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Tabarrok's Wager

  • Aug. 23rd, 2004 at 5:46 PM
side-beard-flip
An economists counteroffer [PDF] to Pascal's Wager. A nice demonstration of how infinite payoffs distort the analysis of games. The summary is that the author offers a recommendation on his direct line to God that you should get into heaven - at the cost of all your worldly goods. If you believe there is a non-zero chance that he is telling the truth (however small), it is correct for you to take him up on it. Can be considered a reductio ad absurdum of Pascal's Wager, basically saying that if the payoff to getting into heaven really is infinite, then no amount of worldly resources/happiness are too much to sacrifice for an increased chance, no matter how small, of getting there. The fact that people don't act this way is strong evidence that they don't consider a happy afterlife to have infinite value.

Comments

[info]alexx_kay wrote:
Aug. 23rd, 2004 06:21 pm (UTC)
The fact that people don't act this way is strong evidence that they don't consider a happy afterlife to have infinite value.

It would be strong evidence, if people were actually rational actors. As is, I simply find it amusing.

My counter to Pascal is as follows:
I accept that a happy afterlife has infinite value, and that therefore any way of increasing your chances is worthwhile. But how do you know which actions will increase your chances? Which religion is right? Are any of them? Might not GHod be a rationalist, who wishes to encourage critical thinking? In that instance, having faith in god (any god) might bar you from heaven all by itself.
[info]patrissimo wrote:
Aug. 23rd, 2004 06:27 pm (UTC)
yeah
my answer to Pascal's Wager is always that its a false dichotomy, the matrix is not 2x2. It needs an entry for every single known religion. Heck, maybe every possible religion, since the One True Faith might not be known. Then we need probabilities for each. (I like using %age of adherents among human race, which eliminates nonexistent faiths). Then you need to fill in the consequences for every (truth, what I believe in) pair. Then, and only then, can you calculate the optimal strategy.

(Infinites still screw this up, since you'll be adding and subtracting them from each other.)
[info]songmonk wrote:
Aug. 23rd, 2004 06:44 pm (UTC)
Re: yeah
I don't know much about the history of it, but I've always wondered: did Pascal *really* believe in what is known as Pascal's Wager? He was a pretty smart guy, right? Was he so closed minded that he did not consider possibilities other than the ones described in it? (Not to mention other problems with it like it taking more than lip service and a choice of convenience to get into heaven.)
[info]patrissimo wrote:
Aug. 23rd, 2004 06:54 pm (UTC)
Fraid so
Pascal was *NUTS*. A religious maniac. He luckily escaped death, took it as a sign from God, and spent the last 8 years of his life in a monestary until he died from TB and stomach cancer. Like Newton, a sad tale of brilliance gone awry...
[info]inpetto wrote:
Aug. 23rd, 2004 06:42 pm (UTC)
The fact that people don't act this way is strong evidence that they don't consider a happy afterlife to have infinite value.
Really, I question whether infinite value has any particular meaning relevant to modeling humans making choices. Just because the model uses real numbers and infinity is a kind of quantity (although it is not a real number) does not mean one can throw the concept of infinite utility into the pot and proceed with the analysis. Perhaps this was the author's point.
[info]iron_sky wrote:
Aug. 23rd, 2004 08:25 pm (UTC)
I've had the thought for a while now that humans' intuitive decision-making process doesn't handle very small probabilities well. There's some lower limit to the odds we can intuitively understand, and small probabilities are either handled as this minimum "very unlikely" value or as zero.

If you're multiplying very small probabilities with very large results (e.g. lotteries, airplane crashes), and you have poor resolution on the small probabilities end, it's easy to end up with distorted results.

So one explanation for why people wouldn't act on the author's offer is that the offer isn't credible enough to get bumped from the intuitive valuation of zero truth to "very unlikely".

I'd be curious to see the results of a study testing that idea... something where you could get people to make judgements based on very small probabilities without giving them an opportunity for rational analysis.
[info]patrissimo wrote:
Aug. 24th, 2004 01:06 am (UTC)
yep
I totally agree. Humans are very bad at dealing with small probabilities, and multiplying very large numbers by very small ones.
[info]brkvw wrote:
Aug. 24th, 2004 05:04 pm (UTC)
Re: yep
Also agreed.

Pascal (a funny guy if you study his life), and a catholic, “assumes” that a god would be vindictive. This is the only consideration for those that believe in this trite matrix to begin with.

Why do you concern yourself with “all religions?”
[info]gustavolacerda wrote:
Aug. 24th, 2004 05:30 am (UTC)
Nothing has infinite value. In fact, I would bet there is an upper bound on how "happy" one can possibly get; and even with the possibility of an infinite life of being reasonably happy, people simply don't see that far: their "time preference" curve probably decays exponentially.

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