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Pascal's Mugging (2009) [pdf]

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Re: Pascal's Mugging (2009) [pdf]

#41

Post by YeGoblynQueenne »

lidHanteyk wrote: post #31
Strilanc wrote: post #28

Earlier quoted context omitted.

If you set the probability at zero, you won't be convinced when they actually are an operator from the seventh dimension. That is to say, you run into the opposite problem of being Pascal's Muggle [1]. 1: https://www.lesswrong.com/posts/Ap4KfkHyxjYPDiqh2/pascal-s-m... > A wind begins to blow about the alley, whipping the Mugger's loose clothes about him as they shift from ill-fitting shirt and jeans into robes of inf…

In no particular order: * Helping a googleplex of people immediately vs over a period of time are two different complexities of action. * Recall that hypotheses are selected from an ambient pool of possibilities. Then we might imagine that some hypotheses dominate others, so that regardless of how much evidence is offered, we always insist that the evidence supports a simpler alternative. To wit: "Well, if I'm not a…

That's a good point: if the Mugger is an Operator from the Fifth Dimension and he has such great magickal powers, why does he need the 10lb in Pascal's wallet? Or, if he does need them, why can't he just get them?

Like, we are asked to believe that, given that the Mugger is an Operator from the Seventh Dimension, he has the power to offer 10 quintillion Utils to Pascal, but not the power to just take the 10lb from his wallet.

I think the whole paradox can still stand, given that the Mugger can then just offer an amount of Utils that compensates from the much smaller conditional probability of the Mugger being only sorta omnipotent.

On the other hand, I think we can easily resolve the paradox by inserting the Crowbar of Cynical Jadedness: If it sounds too good to be true, then its probability of being either good, or true is zero (it can be one or the other with a non-zero probability, but not both). 10 quintillion utils (or however many) sounds too good to be true, so it can't be true. A Used Car Salesman will never offer you a good deal. The Mugger is only lying to get Pascal's money.

Re: Pascal's Mugging (2009) [pdf]

#42

Post by YeGoblynQueenne »

Strilanc wrote: post #28
YeGoblynQueenne wrote: post #27

I don't know the background to this but if I understand correctly, it kind of pivots on the probability that the mugger is indeed an Operator from the Seventh Dimension, that Pascal places at 1 in a quadrillion. In that case, I have to wonder where this estimate comes from? I get that it's just an arbitrary number and that any number would do, as long as it wasn't zero, but that's exactly the point: why can't Pascal…

If you set the probability at zero, you won't be convinced when they actually are an operator from the seventh dimension. That is to say, you run into the opposite problem of being Pascal's Muggle [1]. 1: https://www.lesswrong.com/posts/Ap4KfkHyxjYPDiqh2/pascal-s-m... > A wind begins to blow about the alley, whipping the Mugger's loose clothes about him as they shift from ill-fitting shirt and jeans into robes of inf…

Thanks, that's an interesting read. But I don't think it addresses my question: why shouldn't Pascal place the probability that the Mugger is an Operator from the Seventh dimension to _zero_ (rather than an infinitissemally small number)?

The point is that, at the time when the Mugger declares himself to be an Operator from the Seventh Dimension who can offer large rewards etc, there is no evidence to suggest he's saying the truth. No evidence at all. Accordingly, the probability that he's telling the truth must be zero. Where does a non-zero probability value come from?

Are you then saying that the probability of any reward should never be placed to zero because that would not maximise rewards?

Re: Pascal's Mugging (2009) [pdf]

#43

Post by YeGoblynQueenne »

edflsafoiewq wrote: post #30
YeGoblynQueenne wrote: post #27

I don't know the background to this but if I understand correctly, it kind of pivots on the probability that the mugger is indeed an Operator from the Seventh Dimension, that Pascal places at 1 in a quadrillion. In that case, I have to wonder where this estimate comes from? I get that it's just an arbitrary number and that any number would do, as long as it wasn't zero, but that's exactly the point: why can't Pascal…

> I beseech you, in the bowels of Christ, think it possible that you may be mistaken. https://en.wikipedia.org/wiki/Cromwell%27s_rule

I think this is the same idea in another comment, above, about Pascal's Muggle. I think there's a bit of a confusion here though. I can adjust the probabilities of any event given new evidence.

For example, at this point in time I believe that the probability that I can fly if I flap my arms up and down is zero. I have no evidence that this is possible and I understand enough of the relevant physics to know that this is not just improbable, it is impossible.

However, if tomorrow I flapped my arms and found that I could fly, there would be nothing stopping me from re-evaluating my belief and assigning a higher probability to the chance that I can fly if I flap my arms.

But I think the problems begin with the misguided ambition to be able to predict the future even when there is no evidence to support any prediction. You can't know what you can't know. You can assign any probability you like to what you can't know, but even if you end up assigning the right probability that will be the result of blind chance, not the result of correct reasoning.

Anyway this is why I prefer logical inference to probabilistic inference. I understand that I'm in a minority on this, but for me it makes a lot more sense to maintain a state of provisional belief with an absolute value (in {0,1}), provisional in the sense that new evidence can always change your belief, than to live in a perpetual state of uncertainty which never resolves itself no matter how much evidence you see, because there is always a chance that you're wrong. There always _is_ a chance that you're wrong but it just seems cumbersome to have to maintain a ledger of competing probabilities for everything that has happened, and everything that hasn't yet happened, just on the off chance that anything can happen, including mutually exclusive events.

In principle, anything might happen. In practice, not everything will. There must be a sensible way to figure out what we need to prepare for and what we can safely ignore. And the whole Pascal's Mugger paradox, while it's meant to attack Pascal's Wager's logic, ends up for me as an illustration of why proabilistic inference is deeply borked.

Re: Pascal's Mugging (2009) [pdf]

#44

Post by EvanWard97 »

Expected value != expected utility.

Just taking this seriously pretty much resolves all these problems.

It makes sense to take high cost/reward, low probability events seriously if the expected utility works out. Examples include reducing existential risk substantially, even at cost to short-term utility (say, in the form of well-being) to increase the probability that we can eventually figure out how to optimally arrange matter and energy and trigger a utilitronium shockwave.

Re: Pascal's Mugging (2009) [pdf]

#45

Post by MaxBarraclough »

adamchalmers wrote: post #40
MaxBarraclough wrote: post #23

Earlier quoted context omitted.

Pascal's Wager fails for the simpler reason that it ignores the possibility that believing in god could send you to hell. I see a similar problem here. Pascal should consider the possibility that the mugger will use his (Pascal's) silly action as the basis for punishment, in place of the promised reward. Slim probability, potentially very high cost. The fact that this risk has gone unstated doesn't mean it isn't ther…

I agree. This problem is still useful though, because to analyse a lot of counterfactual muggers, you must be able to analyse one mugger!

I agree that both problems are worth analysing, even if they're both absurd. Same goes for the Hangman's Paradox, a personal favourite. [0]

I gather that Pascal had never intended Pascal's Wager to be a watertight argument, it was intended more as a plaything for showing how unlikely it was anyone could make a watertight case for the existence of God.

[0] https://en.wikipedia.org/wiki/Hangman%27s_Paradox

Re: Pascal's Mugging (2009) [pdf]

#46

Post by roenxi »

ikeboy wrote: post #35
roenxi wrote: post #20

Earlier quoted context omitted.

It is pretty simple to formalise - if there is a pool of people who routinely accept positive-expected-value gambles where there is a P = 99.999999999% chance of going broke then we expect everyone in that pool will be broke unless the size of the pool is comparable to 1/(1-P). Tighten up the bounds on 'comparable' a bit and that is formalised. The mistake is accepting uncritically that expected value is the best met…

You need to maximize expected utility. In order to avoid this, you need utility to be bounded: there must be some multiple of your current utility that's impossible to ever have regardless of what happens.

Agreed that most people could reject the mugging on those grounds but I think that is more than is needed.

Even if someone being mugged had an unbounded utility function the finite resources argument forces them to rationally reject the deal. We've reintroduced infinities; so now our rationalist must accept that there are infinitely many situations with the same properties as the Mugging (positive expected value, Almost Sure to lose the stake). Their strategy would have to be to reject deals like the Mugging and seek out deals that have positive expected return and probably keep the stake/have a tiny stake compared to their reserves.

I'm basically saying a rationalist with finite wealth is probably using the Kelly criterion [0] and would reject the Mugging on that basis.

[0] https://en.wikipedia.org/wiki/Kelly_criterion

Re: Pascal's Mugging (2009) [pdf]

#47

Post by Dylan16807 »

roenxi wrote: post #19
maest wrote: post #16

Earlier quoted context omitted.

I thought the "solution" for St Peteresburg paradox was to consider utility as a non-linear function of wealth. And this makes the series converge. Also, I don't find the Pascal's Mugger example convincing, as the probability that the mugger will return with the money is inversely proportional to the multiple they are promissing (for very large multiples this is because they have finite resources, but even at lower m…

> as the probability that the mugger will return with the money is... That can't be reasonably estimated though. Putting aside the fact that we can't really assert the relation you posit, there is also a finite probability that the mugger is some sort of illuminati member with the ability to create an arbitrary amount of money. Ie, there is some tiny-but-positive probability that he can create an arbitrary amount of…

They can't really offer you more than the amount of resources in the entire world, though. Money past some point in the trillions stops being money, because you can't exchange it for anything. So even for an illuminati member, the expected value can only go so high, and I don't know if that value is higher or lower than a dollar.

Re: Pascal's Mugging (2009) [pdf]

#48

Post by ikeboy »

roenxi wrote: post #46
ikeboy wrote: post #35

Earlier quoted context omitted.

You need to maximize expected utility. In order to avoid this, you need utility to be bounded: there must be some multiple of your current utility that's impossible to ever have regardless of what happens.

Agreed that most people could reject the mugging on those grounds but I think that is more than is needed. Even if someone being mugged had an unbounded utility function the finite resources argument forces them to rationally reject the deal. We've reintroduced infinities; so now our rationalist must accept that there are infinitely many situations with the same properties as the Mugging (positive expected value, Alm…

>We've reintroduced infinities; so now our rationalist must accept that there are infinitely many situations with the same properties as the Mugging (positive expected value, Almost Sure to lose the stake).

Yes, in the presence of infinities the decision function is inconsistent.

>Their strategy would have to be to reject deals like the Mugging and seek out deals that have positive expected return and probably keep the stake/have a tiny stake compared to their reserves.

Try formalizing that.

Kelly criterion doesn't work. Your link says it maximizes log wealth. If potential wealth is unbounded, you will still take bets that are positive E(log utility).

Re: Pascal's Mugging (2009) [pdf]

#49

Post by Dylan16807 »

YeGoblynQueenne wrote: post #42
Strilanc wrote: post #28

Earlier quoted context omitted.

If you set the probability at zero, you won't be convinced when they actually are an operator from the seventh dimension. That is to say, you run into the opposite problem of being Pascal's Muggle [1]. 1: https://www.lesswrong.com/posts/Ap4KfkHyxjYPDiqh2/pascal-s-m... > A wind begins to blow about the alley, whipping the Mugger's loose clothes about him as they shift from ill-fitting shirt and jeans into robes of inf…

Thanks, that's an interesting read. But I don't think it addresses my question: why shouldn't Pascal place the probability that the Mugger is an Operator from the Seventh dimension to _zero_ (rather than an infinitissemally small number)? The point is that, at the time when the Mugger declares himself to be an Operator from the Seventh Dimension who can offer large rewards etc, there is no evidence to suggest he's sa…

Probability zero is the same as saying that it would take infinite evidence to convince you. Even if someone provides amazingly convincing evidence, better than you've ever seen, a flat 0 or 1 eats it.

> there is no evidence to suggest he's saying the truth. No evidence at all. Accordingly, the probability that he's telling the truth must be zero.

I don't think that logic works. What if the claim was "I have a five dollar bill in my pocket"?

Re: Pascal's Mugging (2009) [pdf]

#50

Post by TeMPOraL »

YeGoblynQueenne wrote: post #42
Strilanc wrote: post #28

Earlier quoted context omitted.

If you set the probability at zero, you won't be convinced when they actually are an operator from the seventh dimension. That is to say, you run into the opposite problem of being Pascal's Muggle [1]. 1: https://www.lesswrong.com/posts/Ap4KfkHyxjYPDiqh2/pascal-s-m... > A wind begins to blow about the alley, whipping the Mugger's loose clothes about him as they shift from ill-fitting shirt and jeans into robes of inf…

Thanks, that's an interesting read. But I don't think it addresses my question: why shouldn't Pascal place the probability that the Mugger is an Operator from the Seventh dimension to _zero_ (rather than an infinitissemally small number)? The point is that, at the time when the Mugger declares himself to be an Operator from the Seventh Dimension who can offer large rewards etc, there is no evidence to suggest he's sa…

As the saying goes, "zero and one are not probabilities". Like 'Dylan16807 says, they eat evidence. When doing maths, when transforming to log probabilities, 0 becomes -Infinity; when transforming to odds ratios, 1 goes to infinity.

A longer explanation: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-ar....

See also https://en.wikipedia.org/wiki/Cromwell%27s_rule, mentioned by 'edflsafoiewq.

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