If one lottery ticket is worth while, why not two? Are you assigning a nonlinear value to the probability of winning the lottery? That causes a number of problems.
At the risk of looking even more like an idiot: Buying one $1 lottery ticket earns you a tiny chance − 1 in 175,000,000 for the Powerball—of becoming absurdly wealthy. The Powerball gets as high as $590,500,000 pretax. NOT buying that one ticket gives you a chance of zero. So buying one ticket is “infinitely” better than buying no tickets. Buying more than one ticket, comparably, doesn’t make a difference.
I like to play with the following scenario. A LessWrong reader buys a lottery ticket. They almost certainly don’t win. They have one dollar less to donate to MIRI and because they’re not wealthy they may not have enough wealth to psychologically justify donating anything to MIRI anyway. However, in at least one worldline, somewhere, they win a half a billion dollars and maybe donate $100,000,000 to MIRI. So from a global humanity perspective, buying that lottery ticket made the difference between getting FAI built and not getting it built. The one dollar spent on the ticket, in comparison, would have had a totally negligible impact.
I fully realize that the number of universes (or whatever) where the LessWrong reader wins the lottery is so small that they would be “better off” keeping their dollar according to basic economics, but the marginal utility of one extra dollar is basically zero.
edit: Digging myself in even deeper, let me attempt to simplify the argument.
You want to buy a Widget. The difference in net utility, to you, between owning a Widget and not owning a Widget is 3^3^3^3 utilons. Widgets cost $100,000,000. You have no realistic means of getting $100,000,000 through your own efforts because you are stuck in a corporate drone job and you have lots of bills and a family relying on you. So the only way you have of ever getting a Widget is by spending negligible amounts of money buying “bad” investments like lottery tickets. It is trivial to show that buying a lottery ticket is rational in this scenario: (Tiny chance) x (Absurdly, unquantifiably vast utility) > (Certain chance) x ($1).
Replace Widget with FAI and the argument may feel more plausible.
So buying one ticket is “infinitely” better than buying no tickets.
So your utility function is nonlinear with respect to probability. You don’t use expected utility. It results in certain inconsistencies. This is discussed in the article the allais paradox, but I’ll give a lottery example here.
Suppose I offer you a choice between paying one dollar and getting a one in a million chance of winning $500,000, and paying two dollars and getting a one in one million chance of winning $500,000 and a one in two million chance of winning $500,001. You figure that what’s basically a 0.00015% chance of winning vs. a 0.0001% chance isn’t worth paying another dollar for, so you just pay the one dollar.
On the other hand, suppose I only offer you the first option, but, once you see if you’ve won, you get another chance. If you win, you don’t really want another lottery ticket, since it’s not a big deal anymore. So you buy a ticket, and if you lose, you buy another ticket. This results in a 0.0001% chance of ending up with $499,999, a 0.00005% chance of ending up with $499,998, and a 99.99985% chance of ending up with −2$. This is exactly the same set of probabilities as you had for the second option before.
The one dollar spent on the ticket, in comparison, would have had a totally negligible impact.
No it would not. Or at least, it’s highly unlikely for you to know that.
Suppose MIRI has their probability of success increased by 50 percentage points if they get a 100 million dollar donation. This means that, if 100 million people all donate a dollar, their probability of success goes up by 50 percentage points. Each successive one will change the probability by a different amount, but on average, each donation will increase the chance of success by one in 200 million. Furthermore, it’s expected that the earlier donations would make a bigger difference, due to the law if diminishing returns. This means that donating one dollar improves MIRI’s probability of success by more than one in 200 million, and is therefore better than getting a one in 100 million chance of donating 100 million dollars.
Even if MIRI does end up needing a minimum amount of money or something and becomes an exception to the law of diminishing returns, they know more about their financial situation, and since they’re dealing with large amounts of money all at once, they can be more efficient about it. They can make a bet precisely tailored to their interests and with odds that are more fair.
So buying one ticket is “infinitely” better than buying no tickets.
You’re looking at the (potential) benefits and ignoring the costs. The costs are not negligible: “Thirteen percent of US citizens play the lottery every week. The average household spends around $540 annually on lotteries and poor households spend considerably more than the average.” (source).
Buying more than one ticket, comparably, doesn’t make a difference.
Buying a second ticket doubles your chances, obviously.
A LessWrong reader buys a lottery ticket … in at least one worldline, somewhere, they win a half a billion dollars
For each timeline where you buy a lottery ticket there is one where you don’t. Under MWI you don’t make any choices—you choose everything, always.
the marginal utility of one extra dollar is basically zero
You’ve never been poor, have you? :-/
It is trivial to show that buying a lottery ticket is rational in this scenario
It is just as trivial to show that you should spend all your disposable income and maybe more on lottery tickets in this scenario.
You’re looking at the (potential) benefits and ignoring the costs. The costs are not negligible: “Thirteen percent of US citizens play the lottery every week. The average household spends around $540 annually on lotteries and poor households spend considerably more than the average.” (source).
I’m only commenting to the rationality of one individual buying one ticket, not the ethics of the existence of lotteries.
Buying a second ticket doubles your chances, obviously.
Buying one ticket takes you from zero to one, buying two tickets takes you from one to two. 1⁄0 = infinity, 2⁄1 = 2. Buying anything more than 1 ticket has sharply diminishing utility. I realize this is a somewhat silly line of argument, so I’m not going to sink any more energy defending it.
For each timeline where you buy a lottery ticket there is one where you don’t. Under MWI you don’t make any choices—you choose everything, always.
I don’t think we understand each other on this point. I was referring not to choosing, just winning. And the measure of the winning universes is a tiny fraction of all universes. But that doesn’t matter when the utility of winning is sufficiently large. And the chance of a given individual buying a ticket isn’t 50% in any meaningful quantum-mechanical sense, so “For each timeline where you buy a lottery ticket there is one where you don’t” isn’t true.
You’ve never been poor, have you? :-/
No, and I wouldn’t recommend that a poor person buy lottery tickets. My original claim was that buying lottery tickets can be rational, not that it is rational in the general case.
It is just as trivial to show that you should spend all your disposable income and maybe more on lottery tickets in this scenario.
That’s true. People also say that you should donate all your disposable income to MIRI, or to efficient charities, for exactly the same reasons, and I don’t do those things for the same reason that I don’t spend all my money on lottery tickets—I’m a human. My line of argument only applies when you want a Widget and have no other way of affording it.
I don’t really feel strongly enough about this to continue defending it, it’s just that I’m quite sure I’m right in the details of my argument and would welcome an argument that actually changes my mind / convinces me I’m wrong.
Buying one $1 lottery ticket earns you a tiny chance − 1 in 175,000,000 for the Powerball—of becoming absurdly wealthy.
NOT buying that one ticket gives you a chance of zero.
There are ways to win a lottery without buying a ticket. For example, someone may buy you a ticket as a present, without your knowledge, which then wins.
So buying one ticket is “infinitely” better than buying no tickets.
No, it is much more likely that you’ll win the lottery by buying tickets than by not buying tickets (assuming it’s unlikely to be gifted a ticket), but the cost of being gifted a ticket is zero, which makes not buying tickets an “infinitely” better return on investment.
If one lottery ticket is worth while, why not two? Are you assigning a nonlinear value to the probability of winning the lottery? That causes a number of problems.
At the risk of looking even more like an idiot: Buying one $1 lottery ticket earns you a tiny chance − 1 in 175,000,000 for the Powerball—of becoming absurdly wealthy. The Powerball gets as high as $590,500,000 pretax. NOT buying that one ticket gives you a chance of zero. So buying one ticket is “infinitely” better than buying no tickets. Buying more than one ticket, comparably, doesn’t make a difference.
I like to play with the following scenario. A LessWrong reader buys a lottery ticket. They almost certainly don’t win. They have one dollar less to donate to MIRI and because they’re not wealthy they may not have enough wealth to psychologically justify donating anything to MIRI anyway. However, in at least one worldline, somewhere, they win a half a billion dollars and maybe donate $100,000,000 to MIRI. So from a global humanity perspective, buying that lottery ticket made the difference between getting FAI built and not getting it built. The one dollar spent on the ticket, in comparison, would have had a totally negligible impact.
I fully realize that the number of universes (or whatever) where the LessWrong reader wins the lottery is so small that they would be “better off” keeping their dollar according to basic economics, but the marginal utility of one extra dollar is basically zero.
edit: Digging myself in even deeper, let me attempt to simplify the argument.
You want to buy a Widget. The difference in net utility, to you, between owning a Widget and not owning a Widget is 3^3^3^3 utilons. Widgets cost $100,000,000. You have no realistic means of getting $100,000,000 through your own efforts because you are stuck in a corporate drone job and you have lots of bills and a family relying on you. So the only way you have of ever getting a Widget is by spending negligible amounts of money buying “bad” investments like lottery tickets. It is trivial to show that buying a lottery ticket is rational in this scenario: (Tiny chance) x (Absurdly, unquantifiably vast utility) > (Certain chance) x ($1).
Replace Widget with FAI and the argument may feel more plausible.
So your utility function is nonlinear with respect to probability. You don’t use expected utility. It results in certain inconsistencies. This is discussed in the article the allais paradox, but I’ll give a lottery example here.
Suppose I offer you a choice between paying one dollar and getting a one in a million chance of winning $500,000, and paying two dollars and getting a one in one million chance of winning $500,000 and a one in two million chance of winning $500,001. You figure that what’s basically a 0.00015% chance of winning vs. a 0.0001% chance isn’t worth paying another dollar for, so you just pay the one dollar.
On the other hand, suppose I only offer you the first option, but, once you see if you’ve won, you get another chance. If you win, you don’t really want another lottery ticket, since it’s not a big deal anymore. So you buy a ticket, and if you lose, you buy another ticket. This results in a 0.0001% chance of ending up with $499,999, a 0.00005% chance of ending up with $499,998, and a 99.99985% chance of ending up with −2$. This is exactly the same set of probabilities as you had for the second option before.
No it would not. Or at least, it’s highly unlikely for you to know that.
Suppose MIRI has their probability of success increased by 50 percentage points if they get a 100 million dollar donation. This means that, if 100 million people all donate a dollar, their probability of success goes up by 50 percentage points. Each successive one will change the probability by a different amount, but on average, each donation will increase the chance of success by one in 200 million. Furthermore, it’s expected that the earlier donations would make a bigger difference, due to the law if diminishing returns. This means that donating one dollar improves MIRI’s probability of success by more than one in 200 million, and is therefore better than getting a one in 100 million chance of donating 100 million dollars.
Even if MIRI does end up needing a minimum amount of money or something and becomes an exception to the law of diminishing returns, they know more about their financial situation, and since they’re dealing with large amounts of money all at once, they can be more efficient about it. They can make a bet precisely tailored to their interests and with odds that are more fair.
You’re looking at the (potential) benefits and ignoring the costs. The costs are not negligible: “Thirteen percent of US citizens play the lottery every week. The average household spends around $540 annually on lotteries and poor households spend considerably more than the average.” (source).
Buying a second ticket doubles your chances, obviously.
For each timeline where you buy a lottery ticket there is one where you don’t. Under MWI you don’t make any choices—you choose everything, always.
You’ve never been poor, have you? :-/
It is just as trivial to show that you should spend all your disposable income and maybe more on lottery tickets in this scenario.
I’m only commenting to the rationality of one individual buying one ticket, not the ethics of the existence of lotteries.
Buying one ticket takes you from zero to one, buying two tickets takes you from one to two. 1⁄0 = infinity, 2⁄1 = 2. Buying anything more than 1 ticket has sharply diminishing utility. I realize this is a somewhat silly line of argument, so I’m not going to sink any more energy defending it.
I don’t think we understand each other on this point. I was referring not to choosing, just winning. And the measure of the winning universes is a tiny fraction of all universes. But that doesn’t matter when the utility of winning is sufficiently large. And the chance of a given individual buying a ticket isn’t 50% in any meaningful quantum-mechanical sense, so “For each timeline where you buy a lottery ticket there is one where you don’t” isn’t true.
No, and I wouldn’t recommend that a poor person buy lottery tickets. My original claim was that buying lottery tickets can be rational, not that it is rational in the general case.
That’s true. People also say that you should donate all your disposable income to MIRI, or to efficient charities, for exactly the same reasons, and I don’t do those things for the same reason that I don’t spend all my money on lottery tickets—I’m a human. My line of argument only applies when you want a Widget and have no other way of affording it.
I don’t really feel strongly enough about this to continue defending it, it’s just that I’m quite sure I’m right in the details of my argument and would welcome an argument that actually changes my mind / convinces me I’m wrong.
I treat buying lottery tickets as buying a license to daydream. Once you realize you don’t need a license for that… :-)
There are ways to win a lottery without buying a ticket. For example, someone may buy you a ticket as a present, without your knowledge, which then wins.
No, it is much more likely that you’ll win the lottery by buying tickets than by not buying tickets (assuming it’s unlikely to be gifted a ticket), but the cost of being gifted a ticket is zero, which makes not buying tickets an “infinitely” better return on investment.