, the theory should allow one to derive results about preferences for complex decision-making scenarios. This is analogousto the way that the truth value of a complex logical sentence is derived from the truth value ofits component propositions, and the way the probability of a complex event is derived from theprobability of atomic events.LOTTERIES In the language of utility theory, the complex scenarios are called lotteries to emphasizethe idea that the different attainable outcomes are like different prizes, and that the outcome isdetermined by chance. The lottery L, in which there are two possible outcomes—state A withprobability/) and state B with the remaining probability—is written
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