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.
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.