Essentially, the claim is that 20 of SingInst’s regular donors have extra money lying around that they are willing to donate to SingInst iff someone else donates the same amount.
Bear with my broad strokes here.
Let the utility u of donating x dollars to SingInst be diminishing: u = x^(1/3).
Assume that hedonistic spending can be spread over enough options to make diminishing returns negligible: u = x
The donor then donates their first dollar to SingInst, whereupon hedonistic spending provides them more utils.
The utility u of providing x dollars of a dollar-for-dollar service for SingInst donors is: u = (2x)^(1/3), and the donor gets up to ~1.415 dollars (to gain 2.83 dollars worth of donating utility!) before hedonistic spending is a better option. So this answers the first claim: they are willing to donate extra money iff someone else donates, and they intend to spend it on some other form of utility otherwise. The nature of dollar-for-dollar matching increases the utility they gain from their dollar.
As for the second part… there’s no need to commit to a binding agreement to not donate the leftover to SingInst at the end. Say the donor donated a dollar by themselves, then offered up to 41 cents matching contribution. Other donors take advantage of this offer by 20 cents—the donor still has another 21 cents of positive utility before hedonistic spending takes over, but the matching period ends at this point in time. (Why end the matching period? I’ll get there in a second). At this point, those 21 cents will generate .21 utils if spent hedonistically, but only .06 utils if donated without matching.
So the nature of diminishing utility will produce this behaviour. It’s not so suspicious a premise, in the end.
Now, why end the matching period? A utility-maximising donor ought to offer their 41 cents for as long as it takes—the utility of those 41 cents is always going to be higher than any 41-cent section of hedonistic spending (which is where the money is coming from). The answer lies partly in human psychology. A limited-time offer prompts action in a way that open-ended, time-independent offers do not. A progress bar prompts action too. It’s also partly from status: successfully completing campaigns like this raises the prestige of SingInst. Meeting the target before the specified end date raises the prestige of both SingInst and its donors.
These factors are convincing enough reasons to time-limit the matching offer, mostly because they solve the problem of the pledge not being fulfilled. Odd quirk of our brains to blame here.
The rational donor wouldn’t offer to match x for y time; they would simply offer to match x. So the donor would simply offer to match the first dollar and forty-one cents donated. There’s no risk of accidentally being required to donate more than you’d want to.
I thought humans did that a lot on financial markets (make an offer that potentially incurs an infinitely large obligation), in particular when they sell (“write”) certain option contracts?
Bear with my broad strokes here.
Let the utility u of donating x dollars to SingInst be diminishing: u = x^(1/3).
Assume that hedonistic spending can be spread over enough options to make diminishing returns negligible: u = x
The donor then donates their first dollar to SingInst, whereupon hedonistic spending provides them more utils.
The utility u of providing x dollars of a dollar-for-dollar service for SingInst donors is: u = (2x)^(1/3), and the donor gets up to ~1.415 dollars (to gain 2.83 dollars worth of donating utility!) before hedonistic spending is a better option. So this answers the first claim: they are willing to donate extra money iff someone else donates, and they intend to spend it on some other form of utility otherwise. The nature of dollar-for-dollar matching increases the utility they gain from their dollar.
As for the second part… there’s no need to commit to a binding agreement to not donate the leftover to SingInst at the end. Say the donor donated a dollar by themselves, then offered up to 41 cents matching contribution. Other donors take advantage of this offer by 20 cents—the donor still has another 21 cents of positive utility before hedonistic spending takes over, but the matching period ends at this point in time. (Why end the matching period? I’ll get there in a second). At this point, those 21 cents will generate .21 utils if spent hedonistically, but only .06 utils if donated without matching.
So the nature of diminishing utility will produce this behaviour. It’s not so suspicious a premise, in the end.
Now, why end the matching period? A utility-maximising donor ought to offer their 41 cents for as long as it takes—the utility of those 41 cents is always going to be higher than any 41-cent section of hedonistic spending (which is where the money is coming from). The answer lies partly in human psychology. A limited-time offer prompts action in a way that open-ended, time-independent offers do not. A progress bar prompts action too. It’s also partly from status: successfully completing campaigns like this raises the prestige of SingInst. Meeting the target before the specified end date raises the prestige of both SingInst and its donors.
These factors are convincing enough reasons to time-limit the matching offer, mostly because they solve the problem of the pledge not being fulfilled. Odd quirk of our brains to blame here.
don’t forget the simple explanation: It’s risky to offer to match infinite dollars.
The rational donor wouldn’t offer to match x for y time; they would simply offer to match x. So the donor would simply offer to match the first dollar and forty-one cents donated. There’s no risk of accidentally being required to donate more than you’d want to.
I thought humans did that a lot on financial markets (make an offer that potentially incurs an infinitely large obligation), in particular when they sell (“write”) certain option contracts?