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## Axioms of Expected Utility

The Axioms of Expected Utility:• Preferences over possible outcomes are complete, reflexive, and transitive.

• Compound lotteries is able to be reduced to simple lotteries.

• Continuity: For each outcome xi between x1and xn , the consumer can name a probability, p

_{i}, such that s/he is indifferent between getting xi with certainty and playing a lottery (which involves getting x_{n}with probability pi and x1 with probability (1− p_{i})). We utter that x_{i}is the certainty equal to the lottery ~x_{i}where:~x= (x

_{n}with p_{i}and x_{1}with (1−p_{i})).• Substitutability. The lottery~x

_{i}is able to forever be substituted for its certainty equivalent x_{i}in any other lottery.• Monotonicity. If two lotteries with the similar two alternatives each differ only in probabilities then the lottery that gives elevated probability to the most-preferred alternative is preferred to the other lottery.

If preferences over lotteries satisfy above axioms then we is able to assign numbers U(x

_{i}) which is associated with the outcomes x_{i}such that if we compare two lotteries L and L′ which offer probabilities (p1, L, p_{n}) and (p_{1}, ,p_{n}) ′L′ of obtaining those outcomes L will be preferred to L′ if and only if:This signifies that the rank order by expected utilities reflects the rank order of preference over the lotteries and that the rational individual will choose amongst risky alternatives as if s/he is maximizing expected utility.

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