PHIL1004 Lecture Notes - Lecture 2: Blaise Pascal, Decision Theory, Rationality
PA“CAL’“ WAGER LECTURE 2.2 02/03
THE WAGER – BLAISE PASCAL
- By faith we know that God exists.
- All these people hae see the effets, ut the hae ot see the auses
- Decision theory – how you balance your decision.
- Pascal: God is or HE is not. But to which side shall we incline? Reason can decide nothing here. Which
ill ou hoose the? … “ie ou ust of eessit hoose. … Let us eight the gai ad loss i
agerig that God is ….
- No arguet a settle hether God exists. But we must still decide whether we will believe in His
existence.
- A1: wager for God’s eistee
- A2: wager agaist God’s existence
- How good is his bet? Pascal: infinitely good
- Utility is the outcome.
Game 1. Cost to Play = $1. H = $2. T = $0.
A1 (play)
A2 (not play)
S1 (Heads)
(2-1) = 1
0
S2 (Tails)
-1
0
But it costs $1 to play.
Game 2. Cost to play = $1. H = $3. T = $1. Decision theory says you should play the game.
A1 (play)
A2 (not play)
S1 (Heads)
2
0
S2 (Tails)
0
0
Principles of Decision Theory
Dominance Reasoning:
A1 dominates A2 if
a) each utility for A1 is at least as good as the same utility associated with A2
b) at least one utility for A1 is genuinely better
The action with the highest expected utility dominates
Principle of Rationality: if an action dominates another, do that action! You should maximise expected
utility.
Two kinds of DECISION
- Decision under certainty: decide on the basis of utility (outcomes)
- Decision under risk: decide on the basis of utility and its probability of occurring.
- Utility x probability = expected utility
- This tells you how choiceworthy the action is (how much its worth)
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