[roenxi]

This can be easily resolved by considering that the victim of the mugging has finite resources. This is a usual remedy to problems were expected value alone gives stupid results (such as Pascal's Mugging). Something similar happens in lotteries where even if the expected value of buying a ticket is positive it is still not rational for an ordinary person to buy a ticket.

If I have $400 dollars I can't afford to take 1:1000000 risks that cost $200 each. I will go bankrupt with an enormous likelihood whatever the payoff. There is a minimum cutoff involving cost/probability below which it does not make sense to take up the opportunity.

There are links to similar theoretical ideas from the Pascale's Mugging wiki page - although from the casinos perspective not the gambler's - https://en.wikipedia.org/wiki/St._Petersburg_paradox#Finite_... and then https://en.wikipedia.org/wiki/Gambler%27s_ruin for example.

Most people will not take an 99% risk of going bankrupt in a game that will consume all their resource reserves; expected value as a statistic does not meaningfully capture the risk. Positive expectation, losing strategy.

[joe_the_user]

That's a good argument against seemingly plausible but risky approaches.

This particular situation, of someone just pulling "it could be true!" out of their arse, can also be solved by framing things as "the more utility you claim, the less likely it seems and disproportionately so".

IE, if the chance of getting X from the scoundrel is less than 1/(X^2*C), even integral of all the offers together winds up very small.

[petters]

Yes, but it is still not trivial to formalize mathematically without running into trouble: https://www.lesswrong.com/posts/a5JAiTdytou3Jg749/pascal-s-m...

[roenxi]

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 metric to optimise. Nobody ever proved that expected value is a strategically superior metric. In fact it would be quite hard to prove that since it is not true. It leaves people vulnerable to making very stupid decisions as illustrated in Pascals Mugging.

Optimium strategy involves at a minimum considering your available opportunities and available resources. Opportunity alone is not enough.

[ralfd]

> Tighten up the bounds on 'comparable' a bit and that is formalised.

Is this like „draw the rest of the owl“?

[garmaine]

What owl?

[OscarCunningham]

reddit.com/r/restofthefuckingowl

[PhasmaFelis]

Linking to examples of the meme without linking the actual meme doesn't really explain what "draw the rest of the owl" means. https://i.kym-cdn.com/photos/images/newsfeed/000/572/078/d6d...

[ikeboy]

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.

[roenxi]

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

[ikeboy]

>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).

[teambayleaf]

> 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).

Actually Kelly criterion works well, since it would limit your exposure to the game.

In this situation, Pascal as a Kelly-better would bet 12 deniers out of 10 livres (= 0.05% of his wealth), which is a penny.

[maest]

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 multiples this intuitively feels true).

[roenxi]

> 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 money.

At that point, the expected return can be made large compared to the probability that the mugger is lying.

[Dylan16807]

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.

[maest]

It seems to me that the set of worlds where the mugger can return $X is strictly a subset of the set of worlds where the mugger can return $X+epsilon.

So the probability won't be "inversely proportional" in the strict sense, but it will be decreasing with X increasing.

[roenxi]

At some point it converges to some constant probability. The probability of providing an "almost impossible" - say $9^^^^9 - is almost precisely equal to the probability of providing $9^^^^9+1. This is because any mechanism that can provide the first can also provide the second.

Technically one will be a subset of the other but it will be like the sum of an infinite series where the differences are so small that there is a limiting asymptotic on the value of the sum is 0. The probability will converge to the value of "probability an entity can provide arbitrary compensation".

[simonh]

Oh it’s a completely ridiculous, thoroughly flawed and easily refuted argument, for exactly the same reasons Pascal’s Wager is flawed. I think that’s the point.