Monday, September 20, 2010

Minimax Regret and Pascal's Wager

Why do people vote and why do people believe in God? The Minimax Regret argument and Pascal's Wager offer similar logic to answer those questions.

The Minimax Regret theory offered by Ferejohn and Fiorina (1974) creates two states and two alternatives. A vote is decisive or not decisive, and an individual either votes or does not. According to the logic of the argument, an individual wants to minimize the maximum regret he or she will have in the future. Therefore, the individual will always vote because casting a decisive vote provides a benefit greater than 1) the cost of voting and 2) the regret of not voting when it would have been decisive. Even though the probably of casting a decisive vote may be small, the risk of incurring the regret from not voting when it would have been decisive supposedly gives people an incentive to vote.

The French philosopher Pascal offered a similar argument in the 17th century to justify belief in God. The argument presents two states: God exists or God does not exist. It also has two alternatives: live as if God exists or live as if God does not exist. If God does not exist, the individual gains and loses nothing. If God does exist and the individual lives as if God exists, he or she gains “positive infinity” in going to heaven. If God exists and the individual lives as if God does not exist, he or she gains “negative infinity” in going to hell. Therefore, a rational individual would choose to live as if God exists because he or she has everything to gain and nothing to lose.

God exists

God does not exist

Live as if God exists

Gain all (+∞)

Status Quo

Live as if God does not exist

Misery (-∞)

Status Quo

Unlike a good economist, Pascal fails to recognize the cost of living as if God exists. He does not take into account the cost of time spent praying, attending church services, and performing good deeds. There is a fiscal cost of giving money to a church and to the poor. Finally, by leading a morally upright life, an individual faces a high opportunity cost for all the sinful and immoral activities he or she is no longer experiencing. For a present-oriented individual who completely discounts the future, the cost of living as if God exists is not worth the benefit. The rational hedonist would therefore choose to live as if God does not exist.

2 comments:

GW said...

I would argue that Pascal does take the cost of living a life of virtue into account, as he does speak later in his argument of the danger of "wager[ing] too much." The crux of his argument is that "wherever the infinite is and there is not an infinity of chances of loss against that of gain" (whichever choice has a finite probability of infinite gain), "you must give all" (it is rational to pay any finite stakes [e.g. a life of luxurious sin]). In this case even a totally self-interested hedonist, were he to assign a non-zero probability to the existence of God, would have a higher (infinite) expected gain by choosing to believe.

On the other hand, Pascal seems only to have considered the possibility of a Christian god's existence; supposing the existence of many potential gods to choose from (some of whom do not punish non-believers, incidentally), the decision becomes much less clear-cut, as I wonder if the decision matrix is even tractable then.

GW said...

In retrospect, strictly speaking, Tiebout might just tell us to shop around for the best God we can find with the distribution of mercy and damnation that best suits our preferences.