From the existence of such a function it does not follow that “we should find the most efficient group and give it our entire charity budget”
Agreed. To derive that you would also need a smoothness constraint on said function, so that it can be locally approximated as linear; and you need to be donating only a small fraction of the charity’s total budget, so as to stay within the domain of said local approximation.
I assert that the smoothness property is true of sane humans’ altruistic preferences, but that’s not something you can derive a priori, and a sufficiently perverse preference could disagree.
To derive that you would also need a smoothness constraint on said function, so that it can be locally approximated as linear;
You’re solving essentially a global optimization problem; what use is (the existence of) a local linear approximation? If the utility function happens to be the eminently smooth f(x,y)=xy, then under the constraint of x+y=const the optimal solution is going to be an even split. It’s possible to argue that this particular utility function is perverse and unnatural, but smoothness isn’t one of its problems.
You don’t even need contrived examples to show that utility functions do not admit their maxima along one axis. My other point was that charity may not be easily distinguishable from other types of spending[1], and our normal utility functions definitely don’t have that behavior. We do not, among different types of things we require/enjoy, pick out the “most efficient” one and maximize it alone.
[1] As another example of that thesis, consider the sequence: I buy myself a T-shirt—I buy my child a T-shirt—I pool funds with other parents to buy T-shirts for kids in my child’s kindergarden, including for those whose parents are too poor to afford it—I donate to the similar effort in a neighbouring kindergarden—I donate to charity buying T-shirts for African kids.
then under the constraint of x+y=const the optimal solution is going to be an even split.
Yeah, but unless you actually end up at that point, that’s hardly relevant. If people donated rationally, we would always be at that point, but people don’t, and we aren’t.
and our normal utility functions definitely don’t have that behavior.
We’re normally only dealing with one person. If you play videogames, you quickly get to the point where you don’t want to play anymore nearly as much, so you do something else. If you save someone’s life, there’s still another guy that needs saving, and another guy after that, etc. You can donate enough that the charity becomes less efficient, but you have to be rich and the charity has to be small.
Also, consider: If you wanted a shirt, and I bought you one, you’d stop wanting a shirt and spend your money on something else, just like if you bought the shirt. If you wanted to donate $100 to X charity, and I told you that I already did, would you respond the same?
Yeah, but unless you actually end up at that point, that’s hardly relevant. If people donated rationally, we would always be at that point, but people don’t, and we aren’t.
I don’t understand how what you just said relates to my example. To recap, I meant my example, where the maximum is at the even split, to refute the claim that any smooth utility function will obtain its maximum along one “most efficient” axis. The whole argument is only about the rational behavior.
We’re normally only dealing with one person. If you play videogames, you quickly get to the point where you don’t want to play anymore nearly as much, so you do something else. If you save someone’s life, there’s still another guy that needs saving, and another guy after that, etc.
While this is true, and does point at an interesting difference between charity and many other behaviors, it can’t isolate charity, not by a long shot. There are many, many things we do that we stop doing not because of satiety or exhaustion, but because of other priorities.
To give the first example that comes to mind, a personal one, I’m learning piano and I also play table tennis. I enjoy both activities immensely and would like to do either of them a lot more (but can’t because of other commitments). There’s no question of satiety of exhaustion at the level I currently invest in either. I could stop doing one of them and use that time for the other, but I explicitly don’t want do to that and consider that an inferior outcome. I don’t think this preference of mine is either irrational or very unusual.
consider: If you wanted a shirt… If you wanted to donate $100 to X charity...
Here’s a closer “personal spending” analogy to charity: I commit to putting aside $500 every month for a future downpayment on a house (a goal far in the future). A family friend gives me an unexpected present of $500, putting it right into the fund. Am I likely to forego my own deduction this month and use it for other fun things? Depends on the kind of person I am, but probably not.
Kindly’s comment gets it right. It’s not about satiety. If you’re a consequentialist and care about the total amounts of money donated to each charity, rather than about how much you donated, then the decision in favor of the equal split must be very sensitive to the donations of others like you. That’s the relevant difference between selfish spending and charity.
To recap, I meant my example, where the maximum is at the even split, to refute the claim that any smooth utility function will obtain its maximum along one “most efficient” axis.
You only control a tiny portion of the money that gets donated to charity. If there’s currently an equal amount of money donated to each charity, the ideal action would be to donate equally to each. If the difference between the amounts exceeds the amount you donated, which is more likely the case, you donate to the one that there’s been less donated to. For example, if one charity has one million dollars in donations and the other has two million, and you donate a hundred thousand over your life, you should donate all of it to the charity that has a million.
There’s no question of satiety of exhaustion at the level I currently invest in either.
I doubt that. You might still have fun doing each more, but not as much. If you chose to learn the piano before, but now choose to play tennis, something must have changed. If nothing changed, yet you make a different decision, you’re acting irrationally.
Here’s a closer “personal spending” analogy to charity:
Why is that analogy closer? It looks like it’s in far mode instead of near mode, and the result is more controlled by what’s pretty than what makes you happy. For example, if you got a $500 a month raise, you likely wouldn’t save it all for the downpayment, even though there’s no reason to treat it differently. If you got a $500 a month pay cut, you almost certainly wouldn’t stop saving.
Agreed. To derive that you would also need a smoothness constraint on said function, so that it can be locally approximated as linear; and you need to be donating only a small fraction of the charity’s total budget, so as to stay within the domain of said local approximation.
I assert that the smoothness property is true of sane humans’ altruistic preferences, but that’s not something you can derive a priori, and a sufficiently perverse preference could disagree.
You’re solving essentially a global optimization problem; what use is (the existence of) a local linear approximation? If the utility function happens to be the eminently smooth f(x,y)=xy, then under the constraint of x+y=const the optimal solution is going to be an even split. It’s possible to argue that this particular utility function is perverse and unnatural, but smoothness isn’t one of its problems.
You don’t even need contrived examples to show that utility functions do not admit their maxima along one axis. My other point was that charity may not be easily distinguishable from other types of spending[1], and our normal utility functions definitely don’t have that behavior. We do not, among different types of things we require/enjoy, pick out the “most efficient” one and maximize it alone.
[1] As another example of that thesis, consider the sequence: I buy myself a T-shirt—I buy my child a T-shirt—I pool funds with other parents to buy T-shirts for kids in my child’s kindergarden, including for those whose parents are too poor to afford it—I donate to the similar effort in a neighbouring kindergarden—I donate to charity buying T-shirts for African kids.
Yeah, but unless you actually end up at that point, that’s hardly relevant. If people donated rationally, we would always be at that point, but people don’t, and we aren’t.
We’re normally only dealing with one person. If you play videogames, you quickly get to the point where you don’t want to play anymore nearly as much, so you do something else. If you save someone’s life, there’s still another guy that needs saving, and another guy after that, etc. You can donate enough that the charity becomes less efficient, but you have to be rich and the charity has to be small.
Also, consider: If you wanted a shirt, and I bought you one, you’d stop wanting a shirt and spend your money on something else, just like if you bought the shirt. If you wanted to donate $100 to X charity, and I told you that I already did, would you respond the same?
I don’t understand how what you just said relates to my example. To recap, I meant my example, where the maximum is at the even split, to refute the claim that any smooth utility function will obtain its maximum along one “most efficient” axis. The whole argument is only about the rational behavior.
While this is true, and does point at an interesting difference between charity and many other behaviors, it can’t isolate charity, not by a long shot. There are many, many things we do that we stop doing not because of satiety or exhaustion, but because of other priorities.
To give the first example that comes to mind, a personal one, I’m learning piano and I also play table tennis. I enjoy both activities immensely and would like to do either of them a lot more (but can’t because of other commitments). There’s no question of satiety of exhaustion at the level I currently invest in either. I could stop doing one of them and use that time for the other, but I explicitly don’t want do to that and consider that an inferior outcome. I don’t think this preference of mine is either irrational or very unusual.
Here’s a closer “personal spending” analogy to charity: I commit to putting aside $500 every month for a future downpayment on a house (a goal far in the future). A family friend gives me an unexpected present of $500, putting it right into the fund. Am I likely to forego my own deduction this month and use it for other fun things? Depends on the kind of person I am, but probably not.
Kindly’s comment gets it right. It’s not about satiety. If you’re a consequentialist and care about the total amounts of money donated to each charity, rather than about how much you donated, then the decision in favor of the equal split must be very sensitive to the donations of others like you. That’s the relevant difference between selfish spending and charity.
You only control a tiny portion of the money that gets donated to charity. If there’s currently an equal amount of money donated to each charity, the ideal action would be to donate equally to each. If the difference between the amounts exceeds the amount you donated, which is more likely the case, you donate to the one that there’s been less donated to. For example, if one charity has one million dollars in donations and the other has two million, and you donate a hundred thousand over your life, you should donate all of it to the charity that has a million.
I doubt that. You might still have fun doing each more, but not as much. If you chose to learn the piano before, but now choose to play tennis, something must have changed. If nothing changed, yet you make a different decision, you’re acting irrationally.
Why is that analogy closer? It looks like it’s in far mode instead of near mode, and the result is more controlled by what’s pretty than what makes you happy. For example, if you got a $500 a month raise, you likely wouldn’t save it all for the downpayment, even though there’s no reason to treat it differently. If you got a $500 a month pay cut, you almost certainly wouldn’t stop saving.