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CSCI 100
Think Like Computers
Lecture 5
Fall 2008
Decisions
•Some problems are deterministic: actions
lead to known, predictable outcomes
•But others involve chances
Lottery
•Or, they are so complicated that outcomes
is hard to predict
So we assume there are some randomness
Decision-making example
•You are deciding whether to hold a party
inside or outside
•Probability of rain is 1/3
•Indoor party gives reward 2
•Outdoor party with no rain gives reward 3
•Outdoor party with rain gives reward 1
Maximum Expected Utility (MEU)
•The MEU principle says that a rational
agent should choose an action that
maximizes its expected utility.
The utility principle
Theorem 1: If an agent's preferences obey the
axioms of utility theory, then there exists a real-
valued function U that operates on states such that:
U(A) > U(B) ⇔A >B; and
U(A) = U(B) ⇔A ≡B
Theorem 2: The utility of a lottery is the sum of
probabilities of each outcome times the utility of that
outcome: U([p1,S1; p2,S2; ...; pn,Sn] = ∑ipiU(Si)
- expected utility
Expected monetary value
Example: You can take a $1,000,000 prize (A) or
gamble on it by flipping a coin (B). If you
gamble, you will either triple the prize or loose
it.
EMV (expected monetary value) of the lottery is
$1,500,000, but does it have higher utility?
EU(Gamble)=0.5*U(x)+0.5*U(x+3,000,000)
EU(Take)=U(x+1,000,000)
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