Paradoxes such as this one point at some rarely discussed assumptions about the utility function. The major one is that it exists. Or exists as something more than a model which is only good for a range of payoffs.
Pascal's Mugging (2009) [pdf]
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Re: Pascal's Mugging (2009) [pdf]
#12Earlier quoted context omitted.
I really love how this is could be seen as a demonstration that HN (or any other similar interest community, or probably the internet in general) functions like a hive mind, a collective consciousness. I've read that post by Carmack and I wondered exactly that "wonder what Pascal's Mugging is, interesting". Sometimes you go around and wonder various things, but don't look them up or do them in the moment, and then so…
But how useful is it? Pascal's Mugging was submitted to HN and discussed 8 years ago. If the collective consciousness keeps needing reminders of what it once knew, this is probably still inferior to a single intelligent person who reads a lot and remembers it all.
It’s new to me :)
Re: Pascal's Mugging (2009) [pdf]
#13This 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…
Yes, but it is still not trivial to formalize mathematically without running into trouble: https://www.lesswrong.com/posts/a5JAiTdytou3Jg749/pascal-s-m...
Re: Pascal's Mugging (2009) [pdf]
#14I hereby declare that I will expose everyone that gives in to Pascal's mugger to a negative utility so great compared to whatever the mugger promises that it is always best to keep the wallet. I cold be telling the truth. You're welcome.
Re: Pascal's Mugging (2009) [pdf]
#15Earlier quoted context omitted.
I really love how this is could be seen as a demonstration that HN (or any other similar interest community, or probably the internet in general) functions like a hive mind, a collective consciousness. I've read that post by Carmack and I wondered exactly that "wonder what Pascal's Mugging is, interesting". Sometimes you go around and wonder various things, but don't look them up or do them in the moment, and then so…
I have noticed this pattern before: Someone mentions a topic deep inside a thread on HN and next thing you know that topic is on the front page.
It could also be confirmation bias, though. The Baader-Meinhof thing.
Re: Pascal's Mugging (2009) [pdf]
#16This 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…
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).
Re: Pascal's Mugging (2009) [pdf]
#17This 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…
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.
Re: Pascal's Mugging (2009) [pdf]
#18In case someone is not familiar with Pascal's wager, here is a table that shows the expected values:
https://en.wikipedia.org/wiki/Pascal%27s_wager#Analysis_with... (the appearance of infinity breaks the decision theory...)
Re: Pascal's Mugging (2009) [pdf]
#19This 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…
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 money.
At that point, the expected return can be made large compared to the probability that the mugger is lying.
Re: Pascal's Mugging (2009) [pdf]
#20This 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…
Yes, but it is still not trivial to formalize mathematically without running into trouble: https://www.lesswrong.com/posts/a5JAiTdytou3Jg749/pascal-s-m...
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.