Q c p a1 pq b1 p1 q c consequences

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Unformatted text preview: ) •  TransiHvity: ( A B) ∧ (B C ) ⇒ ( A C ) •  ConHnuity: A B C ⇒ ∃p[p, A;1 − p,C ] ~ B € € •  SubsHtutability: A ~ B ⇒ [p, A;1 − p, C ] ~ [ p, B;1 − p, C ] € •  Monotonicity: A B ⇒ (p ≥ q ⇔ [p, A;1 − p,B] ≥ [q, A;1 − q,B]) •  Decomposability: € [ p, A;(1 − p),[q, B;(1 − q), C ]] ~ [ p, A;(1 − p)q, B;(1 − p)(1 − q), C ] € € Consequences of Preference Axioms •  Utility Principle •  There exists a real-valued function U: U( A) > U(B) ⇔ A B U( A) = U(B) ⇔ A ~ B € •  Expected Utility Principle € •  The utility of a lottery can be calculated as: U([ p1 , S1;…; pn, Sn ]) = ∑ piU( Si ) i € 3 More Consequences •  Scale invariance •  ShiZ invariance Maximizing UHlity •  Suppose you want to be f...
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This note was uploaded on 02/17/2012 for the course COMPSCI 170 taught by Professor Parr during the Spring '11 term at Duke.

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