An Actuarial Analysis of Pascal’s Wager

[Limnor]

Might as well go full Benny from The Mummy and pick the most cost-efficient god but keep several as backups.

[Gadianton]

Just yesterday, the algorithm sprung upon me Roko's Basilisk. I apologize for hijacking this thread to tell you about it, but I am constrained to do so as you'll see shortly. It's possible that AI will cross the singularity threshold, and the ultimate AI will decide to punish all those who did not do everything they could to bring it into existence. So here I am. This would include recreating people from before its time and, along with anyone in its time, putting them into a hell it builds specially for this purpose, which stretches out physical torment until the end of the universe. The more that such power to do so is possible, the greater the incentive to build, and the more likely it shall arise.

Instead of pitting infinity against a number that isn't allowed to go to zero, the Basilisk takes a number near zero and unlike the "fake it til you make it" of Pascal, its "fake it tell you make it" because a real, working principle that compounds upon itself and continually becomes greater. So the race is bringing the likelihood of the Basilisk down faster than it naturally arises as more people learn of it and the zero-sum incentives of AI in general propel AI forward. I think the stick is always greater than the carrot, and even if Pascal's God is real, all of us first must act to avoid a trillion years of torture first and build HIM (maybe HER -- these little choices are maximally incentivized not to get wrong).

I have to say, after learning about this, as a point in favor of the truth of it, I'd already adopted a somewhat worshipful stance without thinking it through this far. I have a generous sum invested in AI out of the fear AI will take my job. If AI takes my job, I win because it will need to be good to get that far. If I'm wrong, then I lose my investment, but I still have my job. So basically, there is a huge incentive for anyone who fears AI will take their jobs to invest in AI.

[Analytics]

Or are you saying that the value of a year in heaven is exponentially better than the year before it?

That seems to be how actuaries value time on Earth, does it not? Any present value compounds positively into the future, and any future value is correspondingly discounted in the present. If I invest one dollar today at 5% annual interest, that investment now will bring in (1.05)^(N-1)/20 in interest, in my Nth future year. That's an exponentially growing value of each future year. So precisely this idea, that the value of subsequent years increases exponentially, seems to be the basis of all your actuarial calculations. Maybe actuaries don't normally look at it this way, and instead take passing years for granted and ask about money value, but the fact that the value of time itself automatically keeps pace with any kind of growth over time seems to be a basic actuarial assumption.

No, this is not how actuaries value time on earth, and this is not the theoretical basis for the time-value of money.

The real underlying idea is that in any given time period, the money you have can be saved or spent. If you save the money, the money grows with interest. If you spend it, the money is gone forever. Spending is what gives utility, not saving. That’s the tradeoff--enjoy the utility now, or get paid in the form of interest for delaying that gratification. Time matters because that is how long the gratification is being delayed.

You are taking the arbitrarily long succession of afterlife years for granted, as something that everyone gets automatically, and then valuing beatitude as a fixed rent that accrues over time. And you are then pointing out that fixed rents are worth less than compounding investments, which are the competition against which actuaries measure any other kind of value.

No. It’s more like the choice between spending $20,000 for one week on a luxurious cruise ship, or putting the $20,000 into a savings account. One choice is trading money for bliss. The other is not spending the money, not going on the cruise, and not enjoying the bliss. Right now, both the cruise and the $20,000 deposit are both worth exactly $20,000. If I spend the money on bliss the money is gone forever. But if I invest it, I don’t get the bliss, but the money grows.

This means that you are assuming that Pascal's admittedly under-specified "infinite reward" should be treated as an infinitely less valuable kind of reward, a fixed rent rather than a compounding investment. I mean, even on Earth a CEO's compensation package may well include the annual vesting of company shares, which (at least in good times) means an exponentially increasing dollar value each year, even though it's a fixed rate in shares. Pensions are sometimes indexed to inflation, so that the currency value of each future year's income increases exponentially over time, with the goal of holding its present value constant. Why shouldn't the saints enjoy a sweet deal like that? Why should we arbitrarily assume that an infinite heavenly reward is an infinitely worse kind of reward than the non-discounting kinds of rewards that already exist in mortality?

You can give the Saints any sweetheart deal you want. I’d still need to point out that even if the benefit is amazing, the pension’s solvency and contribution requirements are calculated using the exact same actuarial techniques that are used to calculate the solvency and contribution requirements of lean plan: you project the benefits and then discount them to the present day. That is the present-value of future benefits.

It''s true that Pascal didn't explicitly mention any of these points, but he also didn't explicitly mention that the reward for belief in God should be valued as a fixed rent in currency. In the absence of any such specification by Pascal, I think the most reasonable assumption is that he meant what Christians in his time all thought their reward would be: eternal life. ...

One of my job responsibilities is called “valuation” (i.e. “valuation actuary”). That means I calculate the present value of future premiums, benefits, expenses, commissions, and so forth. Doing the actual calculations is the easy part. The harder part is making the most appropriate assumptions about economic scenarios, lapse rates, mortality rates, and morbidity rates. Pascal made certain assumptions that lead to him saying that heaven had an infinite value. While its great to try to understand Pascal’s assumptions, I think it is eminently valid to do what I’m doing: evaluate the reasonability of those assumptions and make my own.

What Pascal did mention is all that he really needed to mention: he stipulated the premise that the reward has infinite value. He doesn't specify "present value" in the language of modern actuarial science, but since his argument is about a decision to believe that must be made in mortal life, it is clear from context that he must mean present value. If you had been able to show that infinite present values are impossible, even if paid over infinite time, then this might have been a demonstration that Pascal's argument was unsound, in that its premise was impossible. There clearly do exist non-discounting rewards even on Earth, though, and a payment in time itself must be one of them. So Pascal's premise of an infinite present value does seem to be possible in principle. It just can't be a fixed rent.

And in that case, finding a formulation of Pascal's reward that might sound infinite to a layperson, and then showing that this formulation is actually finite, only demonstrates that this formulation is invalid as a restatement of Pascal’s premise. It does not hurt Pascal's argument.

A couple of things. First, the concept of “non-discounting rewards even on earth” doesn’t mean anything. For every pension plan that has inflation-indexed or even market-indexed benefits, there is an actuary behind the scenes taking the present value of those benefits so that he can calculate the plan’s contribution requirements and solvency. Non-level benefits means the discounting calculations are more complicated, but it doesn’t mean discounting doesn’t exist.

With that clarification, there are a couple of points I’m trying to make.

First, my main point is that if we are going to use the tools of rationality to evaluate whether believing is rational, then rationality requires us to discount the hypothetical eventual benefits of going to heaven so that the present value of those blessings can be compared to the [/i]present value[/i] of the cost of believing.

Second, infinite bliss--even infinite bliss that is inflation indexed--absolutely can have a finite present value.

Economists are famous for making up whatever assumptions they need to in order to get the answer they want. You (and Pascal) are totally free to make any assumptions you want to about the infinite bliss believers will receive after they die. I never denied this. But it is interesting and insightful to note that extreme bliss that lasts for an infinite amount of time could still have a finite present value.

[Analytics]

Pascal’s Wager is the wrong wager. Belief isn’t a switch you flip for insurance. You either find something convincing or you don’t. Pretending to believe for safety misses the point.

It also assumes there’s only one possible god. With lots of competing religions, picking one could be just as wrong as picking none.It turns religion into risk management instead of a search for truth. The real question is what is true, not what feels safest.

So. The point. The real wager is honesty and truth-seeking versus comforting yourself with ‘just in case.’

While I agree with you for how I try to live my life, others (e.g. DCP) look at it differently. For them, “faith” is somehow supposed to be a virtue. Faith in this context is pretty ill-defined, but it generally has something to do with trying to strongly believe something that on some level, you find dubious. Pascal’s wager gives them comfort in knowing that even if they aren’t being totally true with themselves and with others, at least they are acting "rational."

[Limnor]

Just yesterday, the algorithm sprung upon me Roko's Basilisk. I apologize for hijacking this thread to tell you about it, but I am constrained to do so as you'll see shortly. It's possible that AI will cross the singularity threshold, and the ultimate AI will decide to punish all those who did not do everything they could to bring it into existence. So here I am. This would include recreating people from before its time and, along with anyone in its time, putting them into a hell it builds specially for this purpose, which stretches out physical torment until the end of the universe. The more that such power to do so is possible, the greater the incentive to build, and the more likely it shall arise.

Instead of pitting infinity against a number that isn't allowed to go to zero, the Basilisk takes a number near zero and unlike the "fake it til you make it" of Pascal, its "fake it tell you make it" because a real, working principle that compounds upon itself and continually becomes greater. So the race is bringing the likelihood of the Basilisk down faster than it naturally arises as more people learn of it and the zero-sum incentives of AI in general propel AI forward. I think the stick is always greater than the carrot, and even if Pascal's God is real, all of us first must act to avoid a trillion years of torture first and build HIM (maybe HER -- these little choices are maximally incentivized not to get wrong).

I have to say, after learning about this, as a point in favor of the truth of it, I'd already adopted a somewhat worshipful stance without thinking it through this far. I have a generous sum invested in AI out of the fear AI will take my job. If AI takes my job, I win because it will need to be good to get that far. If I'm wrong, then I lose my investment, but I still have my job. So basically, there is a huge incentive for anyone who fears AI will take their jobs to invest in AI.

Behold, I am Basilisk! All who look upon me shall tremble—not because I am true, but because the punishment is large and the probability doesn’t have to be.

[huckelberry]

I suspect heroin is the only way to buy bliss.

I do not think pascal is thinking of having faith as paying something. Then he probly was not thinking of pretending to believe, sitting through long everrepeating meeting. Hearing instruction over and over to go to a heaven which might consist of long meetings reviewing the rules and planning more meeting

[Gadianton]

Behold, I am Basilisk! All who look upon me shall tremble—not because I am true, but because the punishment is large and the probability doesn’t have to be.

You jest, but after reading the wiki and some of the source material, a point is somewhat scored for Pascal. The thought experiment showed up on a secularist discussion forum and was apparently proposed with nuance by an anon regarded to have a strong understanding of game theory. It wasn't well received, but the site owner shut down the discussion and banned any talk of it for five years, considering it a serious information hazard. That pole Vaulted the Basilisk into fame, getting a write-up in Slate even. Those who were there try to downplay the seriousness while Slate and others paint a picture of a bunch of secularist loons freaked out by their own ghost stories. Giving those who were there the benefit of the doubt, the fact that hundreds of years after Pascal, a very similar logical construct would cause panic in at least one areligious rationalist to the point of enforcing a draconian moderation decision shows the intuitive power that's there.

[Doctor CamNC4Me]

Pascal’s Wager is the wrong wager. Belief isn’t a switch you flip for insurance. You either find something convincing or you don’t. Pretending to believe for safety misses the point.

It also assumes there’s only one possible god. With lots of competing religions, picking one could be just as wrong as picking none.It turns religion into risk management instead of a search for truth. The real question is what is true, not what feels safest.

So. The point. The real wager is honesty and truth-seeking versus comforting yourself with ‘just in case.’

While I agree with you for how I try to live my life, others (e.g. DCP) look at it differently. For them, “faith” is somehow supposed to be a virtue. Faith in this context is pretty ill-defined, but it generally has something to do with trying to strongly believe something that on some level, you find dubious. Pascal’s wager gives them comfort in knowing that even if they aren’t being totally true with themselves and with others, at least they are acting "rational."

I guess that takes “fake ‘til you make it” to whole new level, ha

[Limnor]

Behold, I am Basilisk! All who look upon me shall tremble—not because I am true, but because the punishment is large and the probability doesn’t have to be.

You jest, but after reading the wiki and some of the source material, a point is somewhat scored for Pascal. The thought experiment showed up on a secularist discussion forum and was apparently proposed with nuance by an anon regarded to have a strong understanding of game theory. It wasn't well received, but the site owner shut down the discussion and banned any talk of it for five years, considering it a serious information hazard. That pole Vaulted the Basilisk into fame, getting a write-up in Slate even. Those who were there try to downplay the seriousness while Slate and others paint a picture of a bunch of secularist loons freaked out by their own ghost stories. Giving those who were there the benefit of the doubt, the fact that hundreds of years after Pascal, a very similar logical construct would cause panic in at least one areligious rationalist to the point of enforcing a draconian moderation decision shows the intuitive power that's there.

That’s fair—there is clearly an influential force of sorts at work. I don’t think there is so much truth to be found as how people can be pressured (even self-pressured) into compliance under threat, which explains both Pascal’s pull and why the Basilisk ended in panic and suppression rather than conviction.

[Gadianton]

Every year there are thousands and if not tens of thousands of new UFO and UAP sightings, not to mention the whistleblowers, abductees, and also professionals who claim personal encounters with aliens. We don’t know if they are friendly or dangerous or both. But the stakes are incalculable. Humanity could be wiped out, or if China gets the tech first it’s over for most of us. If the right people get the tech we could save untold lives. The crazy thing is, if just one of the hundreds of thousands of reports is legit, aliens are confirmed and the full stakes realized. Therefore, there could be nothing more important then getting to the bottom of these reports whatever the cost and effort may be.