Lotteries & MWI
I haven’t been able to find the source of the idea, but I’ve recently been reminded of:
Lotteries are a way to funnel some money from many of you to a few of you.
This is, of course, based on the Multiple Worlds Interpretation: if the lottery has one-in-a-million odds, then for every million timelines in which you buy a lottery ticket, in one timeline you’ll win it. There’s a certain amount of friction—it’s not a perfect wealth transfer—based on the lottery’s odds. But, looked at from this perspective, the question of “should I buy a lottery ticket?” seems like it might be slightly more complicated than “it’s a tax on idiots”.
But I’m reminded of my current .sig: “Then again, I could be wrong.” And even if this is, in fact, a valid viewpoint, it brings up further questions, such as: how can the friction be minimized, and the efficiency of the transfer be maximized? Does deliberately introducing randomness at any point in the process ensure that at least some of your MWI-selves gain a benefit, as opposed to buying a ticket after the numbers have been chosen but before they’ve been revealed?
How interesting can this idea be made to be?
You can certainly look at lotteries that way. But the “friction” you mention is typically rather large. You would probably do better to go and play roulette, or make repeated risky stock-market investments. For that matter, some of your “MWI-selves” will in any case just happen to receive big piles of money from eccentric millionaires, surprisingly successful employers, and the like.
So there’s nothing very special about lotteries, and I suggest that the way to minimize friction and get more money to your possible future selves is to choose random money transfer schemes other than lotteries.
Which random money schemes do you think would be best at this?
Or, for a tougher challenge: for people with relatively limited resources to spend on such a project, which such schemes have a reasonably low barrier to entry?
Bitcoin, interestingly enough. Bitcoin has multiple competing blockchain lotteries which are often provably fair, and which generally take <2% in fees, while offering high-leverage bets; for example, SatoshiDice famously paid out 1920btc on a 0.03 wager.
These are using cryptographic hashes, which are unpredictable but deterministic, so they’re not immediately applicable to MWI. What you could do for MWI purposes is use a quantum RNG to choose at what point in a day (or month) you bet at; since each block gives you a different chance at winning, quantumly choosing between enough blocks can essentially guarantee a win for at least one branch.
So, assuming you had the necessary bitcoins on hand, this is actually a very easy way to leverage up (far easier than some suggestions I’ve seen like trading foreign exchange options). Run the RNG, send it whenever, and within 10-15 minutes you’ll have won a large fortune or lost a small one for a fee of ~1.8% of your bet.
I was actually thinking about this as a strategy for myself. I have a decent number of bitcoins (I began accumulating what I could back in May), but I don’t have a life-changing number of bitcoins. On the other hand, if I bet at, say, 10:1 odds on SatoshiDice, that combined with future bitcoin price increases would be life-changing. I could fire up a quantum RNG, ask it when to bet over the next week, bet, say 25btc, and in one of 10 universes, walk away with ~248btc and cash out for $200k.
Is this a great idea or a terrible idea? I really don’t know.
Don’t forget taxes on gambling winnings which will effectively increase your transaction costs.
It’s a good thing that all this is being done in a currency most conducive to laundering and hiding assets! :)
But what if the NSA agent assigned to you turns you in to the IRS?
I wouldn’t suggest anyone cash out all of their bitcoins… rebalance them instead. I’m actually surprised I haven’t heard about any wealthy people/hedge funds/etc. using volatility harvesting strategies to trade bitcoins, their volatility is so insanely high it seems like an obvious strategy.
I suspect the answer depends strongly on your initial resources and just what you’re trying to achieve. Your best prospect for becoming a billionaire might not be the same as your best for becoming a millionaire. (Though, I dunno, it might.)
If you’re young, intelligent and living in a fairly rich country, and don’t mind waiting a while and doing some work in order to get the money, your best bet may be the unexciting one of trying to get a reasonably lucrative job—software development, medicine, law, finance—and then work hard and live frugally for (depending on other factors, notably including luck) somewhere between about 5 and about 20 years. Given sufficient determination, this gives you an excellent chance of becoming a (dollar) millionaire, and a quite respectable chance of doing much better than that. But it requires a lot more time and effort than buying a lottery ticket; this probably doesn’t meet your “reasonably low barrier to entry” criterion.
Many gambling games have very little “friction”. Some (e.g., poker) greatly reward intelligence and effort; if you can make yourself a good poker player then you can probably turn (say) $1000 into $1000000 with probability somewhat over 10^-3. Some (e.g., roulette) are basically pure chance, so no investment of time and effort is required or indeed helpful. If you want to play them at high stakes you’ll probably need to go to casinos and put up with their rake-off, but the friction is much less than in lotteries.
Once you’ve turned your (presumably small) initial investment into something more substantial (with low probability, but let’s not worry about your counterparts in other Everett branches who weren’t lucky enough) you may do better to switch from pure gambling to stock market speculation. There’s still friction, but I think brokers will eat less of your money than casinos.
I doubt there are many opportunities around that have genuinely low barrier to entry and let you do much better than pure chance would allow—because if there were, they’d already have been used up by arbitrageurs.
Diminishing marginal returns.
The utility of your gaining a $1,000,000 is not a thousand times the disutility of your losing $1000.
There are some special cases. If someone thinks his life is worthless if he doesn’t have something that could be bought or done with a $1,000,000, then the gamble could be justified. The thing that he buys pumps up the utility so much that it’s more than thousands times the utility of $1000. But this is probably a really rare case.
Medical issues that make life miserable but can be fixed with ~1M$ would be a (bit more concrete) example. Relatively rare, as you said.
If losing $1000 does not impact your quality of life, your statement appears to be false. Am I missing something?
ETA: It is obvious that the returns are diminishing under certain assumptions, but not that they diminish significantly.
Point of order: The probability that appears in lottery odds is not the same as the probability that appears in quantum mechanics. One is an expression of our ignorance about the detailed kinematics of tumbling balls in a sphere; the other arises from the evolution of the wave function. It is not obvious that one-in-a-million lottery odds translates directly to an amplitude with magnitude 0.001 for winning the lottery. (And then there’s the issue of complex interference.) It may be the case, but you cannot just point at the MWI and notice that both kinds of probability are referred to by the same word.
Entirely true. This is why I asked, elsewhere in this thread, about possible ways of introducing the ‘correct’ form of randomness, which was answered with several quantum-based random number generators to use as coin-flip decision-makers.
Fair enough, I missed that.
I don’t understand this way of thinking about MWI, but in a single universe, you will only win a one-in-a-million lottery one time in a million on average if you play it many, many millions of times. You can easily buy a million lottery tickets and not get a winner at 1-in-a-million odds—in fact the chances of that happening are just short of 37%. Think of how often in a “throw a six to start” game some poor player hasn’t started after six or more turns.
Sums: Chance of no win in a one-off 1-in-N lottery is (N-1)/N. After N tries, the chance of no win is ((N-1)/N)^N—which astonishingly (to me) converges quite rapidly on 1/e, or just short of 37%.
(Thanks to ciphergoth for pointing the convergence out to me elsewhere.)
To make it less surprising that (1-1/n)^n converges, here are two arguments that may help.
First: take logs. You get n log (1-1/n). Now for small x, log(1+x) = x + lower-order terms, so n log (1-1/n) = n (-1/n + lower-order terms) which obviously → −1.
(Is it obvious enough that log(1+x) = x + lower-order terms? The easiest way to prove that might be to say that log x = integral from 1 to x of 1/t, and for x close to 1 this is roughly the integral from 1 to x of 1, or x-1.)
Second: use the binomial theorem. (1-1/n)^n = sum {k from 0 to n} of (-1)^k (n choose k) n^-k. Now (n choose k) = n(n-1)...(n-k+1) / k!, and for small k this is roughly n^k/k!. So for large n, the “early” terms are approximately +- 1/k!. And for large n, the “late” terms are relatively small because of that factor of n^-k. So (handwave handwave) you have roughly sum (-1)^k 1/k! which is the series for exp(-1).
The typical lottery is a revenue device: it is intended to get money to the operator of the lottery, rather than any one of the participants. My state’s lottery, for example, takes in 40% of revenue as profits, commissions, or operations costs. From a basic search, this does not seem atypical. It’s also a sign that this is a very high-friction investment method, even compared to most other random investment methods. Once received, the lottery jackpot is taxed as income or worse-than-income rates, adding further friction.
You’d also need to spend the money relatively well, either to prevent death or so you get significantly more value from the sum than the ‘losers’ would have from spending the money in other ways. I’m not entirely sure that’s the obvious, at least not for most circumstances. ((Worse, rich people tend to have or develop more expensive tastes. If you can’t avoid that, the return becomes even more expensive.))
I’m also unsure this is an effective strategy, even taking the rather esoteric assumptions required and the pure utilitarianism. I’d value one person living an addition ten years over fifty or five hundred or fifty million people being slightly inconvenienced, but with sufficiently large numbers the ethics may start going the other way around : you can’t discount experiences because someone will end up dead, because it’s quite possible all of your MWI selves end up dead eventually.
Only if either your selection of a lottery ticket or the lottery’s selection of a winning number are quantum-random. Which is usually not the case.
The former is trivial to achieve using random.org or similar.
What measures can a would-be MWI-lottery-winner take to create, or add, relevant quantum-randomness?
This is another website that may be of use. Just fire it up for a while, pause the stream of numbers, and do what you will with them. It is guaranteed to be quantum-random.
This website claims to use a quantum random number generator (i.e. if you ask it for 6 random digits, each possible sequence of digits will appear with quantum measure 10^-6). Technically, it’s not quite guaranteed that using this to select a lottery ticket out of 10^6 possibilities will cause you to win with quantum measure 10^-6, since it is possible that your selection of a lottery ticket could affect which number wins, but it doesn’t seem likely that that would have a huge effect.
How recent does the branch have to be to count as “you”? There’s enough chaos that I’m pretty certain coinflips will turn out different a day after branching.
This is an interesting idea… but it seems likely that there are already a few timelines where I got drunk, walked in to a store, bought a lottery ticket, and won the lottery.
By the way, does anyone know offhand where the blockquoted idea actually originated?
Why would you ever want to transfer wealth from many of ‘you’ to one of ‘you’?
Any time there may be nonconvexity or jumps in outcomes, there may be opportunity. Many investments or expenditures have minimum requirements, where a lot or none is better than some.
If 999,999 of you die in a tornado, but 1 of you happened to win a lottery and had enough resources to build a storm cellar, than that 1-out-of-a-million of you may be the only significant fraction of you left to continue into the future. Concentration of resources can be very useful, and if the cost of concentrating such resources amongst some of you is low enough, it may be worth that cost.
What about the yous that weren’t hit by a tornado? How could you possibly be so doomed that winning the lottery is your best hope of survival? Without knowing it, no less?
Well, to take a theme that’s popular with this website, a portion of a sufficiently large lottery prize could be donated to MIRI and allow for the development of FAI before UFAI...
More practically—in most timelines where I don’t win the lottery, my general physical location falls within astonishingly predictable bounds, and any disaster that happens to hit within those bounds will trim those timelines from the group of timelines in which I continue to live. A lottery win is one way in which I would gain enough resources to get kicked out of my current parameters, and do things such as traveling places I otherwise would never go.
I recall this was the theme of a post from 2010. It appears to have been deleted …
You can move as it is. If you randomly move, that will work better than randomly winning the lottery, at a lower cost. Or are you thinking just a very small lottery to counter the costs of moving?
How many disasters are there that are that large and consistent? All I can think of is meteors and Earthquakes.
I’ll rephrase my question. Why do you want to make things better for one of ‘you’ at the expense of making them worse for many of ‘you’?
I thought my answer answered even your rephrased question; I’ll try again.
Random events happen in all lives. Some cannot be survived with X resources, but can be survived with Y resources. If you’re already above Y, and the cost of a lottery ticket is low enough that it won’t bring you below Y, then you’ll survive anyway, and buying a lottery ticket won’t significantly harm you. However, if you’re already below X, and a lottery win will bring some of you above Y, then buying a lottery ticket still won’t significantly harm you (as you’re going to die anyway), but that fraction of you who are boosted above Y will survive when they otherwise wouldn’t have.
Put another way: having some of me alive is better than having all of me dead.
I guess I was looking at this with the wrong frame of mind. I don’t think quantum immortality is possible, hence my question. I wasn’t even taking it into consideration. But if you believe in quantum immortality, I can see how playing the lottery might be beneficial.
Under MWI I don’t see any need to buy a lottery ticket—there are enough other timelines where the other-you bought a ticket...
And of course, lotteries being revenue generators, the “friction” is rather large.
Not at all.
Are there? Wouldn’t the number of timelines where other-yous buy tickets (and, thus, buy winning tickets) be increased if you are, in fact, willing to buy tickets yourself?
Not as far as I can see. Timelines fork—every time you buy a ticket there’s a timeline where you don’t. And every time you don’t there is a timeline where you do.
That seems to be an argument from infinity—that since 1⁄4 of an infinite number is exactly the same as 1⁄2 of an infinite number, there is no reason to prefer a set of timelines where 1⁄2 of you buy tickets to a set where 1⁄4 of you do.
You could also say that every time you approach a lottery counter, there’s a timeline where you step all the way up to it and one where you don’t; and once you’ve stepped up, there’s a timeline where you make the actual purchase and one where you don’t—and, thus, that for every 4 timelines where you start stepping towards a lottery counter, you only buy a ticket in one of them.
Basically, yes.
Under MWI everything that could happen actually does happen. This means that you can’t change anything summed up across all timelines. You can only change things in one timeline, but when you do another timeline nets it out.
An important item here seems to be the ‘can’ in ‘everything that can happen’; as opposed to things that /can’t/ happen. If a meteor has been orbiting for millions of years in a course that leads it so that, tomorrow night, it lands on my house, there is very little that the various differences across the timelines can do so that it’s not going to land on my house. Any timelines in which I’m anywhere near my house at that time—and that’s going to be most of them—are ones where I’m going to end up dead. However you want to divvy up the timelines involved, there will be a greater proportion of them where I’m dead than I’m alive.
This is the same reasoning which leads to the conclusion that quantum suicide/immortality is a bad idea to try out; and that it’s generally a good idea to maximize the swathe of timelines in which future-you remains alive and healthy. There may be a net sum to all those infinitesimal timelines when added up—but that sum isn’t necessarily going to be ‘0’.
Since you can do only things which can happen, you actions are unable to change the set of things which will happen to multi-you across all timelines.
That’s the predestination argument, isn’t it? Whatever the choices available to multi-me are, it’s impossible for me to compute them all, which provides sufficient uncertainty for something resembling free will to apply. I don’t know whether any given future-me will even have the option to buy a lottery ticket, let alone what the consequences of making that choice one way or the other might be; and so I might as well treat any given timeline as one in which that version of me can make decisions which affect his particular future.
That’s irrelevant in this context. What matters is that under MWI you don’t make a choice, in different branches you make all choices possible for you. You can change things in a particular timeline, but you can’t change the sum of everything in all timelines.
How confident are you that this conclusion, that MWI means choice is meaningless, is the correct interpretation of it? What odds would you be willing to wager on it? What evidence do you base it on?
The proposition is not testable so I can’t see how there could be a wager. The evidence is the usual evidence for MWI—either none or the whole of quantum mechanics, depending on your point of view :-)
But think about it—if (as the MWI says) every time you face a choice you make all possible choices in different branches, what could you possibly do that would affect the set of all branches?
Think of Tic-Tac-Toe’s game-tree; that’s a set of all possible choices that can be made in different branches of the game. Once you have an idea of the shape of the results those choices, such as “putting an X here causes me to lose more often than I win”, you can make your choice based on that information so that you /don’t/ choose the portions of the tree with the worst outcomes, thus narrowing the range of potential futures to ones which are better. Instead of spreading your future probability across 26,830 distinct timelines, in which you win less than half, you could spread your future across, say, 10,000 distinct timelines, in which you win 3/4s of them. (Numbers are just illustrative, not actually the real odds involved.)
Chess has a much more complicated game-tree; real life has an even more complicated game-tree; but the same principles should apply.
Nope. Every time this-you chooses a particular portion of the tree, other-yous choose all the other portions of the tree. You narrow “the range of potential futures” in one specific timeline, you cannot narrow the range of possible futures in all timelines.
I’m not worried about the range of /all/ timelines, only those timelines which proceed into the future from this moment. (And now, the ones from this moment. Etc.)
Let’s say that I decide to use a quantum randomizer to pick my first move in a game of Tic-Tac-Toe, and then play to win, or at least draw; and then I do just that. While it may be a fact that in /some/ timelines I’ll change my mind and not play to win, in the /majority/ of timelines which proceed from that spot, I will continue to play to win.
Hm… how about a different approach. You seem to be arguing that if I’m about to roll some dice, then all possible rolls are going to happen. I’m not arguing against that. What I’m arguing is that some rolls are more likely than others—the classic bell curve—and that by choosing to roll, say, 3d8 instead of 3d6, it’s possible to manipulate the shape of that bell curve, so that a the timelines are divvied up into different proportions than otherwise. Or maybe I use loaded dice, or scribble extra pips on, or just plan old fake-roll a die and set it to a certain number, or otherwise adjust the odds in my favor. Maybe I’ll even change the probability distribution from a simple bell curve to two distinct bell curves, where the maximum probability is rolling a 3 or 18, with next-to-no probability of rolling anything in between. Sure, there will be a /small portion/ of timelines where I don’t cheat, but in the /greater portion/ of timelines where I /do/ cheat, the /sub portion/ where I get the results I desire will be high—much higher than would be expected by simply assuming the standard distribution.
(If anyone else reading this wants to jump in, and either explain to me how I’m getting Lumifer’s idea wrong, or can do a better job explaining the idea I’m trying to get across, feel free...)
It’s turtles all the way down.
This-you chose to roll 3d8 and other-you chose to roll 3d6 and yet more of other-yous chose to roll 1d10, 7d36, etc. etc. Yes, you manipulated the bell curve but in other timelines it also got manipulated, albeit in a different way. When you step in one direction, yes, the timelines spreading out from that step are biased in that direction. But the step itself, when you made it another-you also made a step, in a different direction, and biased another bunch of timelines in that different direction.
The set of all possible futures is the set of all possible futures—you cannot change it.
I think I’ve run out of different ways to try to explain what I’m trying to get across; so we seem to have hit the door-wall debate limit. (“This is a door.” “Yes, but /this/ is a wall.” “Yes, but /this/...”)
If I were to try to explain our difference to an outsider, I might describe your position as being that as there are an infinite number of timelines, any sub-portion of them also contains an infinite number of timelines, and thus any given infinity is equally as important as any other, so there’s no reason to prefer any one bundle of timelines over another. Would you say that that’s valid? If not, could you explain where I’m going wrong? And if so, would you be willing to try to describe the idea I’ve been trying to explain?
If you are not willing to experimentally test quantum suicide/immortality, you should not be serious about MWI-based arguments for playing lottery.
As far as I know, even a successful test of quantum immortality involves greatly thinning out the number of timelines in which one exists, which is an extremely high price to pay for learning it. The cost of trying out a MWI-based lottery, even if it fails, can be relatively small. There seems to be more than enough difference to be willing to test the latter but not the former.
Presumably you mean a thought experiment, not an actual test.
How would you know if it succeeded or failed?
No, I meant an actual test—putting one’s money where one’s brains are. To, as one sequence put it, treat the quantum immortality hypothesis as something which pays the rent in measured experience.
Indirectly. Mostly through whatever other evidence supports MWI at all.
In extremis, if I do ever win a lottery, change my behaviour, and just barely escape the destruction of my home (or my home town), then that would be at least weak evidence favoring MWI through Everett Immortality.
Why not try to write out the actual probabilities in a rigorous way and see what comes out? It’s possible that it would be very much unlike what your intuition tells you.
Doing this ‘rigorously’ is a bit tricky, given the levels of uncertainty involved in just about every number, which even Feynman estimation can only reduce so far. What I have been consciously trying to do is estimate the decibans of probability, since logarithmic measurements help my all-too-limited intuition keep a better handle on the math involved.
The way I wrote my reply was misleading, sorry. I’m not talking about the specific numbers, I’m talking about the model itself. Remember that even in MWI, for any freak incident that allows you to avoid some disaster, there are zillions of far likelier ways of avoiding that disaster. Consider the following:
You point a gun at your head, pull the trigger, the bullet blasts through your head, but miraculously only causes damage to unimportant areas and you stay alive.
While that scenario could happen, it’s far more likely that:
You stand there with a gun to your head and your finger on the trigger, and you suddenly realize “What the hell am I doing?” and put the gun down. You remain alive.
Going back to your ‘narrowly-avoiding destruction of house’ scenario, it’s not likely that it will occur due to some freak occurence. It’s more likely that it will occur due to some mundane occurence. You’ll be out of the house buying groceries. Only half your house will be destroyed. Etc. And even if it does happen due to some freak occurrence, it will only probably be a singular event in your lifetime, giving you no meaningful way to update your beliefs.
To phrase it another way, MWI doesn’t make the improbable probable. It can’t. Otherwise we’d be seeing freak occurrences happen to us all the time. As Elezier said, it all adds up to normality. Even if Everett immortality is correct and you wind up living for a million years, you’ll look back at your life and realize that the path to your immortality was… pretty mundane, probably. You were frozen upon death and revived 100 years later into the nanotech revolution. Your consciousness merged with a computer. Etc. All stuff that we consider relatively likely here on LessWrong.
And my intuition tells me that if you actually construct a simple model this is precisely what you will find. That the probability of P(x | M), where x is the path to your immortality, and M is MWI being true, will be the same as P(x | ~M), preventing you from making any updates to your belief. I haven’t actually constructed a rigorous model here and I’d love to be proven wrong, but it’s what my intuition tells me.
Huh? That’s not evidence at all.
If my home is ever unsurvivably destroyed, then the sequence of events lottery win → move away → previous home destroyed is more likely to be what I experienced in a universe where the laws of physics contain MWI (due to Everett Immortality) than they are to be what I’d have experienced in a universe lacking MWI (and in which I could confidently predict that I’m not going to experience winning a lottery). Thus, a simple Bayesian analysis would mean that experiencing lottery → move → destruction should increase my estimate that MWI is true. Maybe not by much, but more than nothing.
Let me repeat myself: Huh?
You weren’t killed in the recent tornadoes in Illinois. Is this also “evidence” for MWI?
If it is evidence for MWI, it’s exteremely weak, perhaps on the order of epsilon; because in both MWI and non-MWI versions of physics, I don’t have any particular reason to have predicted that I would travel to Illinois at all.
You are expressing, basically, a personal anthropic principle. It is NOT evidence for MWI.
How do you know that it isn’t?