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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 $\nu$
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 $\nu$. Now to determine the strategy that is best, you should compare the two expected values

\begin{displaymath}-pu+(1-p)\nu\qquad{\rm {and}}\qquad p0+(1-p)(-x),\end{displaymath}

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 $\nu$ 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

\begin{displaymath}\nu=\infty\end{displaymath}

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


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