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### Pascal's rationalisation of religion

Great Expectations:
This is an application of the idea of expectation! Blaise Pascal (1623-1662) gave an interesting argument to show that a rational person should believe in the existence of God. Pascal said that we have to make a wager whether to believe or not to believe. He suggests that we are playing a game with two strategies, believe and not believe, with payoffs as follows:

 God does not exist God does exist Probability p (1-p) Believe -u Do not believe 0 -x

Here -u represents the cost to you of passing up some worldly pleasures as a consequence of believing that God exists. If you do not believe, and God is a vengeful God, you will lose x. If God does exist, and you believe that God exists, then the payoff is . Now to determine the strategy that is best, you should compare the two expected values

and choose the larger of the two. In general, the choice will depend on the value of p. But Pascal assumed that the value of is infinite, and so the strategy of believing is best no matter what probability you assign for the existence of God. Whether Pascal is correct in assigning

is, of course, hardly a matter for mere mathematicians!!!

Next: Indicator variables and Bernouilli Up: Discrete Random Variable 11/6 Previous: Properties of Expectation 11/6
Susan Holmes
1998-12-07