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Critical Thinking Lecture 14 Pascal ’ s wager

Critical Thinking Lecture 14 Pascal ’ s wager. By David Kelsey. Pascal. Blaise Pascal lived from 1623-1662. He was a famous mathematician and a gambler. He invented the theory of probability. Probability and decision theory. Pascal thinks that we can ’ t know for sure whether God exists.

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Critical Thinking Lecture 14 Pascal ’ s wager

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  1. Critical ThinkingLecture 14Pascal’s wager By David Kelsey

  2. Pascal • Blaise Pascal lived from 1623-1662. • He was a famous mathematician and a gambler. • He invented the theory of probability.

  3. Probability anddecision theory • Pascal thinks that we can’t know for sure whether God exists. • Decision theory: used to study how to make decisions under uncertainty, I.e. when you don’t know what will happen. • Lakers or Knicks: • Rain coat: • Rule for action: when making a decision under a time of uncertainty always perform that action that has the highest expected utility!

  4. Expected Utility • The expected utility for any action: the payoff you can expect to gain on each attempt if you continued to make attempts... • It is the average gain or loss per attempt. • The payoff or value of an outcome: what is to be gained or lost if that outcome occurs. • To compute the expected value of an action: • ((The prob. of a success) x (The payoff of success)) + ((the prob. of a loss) x (the payoff of a loss)) • Which game would you play? • The Big 12: pay 1$ to roll two dice. • Lucky 7: pay 1$ to roll two dice. • E.V. of Big 12: • E.V. of Lucky 7:

  5. Payoff matrices • Gamble: Part of the idea of decision theory is that you can think of any decision under uncertainty as a kind of gamble. • Payoff Matrix: used to represent a scenario in which you have to make a decision under uncertainty. • On the left: our alternative courses of action. • At the top: the outcomes. • Next to each outcome: add the probability that it will occur. • Under each outcome: the payoff for that outcome • Calling a coin flip: • If you win it you get a quarter and if you lose it you lose a quarter. • The coin comes up heads: ___ It comes up tails: ___ • You call heads ___ ___ • You call tails ___ ___

  6. The Expected Utility of the coin flip • So when making a decision under a time of uncertainty: construct a payoff matrix • Which action: • Perform the action with the highest expected utility! • To compute the expected value of an action: • ((The prob. of a success) x (The payoff of success)) + ((the prob. of a loss) x (the payoff of a loss)) • For our coin tossing example: • The EU of calling head: • … • The EU of calling tails: • … • Choose either action…

  7. Taking the umbrellato work • Do you take an umbrella to work? You live in Seattle. There is a 50% chance it will rain. • Taking the Umbrella: a bit of a pain. You will have to carry it around. • Payoff = -5. • If it does rain & you don’t have the umbrella: you will get soaked • payoff of -50. • If it doesn’t rain then you don’t have to lug it around: • payoff of 10. • It rains (___) It doesn’t rain (___) • Take umbrella ___ ___ • Don’t take umbrella ___ ___ • EU (take umbrella) = … • EU (don’t take umbrella) = … • Take the umbrella to work!

  8. Pascal’s wager • Choosing to believe in God: Pascal thinks that choosing whether to believe in God is like choosing whether to take an umbrella to work in Seattle. • It is a decision made under a time of uncertainty: • But We can estimate the payoffs: • Believing in God is a bit of pain whether or not he exists: • An infinite Reward: … • Infinite Punishment: …

  9. Pascal’s payoff matrix • God exists (___) God doesn’t exist (___) • Believe ____ ____ • Don’t believe ____ ____ • Assigning a probability to God’s existence: • A bit tricky since we don’t know. • For Pascal: • since we don’t know if God exists we know the probability of his existence is greater than 0. • EU (believe) = … • EU (don’t believe) = … • Believe in God: …

  10. Pascal’s argument • Pascal’s argument: • 1. You can either believe in God or not believe in God. • 2. Believing in God has greater EU than disbelieving in God. • 3. You should perform whatever action has the greatest EU. • 4. Thus, you should believe in God.

  11. Denying premise 1 • The first move: • Can you choose to believe? • The second move: • Would God reward selfish believers?

  12. Denying premise 2 • Deny premise 2: • Infinite payoff’s make no sense: • Can we even assign a non-zero probability to God’s existence?

  13. The Many Gods objection • We could Deny premise 2 in another way: • Many Gods & the Perverse Master…

  14. The Perverse Master • The new payoff matrix: • God exists (__) Perverse Master exists (__) Neither exists (___) • Believe _____ _____ ___ • Don’t Believe _____ _____ ___ • Disbelief seems no worse off than belief: • EU (believe) = … • EU (don’t believe) = … • Is it less likely that the perverse Master exists than does God?

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