I’ve been thinking of how to assign credit for a donor lottery.
Some ways that seem compelling:
A: You get X% credit for the actual impact of the winner
B: You get 100% credit for the impact if you win, and 0% credit otherwise
C: You get X% credit for what your impact would have been, if you won
Some principles about assigning credit:
Credit is predictable and proportional to the amount you pay to fund an outcome (violated by B)
Credit depends on what actually happens in real life (violated by C)
Your credit depends on what you do, not what uncorrelated other people do (violated by A)
Some actual uses of assigning credit and what they might say:
When I’m tracking my own impact, I use something kind of like C—there’s a line on my spreadsheet that looks like “Donor lottery - £X”, which I smile at a little more than the Long Term Future Fund, because C is how I estimate my expected impact ahead of time.
Impact certificates can’t be distributed according to C because they correspond to actual impacts in the world, and are minted by the organizations that receive the grants and sold in exchange for the grants. You could kind of recover C by selling the rights to any impact certificates you would receive before the lottery is drawn.
A means that your credit is correlated with the decisions of other participants, which the CEA Donor Lottery is designed to avoid and which makes the decision whether to participate harder.
Another principle, conservation of total expected credit:
Say a donor lottery has you, who donates a fraction p of the total with an impact judged by you if you win of X, the other participants, who collectively donate a fraction q of the total with an average impact as judged by you if they win of Y, and the benefactor, who donates a fraction 1−p−q of the total with an average impact if they win of 0. Then total expected credit assigned by you should be pX+qY (followed by A, B and C), and total credit assigned by you should be X if you win, Y if they win, and 0 otherwise (violated by C).
Under A, if you win, your credit is pX, their credit is qX, and the benefactor’s credit is (1−p−q)X, for a total credit of X. If they win, your credit is pY, their credit is qY, and the benefactor’s credit is (1−p−q)Y, for a total credit of Y.
Your expected credit is p(pX+qY), their expected credit is q(pX+qY), and the benefactor’s expected credit is (1−p−q)(pX+qY), for a total expected credit of pX+qY.
Under B, if you win, your credit is X and everyone else’s credit is 0, for a total credit of X. If they win, their credit is Y and everyone else’s credit is 0, for a total credit of Y. If the benefactor wins, everyone gets no credit.
Your expected credit is pX and their expected credit is pY, for a total expected credit of pX+qY.
Under C, under all circumstances your credit is pX and their credit is qY, for a total credit of pX+qY.
Your expected credit is pX and their expected credit is qY, for a total expected credit of pX+qY.
I’ve been thinking of how to assign credit for a donor lottery.
Some ways that seem compelling:
A: You get X% credit for the actual impact of the winner
B: You get 100% credit for the impact if you win, and 0% credit otherwise
C: You get X% credit for what your impact would have been, if you won
Some principles about assigning credit:
Credit is predictable and proportional to the amount you pay to fund an outcome (violated by B)
Credit depends on what actually happens in real life (violated by C)
Your credit depends on what you do, not what uncorrelated other people do (violated by A)
Some actual uses of assigning credit and what they might say:
When I’m tracking my own impact, I use something kind of like C—there’s a line on my spreadsheet that looks like “Donor lottery - £X”, which I smile at a little more than the Long Term Future Fund, because C is how I estimate my expected impact ahead of time.
Impact certificates can’t be distributed according to C because they correspond to actual impacts in the world, and are minted by the organizations that receive the grants and sold in exchange for the grants. You could kind of recover C by selling the rights to any impact certificates you would receive before the lottery is drawn.
A means that your credit is correlated with the decisions of other participants, which the CEA Donor Lottery is designed to avoid and which makes the decision whether to participate harder.
Another principle, conservation of total expected credit:
Say a donor lottery has you, who donates a fraction p of the total with an impact judged by you if you win of X, the other participants, who collectively donate a fraction q of the total with an average impact as judged by you if they win of Y, and the benefactor, who donates a fraction 1−p−q of the total with an average impact if they win of 0. Then total expected credit assigned by you should be pX+qY (followed by A, B and C), and total credit assigned by you should be X if you win, Y if they win, and 0 otherwise (violated by C).
Under A, if you win, your credit is pX, their credit is qX, and the benefactor’s credit is (1−p−q)X, for a total credit of X. If they win, your credit is pY, their credit is qY, and the benefactor’s credit is (1−p−q)Y, for a total credit of Y.
Your expected credit is p(pX+qY), their expected credit is q(pX+qY), and the benefactor’s expected credit is (1−p−q)(pX+qY), for a total expected credit of pX+qY.
Under B, if you win, your credit is X and everyone else’s credit is 0, for a total credit of X. If they win, their credit is Y and everyone else’s credit is 0, for a total credit of Y. If the benefactor wins, everyone gets no credit.
Your expected credit is pX and their expected credit is pY, for a total expected credit of pX+qY.
Under C, under all circumstances your credit is pX and their credit is qY, for a total credit of pX+qY.
Your expected credit is pX and their expected credit is qY, for a total expected credit of pX+qY.