Unformatted text preview: • Expected utility : Note that the function U ( p ) is linear: U ( ⊕ K k = 1 α k p k ) = X z ∈ Z [⊕ K k = 1 α k p k ] ( z ) v ( z ) = X z ∈ Z [ K X k = 1 α k p k ( z ) ] v ( z ) = K X k = 1 α k [ X z ∈ Z p k ( z ) v ( z ) ] = K X k = 1 α k U ( p k ). It follows that any such preference relation satisFes I . Since the function U ( p ) is continuous in the probability vector, it also satisFes C . • Increasing the probability of a “good” consequence : Such a pref-erence relation satisFes the two axioms since it can be repre-sented by the expectation of v where v ( z ) = 1 for z ∈ G and v ( z ) = 0 for z ∈ B ....
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- Fall '10
- Utility, Probability theory, 1 k, continuity assumption