I’m fairly confused about the above, and haven’t succeeded in rigorously defining a satisfying model from which I can compute the expected utility of a donation. My intuition is that the expected value of a donation should work out to the good done by the number of nets that can be purchased and distributed with that amount of money, but I can’t justify it.
Suppose they distribute bed nets in batches of D, and your donation can buy K < D nets. There is a probability of K/D that your donation triggers another batch of D nets, hence expected number of nets = (K/D)*D = K. (By a slightly longer argument, this is still true even when K >= D.)
Note that by the same reasoning, cutting 1 minute off your journey to catch a train, when you have no knowledge of the train timetable, has an expected saving of 1 minute on your whole journey, regardless of how frequently the trains run.
But your calculation changes if you have even a small amount of information about the timetables. Can we get this information from the organizations in question?
You can figure out things in the short term that way, but if you want to know if the marginal money will be used in a year, you’ll have to know every project they run in the mean time and how much each will cost. This will include projects that haven’t even been planned yet.
This isn’t a train that doesn’t hold close to its time table. This is a train that leaves when it seems like a good idea. And you’re trying to predict the time to within a few minutes weeks ahead of time. You won’t even be able to predict which train you’d catch.
Suppose they distribute bed nets in batches of D, and your donation can buy K < D nets. There is a probability of K/D that your donation triggers another batch of D nets, hence expected number of nets = (K/D)*D = K. (By a slightly longer argument, this is still true even when K >= D.)
Note that by the same reasoning, cutting 1 minute off your journey to catch a train, when you have no knowledge of the train timetable, has an expected saving of 1 minute on your whole journey, regardless of how frequently the trains run.
But your calculation changes if you have even a small amount of information about the timetables. Can we get this information from the organizations in question?
You can figure out things in the short term that way, but if you want to know if the marginal money will be used in a year, you’ll have to know every project they run in the mean time and how much each will cost. This will include projects that haven’t even been planned yet.
This isn’t a train that doesn’t hold close to its time table. This is a train that leaves when it seems like a good idea. And you’re trying to predict the time to within a few minutes weeks ahead of time. You won’t even be able to predict which train you’d catch.