I think it is similar to option 4 or 6?
Yep! With the addendum that I'm also limiting the utility function by the same sorts of bounds. Eliezer in Pascal's Muggle (as I interpret him, though I'm putting words in his mouth) was willing to bound agents subjective probabilities, but was not willing to bound agents utility functions.
Why is seconds the relevant unit of measure here?
The real unit is "how many bits of evidence you have seen/computed in your life". The number of seconds you've lived is just something proportional to that -- the Big Omega notation fudges away proportionality constant.
TLDR Kelly bets are risk avoidant. I think Kelly bets prevent you from pouring all your money into a pascal-mugging change of winning ungodly sums of money, but Kelly bets will pay a mugger exorbitant blackmail to avoid a pascal-mugging chance losing even a realistic amount money
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Starting with a pedantic point. None of the Pascal Mugging situations we've talked about are true Kelly bets. The mugger is not offering to multiply your cash bet if you win. Your winnings are saved lives, and they cannot be converted into a payroll.
But we can still translate a Pascal's mugging into the language of a Kelly bet. A translation of the standard Pascal mugging might be: the mugger offers to googolplex-le your money[1], and you think he has a one in a trillion chance of telling the truth. A Kelly bet would say that despite these magnificent EV of the payouts, you should put only ≈a trillionth of your wealth into this bet. So in this case, the one like the original Pascal's mugging, the one you responded to, the Kelly bet does the "right" thing and doesn't pay the mugger.
But now suppose the Pascal mugger says "I am a jealous god. If you don't show your belief in Me by paying Me $90,000 (90% of your wealth), I will send you and a googolplex other people to hell and take all (or all but a googolplexth) of your wealth". And suppose you think that there's a 1 in 1 trillion chance he's telling the truth.
Can we translate this into a Kelly bet? Yes! (I think?) The Kelly criteria tells you how to allocate your portfolio among many assets. Normally we assume there's a "safe" asset, a "null" asset, one where you are sure to get exactly you money back (the asset into which you put most of your portfolio when you make a small bet). But that asset is optional. We can model this Kelly bet by saying there are two assets into which you can allocate your portfolio. Asset A's payoff is "return 10% (loses 90%) of the bet with certainty". Asset B's payoff is "with probability 999,999,999,999/1 trillion (almost 1), return your money even, but with chance 1 in 1 trillion, lose ≈everything". There is no "safe cash" option -- you must split your portfolio between assets A and B.
Here, Kelly criterion really, really hates losing ≈all your bankroll. It says to put almost everything into the safe asset A (pay the mugger), because even a 1 in 1 trillion chance of losing ≈everything isn't worth it. Log of ≈0 (lost almost everything) is a very negative number.
Perhaps it would be useful to write exact math out.
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Importantly, I think for the math to work out he has to be offering a payoff proportional to your bet, not a fixed payoff?
Suppose the mugger says that if you don't give him $5, he'll take away 99.999999999999999% of your wealth. I don't think Kelly bets save you there? The logarithms of Kelly bets help you on the positive side but hurt you on the negative side.
But what about Pascal's Muggle? If you want to cancel out 3↑↑↑3 by multiplying it with a comparably small probability, the probability has to be incredibly, incredibly, small; smaller than a Bayesian can update after 13 billion years of viewing evidence. So where did that small number come from? If the super-exponenctial smallness came from priors, then you can't update away from it reasonably -- you're always going to believe the proposition is false, even if given an astronomical amount of evidence. Are you biting the bullet and saying that even if you find yourself in a universe where this sort of thing seems normal and like it will happen all the time, you will say a priori this this apparently normal stuff is impossible?
You should bound your utility function (not just probabilities) on how much information your brain can handle. Your utility function's dynamic range should never outpace your brain's probability's dynamic range. Also you shouldn't claim to put $Googolpex utility on anything until you're at least [1] seconds old.
Utility functions come from your preferences over lotteries. Not every utility function corresponds to a reasonable preference over lotteries. You can claim "My utility function assigns a value of Chaitin's constant to this outcome", but that doesn't mean you can build a finite agent that follows that utility function (it would be uncomputable). Similarly, you can claim "my agent follows a utility function assigns to outcomes A B and C values of $0, $1, and $googolplex", but you can't build such a beast with real physics (you're implicitly claiming your agent can distinguish between probabilities so fine that no computer with memory made from all the matter in the eventually observable universe could compute it).
And (I claim) almost any probability you talk about should be bounded by O(2^(number of bits you've ever seen)). That's because (I claim) almost all your beliefs are quasi-empirical, even most of the a priori ones. For example, Descartes considered the proposition "The only thing I can be certain of is that I can't be certain of anything" before quasi-empirically rejecting that proposition in favor of "I think, therefore I am". Descartes didn't just know a priori that proposition was false -- he had to spend some time computing to gather some (mental) evidence. It's easy to quickly get probabilities exponentially small by collecting evidence, but you shouldn't get them more than exponentially small.
You know the joke about the ultrafinitist mathematician who says he doesn't believe in the set of all integers? A skeptic asks "is 1 an integer?" and the ultrafinitist says "yes". The skeptic asks "is 2 an integer?", the ultrafinitist wait's a bit, then says "yes". The skeptic asks "is 100 an integer?", the ultrafinitist waits a bit, waits a bit more, then says "yes". This continues, with the ultafinitist waiting more and more time before confirming the existence of bigger and bigger integers, so you can never catch him in a contradiction. I think you should do something like that for small probabilities.
1Here's a pure quantum, information theoretic, no computability assumptions version that might or might not be illustrative. I don't actually know if the quantum computer I'm talking about could be built -- I'm going off intuition. EDIT I think this is 2 party quantum computation and none of the methods I've found are quite as strong as what I list here (real methods require e.g. a number of entangled qbits on order of the size of the computation).
You have two quantum computers, Alice and Bob, preforming the same computation steps. Alice and Bob have entangled qbits. If you observe the qbits of either Alice or Bob in isolation, you'll forever get provably random noise from both of them. But if you bring Alice and Bob together and line up their qbits and something something mumble, you get a pure state and can read off their joint computation.
Now we have all sorts of fun thought experiments. You run Alice and Bob, separating them very far from one another. Is Alice currently running a mind computation? Provably not, if someone looked at Bob last year. But Bob is many many light years away -- how can we know if someone looked at Bob? What if we separate Alice and Bob past each other's cosmic horizons, such that the acceleration of the expanding universe makes it impossible for them to ever reach each other again even if they run towards each other at the speed of light? Or send Bob to Alpha Centauri and back at close to the speed of light so he's aged only 1 year where Alice has aged 8. Has Alice been doing the mind thing for the past 7 years? Depends on whether you look at Bob or not.
(but I'll note that for me, this version, like the homomorphic version, is mostly saying that your description of a quantum physics state shouldn't be purely local. A purely local description must discard information, something something mixed state Von Neumann entropy)
Forgive me, I'm probably being stupid again 😬.
On efficient computability being necessary for reality: I'm not sure I understand the logic behind this. Would you not always get diagonalization problems if you want supervening "real" things to be blessed with R-efficiently computability? For example, take R to be something like a Solomonoff induction. R-efficiently computable there means Turing computable. For our M which supervenes on R, instead of Minds, let's let M be the probability p of a given state. The mapping function g: R->M, mapping states to the probability of states, cannot be R-efficiently computed (no matter what sort of Turing machine or speed prior you use for R) for diagonalization reasons. So the probabilities of states aren't a "real" thing? It seems like a lot of natural emergent things wouldn't be R-efficiently computable.
On homomorphic encryption being un-reversible: quantum computers are reversible, right? So if you say physics is as powerful as a quantum computer, and you want homomorphic encryption to be uncomputable in polynomial time, you have to make P's physics "state" throw quantum information away over time (which it could, in e.g. Copenhagen or objective collapse interpretations, but does not in e.g. many worlds) or maybe restrict the size of the physical universe you're giving as state to not include information we radiated away many years ago (less than 62.9 billion light years).
(Don't feel obligated to reply)
Forgive me, I only scanned.You're talking about exponentially unlikely physical states, like the kind where you disintegrate from location 1 and just by chance an identical copy of you appears in location 2 for no reason, or the thermodynamic arrow of time runs backwards, or states that encode a mind you can't decode without the right homomorphic key but then the homomorphic key appears in your alphabet soup just by chance, or your whole life was an elaborate prank for a reality TV show and most of the universe is actually made of cheese, or there's a giant superintelligent pink elephant in every room but just by chance nobody notices them, or the Easter Bunny and Harry Potter both appear and their magic works just by chance each time they try to use it (in a way conforming to the standard model), or whatever. These states with ≈0 measure might be theoretically possible but personally I don't put much stock in thought experiments about them?
EDIT still only scanned, but I think I misread the post. I (unconfidently) think the post is about if someone homomorphically encrypts a mind computation, then moves the information in the key past the cosmic event horizon of the expanding universe so the information in the key and the encrypted mind can never return together again. (Or are exponentially unlikely to). You can get an effect like this by e.g. burning the key and letting the infrared light of the fire escape to the blackness of the night sky.
I suspect this about many things, e.g. the advice in the US to never talk to the police.
With the Streisand effect I'm less sure. Conflict sells. The areas in e.g. popular science I know the most about tend not to be the ones that are most established or important -- they tend to be the ones that are controversial (group selection, deworming wars, arsenic biology).
It amuses me that ElectionBettingOdds.com is still operational and still owned by FTX Trading Ltd.