For a more concrete example of how this might work, suppose I steal one cent each from one billion different people, and Eliezer steals $100,000 from one person. The total amount of money I have stolen is greater than the amount that Eliezer has stolen; yet my victims will probably never even realize their loss, whereas the loss of $100,000 for one individual is significant. A cent does have a nonzero amount of purchasing power, but none of my victims have actually lost the ability to purchase anything; whereas Eliezer’s, on the other hand, has lost the ability to purchase many, many things.
Isn’t this a reductio of your argument? Stealing $10,000,000 has less economic effect than stealing $100,000, really? Well, why don’t we just do it over and over, then, since it has no effect each time? If I repeated it enough times, you would suddenly decide that the average effect of each $10,000,000 theft, all told, had been much larger than the average effect of the $100,000 theft. So where is the point at which, suddenly, stealing 1 more cent from everyone has a much larger and disproportionate effect, enough to make up for all the “negligible” effects earlier?
Money is not a linear function of utility. A certain amount is necessary to existance (enough to obtain food, shelter, etc.) A person’s first dollar is thus a good deal more valuable than a person’s millionth dollar, which is in turn more valuable than their billionth dollar. There is clearly some additional utility from each additional dollar, but I suspect that the total utility may well be asymptotic.
The total disutility of stealing an amount of money, $X, from a person with total wealth $Y, is (at least approcximately) equal to the difference in utility between $Y and $(Y-X). (There may be some additional disutility from the fact that a theft occurred—people may worry about being the next victim or falsely accuse someone else or so forth—but that should be roughly equivalent for any theft, and thus I shall disregard it).
So. Stealing one dollar from a person who will starve without that dollar is therefore worse than stealing one dollar from a person who has a billion more dollars in the bank.
Stealing one dollar from each of one billion people, who will each starve without that dollar, is far, far worse than stealing $100 000 from one person who has another $1e100 in the bank.
Stealing $100 000 from a person who only had $100 000 to start with is worse than stealing $1 from each of one billion people, each of whom have another billion dollars in savings.
Now, if we assume a level playing field—that is, that every single person starts with the same amount of money (say, $1 000 000) and no-one will starve if they lose $100 000, then it begins to depend on the exact function used to find the utility of money.
There are functions such that a million thefts of $1 each results in less disutility that a single theft of $100 000. (If asked to find an example, I will take a simple exponential function and fiddle with the parameters until this is true). However, if you continue adding additional thefts of $1 each from the same million people, an interesting effect takes place; each additional theft of $1 each from the same million people is worse than the previous one. By the time you hit the hundred-thousandth theft of $1 each from the same million people, that last theft is substantially more than ten times worse than a single theft of $100 000 from one person.
Yeah, but also keep in mind that people’s utility functions cannot be very concave. (My rephrasing is pretty misleading but I can’t think of a better one, do read the linked post.)
Hmmm. The linked post talks about the perceived utility of money; that is, what the owner of the money thinks it is worth. This is not the same as the actual utility of money, which is what I am trying to use in the grandparent post.
I apologise if that was not clear, and I hope that this has cleared up any lingering misunderstandings.
It seems like you and Hul-Gil are using different formulae for evaluating utility (or, rather, disutility); and, therefore, you are talking past each other.
While Hul-Gil is looking solely at the immediate purchasing power of each individual, you are considering ripple effects affecting the economy as a whole. Thus, while stealing a single penny from a single individual may have negligible disutility, removing 1e9 such pennies from 1e9 individuals will have a strong negative effect on the economy, thus reducing the effective purchasing power of everyone, your victims included.
This is a valid point, but it doesn’t really lend any support to either side in your argument with Hul-Gil, since you’re comparing apples and oranges.
I’m pretty sure Eliezer’s point holds even if you only consider the immediate purchasing power of each individual.
Let us define thefts A and B:
A : Steal 1 cent from each of 1e9 individuals.
B : Steal 1e7 cents from 1 individual.
The claim here is that A has negligible disutility compared to B. However, we can define a new theft C as follows:
C: Steal 1e7 cents from each of 1e9 individuals.
Now, I don’t discount the possibility that there are arguments to the contrary, but naively it seems that a C theft is 1e9 times as bad as a B theft. But a C theft is equivalent to 1e7 A thefts. So, necessarily, one of those A thefts must have been worse than a B theft—substantially worse. Eliezer’s question is: if the first one is negligible, at what point do they become so much worse?
I think this is a question of ongoing collateral effects (not sure if “externalities” is the right word to use here). The examples that speak of money are additionally complicated by the fact that the purchasing power of money does not scale linearly with the amount of money you have.
Consider the following two scenarios:
A). Inflict −1e-3 utility on 1e9 individuals with negligible consequences over time, or B). Inflict a −1e7 utility on a single individual, with further −1e7 consequences in the future.
vs.
C). Inflict a −1e-3 utility on 1e9 individuals leading to an additional −1e9 utility over time, or B). Inflict a one-time −1e7 utility on a single individual, with no additional consequences.
Which one would you pick, A or B, and C or D ? Of course, we can play with the numbers to make A and C more or less attractive.
I think the problem with Eliezer’s “dust speck” scenario is that his disutility of option A—i.e., the dust specs—is basically epsilon, and since it has no additional costs, you might as well pick A. The alternative is a rather solid chunk of disutility—the torture—that will further add up even after the initial torture is over (due to ongoing physical and mental health problems).
The “grand theft penny” scenario can be seen as AB or CD, depending on how you think about money; and the right answer in either case might change depending on how much you think a penny is actually worth.
Isn’t this a reductio of your argument? Stealing $10,000,000 has less economic effect than stealing $100,000, really? Well, why don’t we just do it over and over, then, since it has no effect each time? If I repeated it enough times, you would suddenly decide that the average effect of each $10,000,000 theft, all told, had been much larger than the average effect of the $100,000 theft. So where is the point at which, suddenly, stealing 1 more cent from everyone has a much larger and disproportionate effect, enough to make up for all the “negligible” effects earlier?
See also: http://lesswrong.com/lw/n3/circular_altruism/
Money is not a linear function of utility. A certain amount is necessary to existance (enough to obtain food, shelter, etc.) A person’s first dollar is thus a good deal more valuable than a person’s millionth dollar, which is in turn more valuable than their billionth dollar. There is clearly some additional utility from each additional dollar, but I suspect that the total utility may well be asymptotic.
The total disutility of stealing an amount of money, $X, from a person with total wealth $Y, is (at least approcximately) equal to the difference in utility between $Y and $(Y-X). (There may be some additional disutility from the fact that a theft occurred—people may worry about being the next victim or falsely accuse someone else or so forth—but that should be roughly equivalent for any theft, and thus I shall disregard it).
So. Stealing one dollar from a person who will starve without that dollar is therefore worse than stealing one dollar from a person who has a billion more dollars in the bank.
Stealing one dollar from each of one billion people, who will each starve without that dollar, is far, far worse than stealing $100 000 from one person who has another $1e100 in the bank.
Stealing $100 000 from a person who only had $100 000 to start with is worse than stealing $1 from each of one billion people, each of whom have another billion dollars in savings.
Now, if we assume a level playing field—that is, that every single person starts with the same amount of money (say, $1 000 000) and no-one will starve if they lose $100 000, then it begins to depend on the exact function used to find the utility of money.
There are functions such that a million thefts of $1 each results in less disutility that a single theft of $100 000. (If asked to find an example, I will take a simple exponential function and fiddle with the parameters until this is true). However, if you continue adding additional thefts of $1 each from the same million people, an interesting effect takes place; each additional theft of $1 each from the same million people is worse than the previous one. By the time you hit the hundred-thousandth theft of $1 each from the same million people, that last theft is substantially more than ten times worse than a single theft of $100 000 from one person.
Yeah, but also keep in mind that people’s utility functions cannot be very concave. (My rephrasing is pretty misleading but I can’t think of a better one, do read the linked post.)
Hmmm. The linked post talks about the perceived utility of money; that is, what the owner of the money thinks it is worth. This is not the same as the actual utility of money, which is what I am trying to use in the grandparent post.
I apologise if that was not clear, and I hope that this has cleared up any lingering misunderstandings.
It seems like you and Hul-Gil are using different formulae for evaluating utility (or, rather, disutility); and, therefore, you are talking past each other.
While Hul-Gil is looking solely at the immediate purchasing power of each individual, you are considering ripple effects affecting the economy as a whole. Thus, while stealing a single penny from a single individual may have negligible disutility, removing 1e9 such pennies from 1e9 individuals will have a strong negative effect on the economy, thus reducing the effective purchasing power of everyone, your victims included.
This is a valid point, but it doesn’t really lend any support to either side in your argument with Hul-Gil, since you’re comparing apples and oranges.
I’m pretty sure Eliezer’s point holds even if you only consider the immediate purchasing power of each individual.
Let us define thefts A and B:
A : Steal 1 cent from each of 1e9 individuals. B : Steal 1e7 cents from 1 individual.
The claim here is that A has negligible disutility compared to B. However, we can define a new theft C as follows:
C: Steal 1e7 cents from each of 1e9 individuals.
Now, I don’t discount the possibility that there are arguments to the contrary, but naively it seems that a C theft is 1e9 times as bad as a B theft. But a C theft is equivalent to 1e7 A thefts. So, necessarily, one of those A thefts must have been worse than a B theft—substantially worse. Eliezer’s question is: if the first one is negligible, at what point do they become so much worse?
I think this is a question of ongoing collateral effects (not sure if “externalities” is the right word to use here). The examples that speak of money are additionally complicated by the fact that the purchasing power of money does not scale linearly with the amount of money you have.
Consider the following two scenarios:
A). Inflict −1e-3 utility on 1e9 individuals with negligible consequences over time, or B). Inflict a −1e7 utility on a single individual, with further −1e7 consequences in the future.
vs.
C). Inflict a −1e-3 utility on 1e9 individuals leading to an additional −1e9 utility over time, or B). Inflict a one-time −1e7 utility on a single individual, with no additional consequences.
Which one would you pick, A or B, and C or D ? Of course, we can play with the numbers to make A and C more or less attractive.
I think the problem with Eliezer’s “dust speck” scenario is that his disutility of option A—i.e., the dust specs—is basically epsilon, and since it has no additional costs, you might as well pick A. The alternative is a rather solid chunk of disutility—the torture—that will further add up even after the initial torture is over (due to ongoing physical and mental health problems).
The “grand theft penny” scenario can be seen as AB or CD, depending on how you think about money; and the right answer in either case might change depending on how much you think a penny is actually worth.