Sunday, September 10, 2017

Pascal's scary Wager



Pascal's wager is usually used as a way to scare people into being religious, because, "What if you're wrong?" Among its many, many problems is that it can be used in the same way to scare people into anything. For the same reasons it fails to be convincing for all those other things, it fails to be a convincing argument to believe in God and accept religion.



Pascal's Wager

Wager God exists
Wager God doesn't exist
You're right
Eternal reward
Nothing
You're wrong
Nothing
Suffering in Afterlife / missed out on eternal reward

Sex wager
The world will end unless you sleep with me.

Wager I'm telling the truth
Wager I'm lying
You're right
You save the world
Nothing
You're wrong
Nothing
World ends

So, your place or mine?

9 comments:

  1. For somebody who truly believes in God and finds serving him the most joyous experience possible, then the risk of being wrong that God exists really is nothing. But to those of us who would find every minute spent serving a god we are 99.9% sure doesn't exist dreadfully boring and meaningless, the risk is most definitely not nothing.

    As for the argument that infinite reward beats finite reward, no matter how low the probability of infinite reward, that would be correct if we could play this life over many times, until we finally hit the jackpot, received our infinite reward, and made up for all the losses we had till then.

    But that's not the case. We've only got one life. And I'm sure as hell not going to ruin it for a <0.1% chance of infinite reward.

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    1. > For somebody who truly believes in God and finds serving him the most joyous experience possible, then the risk of being wrong that God exists really is nothing.

      That Wager isn't for that person. He has a reason to serve God, whether or not God exists. The Wager is supposed to convince the rest of us that betting God exists is the better bet. But we wouldn't bet that way for anything else.

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  2. I see Pascal's Wager as a simplified form of the St. Petersburg paradox (https://en.wikipedia.org/wiki/St._Petersburg_paradox). Whatever solution you use for that would apply to Pascal too, providing you don't work with "no such wealthy banker exists", as Pascal builds that into his problem by making the "banker" God.

    G*3 - your version does not work quite as well as Pascal's. As an example, consider someone with a linear utility function (y=x). To her (i presume it is a her you are aiming your argument at, but I may of course be wrong) the "cost" of the world ending is associated with a utility of 0, vs. her current wealth, say 1. She can then calculate whether to acquiesce by weighting the "cost" of doing so by the probability of you being wrong and comparing it to the "cost" of not doing so and you being right:

    "acquiesce cost" x P(you are wrong) vs. 0 x [1-P(you are wrong)]

    Whichever is the higher is the option she should take. Presumably P(you are wrong) is fairly close to 1, meaning that even with a fairly small cost of accepting your request she may well be best of saying no. I am presuming that there is no "gain" in having saved the world. Things just go on as they are. Even if there is, presumably the gain is not infinite, in which case the point remains.

    Contrast this with Pascal, where as the payoff is infinite, weighted payoff is infinite for any non-zero P, meaning that "wagering God's side" is always preferable *for any unbounded utility function*.

    Your case *would* work for any utility curve that put an infinitly low

    To make yours equivalent you either need an infinite *positive* reward, a specific subset of possible utility functions (it would work fine for a log utility function as log(0) is - infinity), or the supposition that the "world ending" is an event with a negative infinity payoff (in which yours would work for any unbounded utility function, but would effectively rely on God as otherwise why is the world ending an infinitely bad nominal payoff).

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    1. You're right, nothing is exactly analogous to Pascal's Wager because of the infinite payoffs. But, 1. infinities do weird things to the calculations, and more importantly, 2. we can't really conceive of infinities and 3. most people don't use the Wager as a mathematical construct. It's a "gothcha," a, "What if you're wrong? You'll have sacrificed so much good, and be in so much trouble!"

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    2. How about "you'll receive infinite reward in the afterlife if you sleep with me"?

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    3. Some unscrupulous rabbis (like the ex-head of the Breslav group) actually used that one to deceive vulnerable women to sleeping with them

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  3. I never found Pascal Wager at all convincing. Some Christians told me if I do not accept Jesus I will suffer eternal damnation. So I should reject all religions because of this threat ? And what if other religions also make threats ? I have to evaluate all competing threats ? Also, 'believing'in the hope of obtaining supernatural favors seems obsequious, fawning and dishonest.

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    1. It may seem obsequious etc, but if it works it works.

      Re your first point, some would point out that you then need to go with whichever religion promising infinite reward is most likely. What they may miss is that you also need to take into account how good the infinite rewards are and punishments for being wrong are comparatively. You then need to scale for probability of each being correct. Personally from what i have heard the christian hell sounds the worst so Pascal is sounding the bell for jc.

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