shkrobius (shkrobius) wrote,
shkrobius
shkrobius

Why the Pascal's wager does not work?

http://ivanov-petrov.livejournal.com/1697059.html?thread=85093923#t85093923
& http://ivanov-petrov.livejournal.com/1695016.html

One does not need to reject the idea that rationality is maximization of self-interest to find a major flaw with the Pascal's wager. The problem is the structure of the utility itself.

The wager is not the only example of this kind. People rationally choose against infinite reward in any game against the opponent with infinite resources, the classical example being St Peterburg lottery
http://en.wikipedia.org/wiki/St._Petersburg_paradox
http://plato.stanford.edu/archives/fall2004/entries/paradox-stpetersburg/
We are not prepared to spend ANY amount of money on a gamble even when the winning is infinite, because we are biologically conditioned to think of the utility as finite/slowly growing/bound even when it is, mathematically, infinite. That is the chief problem with Pascal's argument: to work, it requires infinite reward, as the probability (in this case, of divine existence) can be arbitrary low, while remaining non-zero. But there is no such thing in the human mind as infinite reward.

There are several ways of resolving such paradoxes, but they all share one feature: we are finite beings that cannot comprehend infinite reward, so the argument does not work on us. Instead of thinking of the reward in terms of the absolute utility, we think about it in terms of expected or marginal utility. There is a branch of decision theory dealing with risk aversion resulting from precisely such limitations of our mind. What forces you against the wager, on the final count, is rationality (rather than belief or lack thereof), but it is the rationality of normal economic choice in which the resources are finite and risk aversion is mathematically sound strategy. It is this rationality that underlies the aversion to risk. So what we have here is not rationality vs. belief but the conflict of two forms rationality: one that is based on mathematical reasoning and another reasoning that is based on learned behavior and marginal utility and the decision theory that (possibly) underlies it. We are designed in such a way that Pascal's wager does not work on us.

Why? Had faith been rational choice for infinite gain, free will would not be possible, as this faith would be the dictum of practical reason rather than a matter of choice. So it makes perfect rational sense that our rationality is the way it is, rejecting the wager, precisely from the theological perspective.

The infinite reward is essential to the wager. First, it is leveraging the odds that can be arbitrarily small. The second is that since it is infinite, it includes any possible reward. If IP does not like sweets, he still wants something else. Whatever IP wants, it will be in this reward. All that transpires from IP's argument is that he does not want $1,000. Furthermore, if he considers emotional independence to be his reward, it is part of this infinite reward, too. The problem is that IP still considers infinite reward as a finite one. That's not the Pascal's wager.
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