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**Unformatted text preview: **Utility Theory; page 1 of 7 Artificial Intelligence Utility Theory for Risk-Sensitive Decision Making Russell and Norvig - Chapter 16 this is not in the Nilsson Utility Theory; page 2 of 7 Utility Theory (1) probability 1.0: win 4,500,000 dollars probability 0.5: win 10,000,000 dollars probability 0.5: win 0 dollars Utility Theory; page 3 of 7 Utility Theory (2) 1.0 0.5 0.5 4,500,000 10,000,000 4,500,000 5,000,000 0.5 0.7 0.0 0.6 0.4 prob reward exp reward utility exp utility utility function: money -> utility dollars utility 10,000,000 1 strictly monotonically increasing its existence follows from simple axioms Utility Theory; page 4 of 7 Utility Theory (3) axioms Orderability Transitivity Continuity Substitutability Monotonicity Decomposability (A > B) OR (B > A) OR (A = B) (A > B) AND (B > C) IMPLIES (A > C) A > B > C IMPLIES THERE EXISTS p SUCH THAT [p, A; 1-p, C] = B A = B IMPLIES [p, A; 1-p, C] = [p, B; 1-p, C] A > B IMPLIES (p >= q EQUIVALENT [p, A; 1-p, B] >= [q, A; 1-q, B])...

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