Pascal’s Muggle Pays

Scope insensitivity can be thought of as evolution’s solution to not getting Pascal’s mugged.

This could be true, but I don't think it is and I think the difference is probably important.

Concern A: I'm just really skeptical that the ancestral environment gave people opportunity to be confronted with Big Numbers that needed to avoid getting mugged over.

Concern B: Scope insensitivity doesn't kick in at 1000 people. It kicks in at... (drumroll)... two people. (i.e. we have studies where advertisements for donations for a single child make more money than advertisements for 2 children or 8)

This suggests something else is going on than simply numbers getting too big to count, and I think it's more likely to have to do with how a strong a connection you feel with the recipient. (I notice I'm confused about why this should matter. My first guesses have something to do with how likely the recepient is to return the favor in some fashion)

Unless I'm missing something, the trouble with this is that, absent a leverage penalty, all of the reasons you've listed for not having a muggable decision algorithm... drumroll... center on the real world, which, absent a leverage penalty, is vastly outweighed by tiny probabilities of googolplexes and ackermann numbers of utilons. If you don't already consider the Mugger's claim to be vastly improbable, then all the considerations of "But if I logically decide to let myself be mugged that retrologically increases his probability of lying" or "If I let myself mugged this real-world scenario will be repeated many times" are vastly outweighed by the tiny probability that the Mugger is telling the truth.

Great post. Fantastic. Dutch booking, in particular, is fascinating — first time I heard it.

On a related note, I think there's a particular type of error that smart people are actually more prone to make — discounting variance.

If I said,

"There's some very real situations where taking a 99% chance of good outcome X produces better outcomes than taking a seeming 1% chance of 1000x" — nobody would disagree with that, it's obvious on the surface. There's secondary effects, morale effects, future resource allocation judgements, etc.

But suddenly, if you say,

"There's some very real situations where a 99% chance of saving a life produces better outcomes than taking a seeming 1% chance of saving 1000 lives" — some people don't accept that that's ever true if you were certain your probabalistic estimates are correct.

Variance is a real thing. It matters. A lot. There's many situations where a 'W' of any size helps get you to the next stage, whereas a "I followed good process but it didn't work" does not — even among the most stoic, far-sighted, analytical, and rational of people.

The $5 for (googolplex of gains)*(likelihood of the googolplex outcome) has a terribly large amount of variance built into it. Sure, $5 might be below the "screw it" threshold, but as soon you as you substitute a number you can do something significantly large with — say, $10,000 — you start to recognize why you wouldn't take the bet even if the EV is great on it. All the upside is caught up in the vanishingly small percentage of times that this highly unlikely positive event happens, and there's a lot of much lower variance activities that produce good outcomes.

If you were the sort of person who would pay Pascal's mugger, you would still not get solicited for money by people pretending to control the fates of 3↑↑↑3 people, because people don't do this in real life, and no one would ever discover that it would work on you. I could have written a LessWrong post arguing that it is rational to pay Pascal's mugger and that I would pay Pascal's mugger if the scenario ever actually happened to me, and I still probably wouldn't get Pascal-mugged because of the people who'd read it, none of them would both want to take advantage of me for $5 and be able to get to me for a cost of less than $5. If you were worried about facing more false Pascal's muggers as a result of being the sort of person who pays Pascal's mugger, but you would actually pay Pascal's mugger if not for this concern, then you'd be more likely to come up with some sort of compromise solution, like paying Pascal's mugger unless they ask for too much or unless you've faced too many of them, rather than just not paying Pascal's mugger. And of course, if you really treated the fates of 3↑↑↑3 people as 3↑↑↑3 times as important as the fate of one person, you'd just keep paying all these Pascal's muggers who figured out it works on you anyway, and if you ran out of money, you'd try to get more money to keep paying them by whatever means you can with the desparation of a broke heroin addict going through withdrawl, because the unimaginably tiny chance that one of these Pascal's muggers is actually legit would still be enough to outweigh the fact that you're attracting false Pascal's muggers to you by acting that way.

This is *really* good.

>They yell at us for voting, and/or asking us to justify not living in a van down by the river on microwaved ramen noodles in terms of our expected additional future earnings from our resulting increased motivation and the networking effects of increased social status.

Could I ask how FDT justifies not living in a van down by the river?

This feels sort of minor, but for your second link you should really credit the writer (AlexMennen), not the site it's published on.

As I said in the other thread:

I've changed my mind. I agree with this.

The probability of you getting struck by lightning and dying while making your decision is $>{10}^{-40}$.

The probability of you dying by a meteor strike, by an earthquake, by .... is $>{10}^{-40}$.

The probability that you don't get to complete your decision for one reason or the other is $>{10}^{-40}$.

It doesn't make sense then to entertain probabilities vastly lower than $10-40$ , but not entertain probabilities much higher than ${10}^{-40}$.

What happens is that our utility is bounded at or below ${10}^{-40}$.

This is because we ignore probabilities at that order of magnitude via revealed preference theory.

If you value $X$ at $K$ times more utility than $Y$, then you are indifferent between exchanging $Y$ for a $\frac{1}{K}$ times chance of getting $X$.

I'm not indifferent between exchanging $\$1000$ for a ${10}^{-40}$ chance of anything, so my utility is bounded at ${10}^{40}$ . It is possible that others deny this is true for them, but they are being inconsistent. They ignore other events with higher probability which may prevent them from deciding, but consider events they assign vastly lower probability.

Realising that your utility function is bounded is sufficient to reject Pascal's mugging.

That said, I agree with you.

Wonderful post! As I mentioned in the comments on Against the Linear Utility Hypothesis and the Leverage Penalty I am in the process of writing a reply to this as well, and about half of what I had planned to write was this. Thank you for writing this up better than I would have!

I would like to add that not paying the muggler before the rift in the sky, but paying him afterwards, might not be a sole result of the decision theory (although it's certainly very related): there is also something interesting going on with the probabilities. It is a priori pretty likely that given that a poorly-dressed person walks up to you on the street, you are about to hear some outlandish claim and a request for money. Therefore your updated probability of this being a random muggler instead of a matrix lord is still pretty high even after hearing the offer. However this probabiliy vanishes to almost nothingness after observing the reality-breaking sky rift - and how close to nothingness this vanishes to is directly dependent on the absurdity of the event witnessed.

In practice I would just pony up the money at the end of your scenario, for the same reasons as you give. So I guess my true rejection to Pascal's Mugging is the one you give. I think I'll still write out the other half of my ideas though, for agents with slightly more computing power than we have.