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mattnewport comments on Is Rationality Maximization of Expected Value? - Less Wrong
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If I can find another 99 people as confused as you I'll be a rich man.
You would also need them to have $100M available to lose.
That is a weakness with my plan.
Oh well. Fold the plan into your back pocket and wait for hyperinflation.
Or just drop a few zeroes off of the numbers and do it now, as if you'd come up with the idea a couple hundred years ago and the inflation up to this point counts as 'hyper'.
Wouw... Thank you for this charitable interpretation. I'll try to respond.
(1) You don't have to construe the gamble as some sort of coin flips. It could also be something like "the weather in Santa Clara, California in 20 September 2012 will be sunny" - i.e. a singular non-repeating event, in which case having 100 hundred people (as confused as me) will not help you.
(2) I've specifically said that if you have enough trials to converge to the expectation (i.e. the point about Weak Law of Large Numbers), then the point I'm making doesn't hold.
(3) Besides, suppose you have a gamble Z with negative expectation with probability of a positive outcome 1-x, for a very small x. I claim that for small enough x, every one should take Z - despite the negative expectation.
What's your x, sunshine? If 0.01 isn't small enough, pick a suitably small x. Nick Bostrom in Pascal's mugging picks 1 over quadrillion to demonstrate a very similar point. I picked 0.01 since I thought concrete values would demonstrate the point more clearly - I feel like they've been more confusing.
In fact, people take such gambles (with negative expectation but with high probability of winning) everyday.
They fly on airplanes and drive to work.
(4) Besides, even if we construe the gamble being repeated like a coin toss, I feel like with 0.99^99 = 0.37, you stand to lose 10M with probability 0.37 . I don't know about you but I wouldn't risk 10M with those kinds of odds. It helps to be precise when you can and not to go with a heuristic like "on average there should be 1 W in every 100 trial"...
A coin flip is not fundamentally a less singular non-repeating event than the weather at a specific location and specific time. There are no true repeating events on a macro scale if you specify location and time. The relevant difference is how confident you can be that past events are good predictors of the probability of future events. Pretty confident for a coin toss, less so for weather. Note however that if your probability estimates are sufficiently accurate / well-calibrated you can make money by betting on lots of dissimilar events. See for example how insurance companies, hedge funds, professional sports bettors, bookies and banks make much of their income.
'Small enough' here would have to be very much smaller than 1 in 100 for this argument to begin to apply. It would have to be 'so small that it won't happen before the heat death of the universe' scale. I'm still not sure the argument works even in that case.
I believe there is a sense in which small probabilities can be said to also have an associated uncertainty not directly captured by the simple real number representing your best guess probability. I was involved in a discussion on this point here recently.
How small should x be? And if the argument does hold, are you going to have two different criteria for rational behavior - one with events where probability of positive outcome is 1-x and one that isn't.
And also, from Nick Bostrom's piece (formatting will be messed up):
Of course, by your reasoning, you would hand your wallet. Bravo.