Decision networks Money B not preferred to CHAPTER 16 RATIONAL DECISION / E.a lokup table for perect tictactoe t(.S: A>B Continuity such that ·14 n ar Maximizing expected utility Rational preferences contd. preferences of a rational agent must obey comtraints. Rational preferencesRational decisions Chapter 16 Chapter 16 1 Outline ♦ Rational preferences ♦ Utilities ♦ Money ♦ Multiattribute utilities ♦ Decision networks ♦ Value of information Chapter 16 2 Preferences An agent chooses among prizes (A, B, etc.) and lotteries, i.e., situations with uncertain prizes Lottery L = [p, A; (1 − p), B] L p 1−p B A Notation: A  B A preferred to B A ∼ B indifference between A and B A ∼  B B not preferred to A Chapter 16 3 Rational preferences Idea: preferences of a rational agent must obey constraints. Rational preferences ⇒ behavior describable as maximization of expected utility Constraints: Orderability (A  B) ∨ (B  A) ∨ (A ∼ B) Transitivity (A  B) ∧ (B  C) ⇒ (A  C) Continuity A  B  C ⇒ ∃ p [p, A; 1 − p, C] ∼ B Substitutability 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]) Chapter 16 4 Rational preferences contd. Violating the constraints leads to self-evident irrationality For example: an agent with intransitive preferences can be induced to give away all its money If B  C, then an agent who has C would pay (say) 1 cent to get B If A  B, then an agent who has B would pay (say) 1 cent to get A If C  A, then an agent who has A would pay (say) 1 cent to get C A B C 1c 1c 1c Chapter 16 5 Maximizing expected utility Theorem (Ramsey, 1931; von Neumann and Morgenstern, 1944): Given preferences satisfying the constraints there exists a real-valued function U such that U(A) ≥ U(B) ⇔ A ∼  B U([p1, S1; . . . ; pn, Sn]) = Σi piU(Si) MEU principle: Choose the action that maximizes expected utility Note: an agent can be entirely rational (consistent with MEU) without ever representing or manipulating utilities and probabilities E.g., a lookup table for perfect tictactoe Chapter 16 6