I guess it depends on the details of the returns to scale for donors. If there are returns to scale across the whole range of possible values of the donor lottery, as long as one person who would do lots of work/has good judgment joins the donor lottery, we should be excited about less conscientious people joining as well.
To be more concrete, imagine the amount of good you can do with a donation goes with the square of the donation. Let’s suppose one person who will be a good donor joins the lottery with $1. Everyone else in the lottery will make a neutral donation if they win. The expected value of the lottery is (good person’s chance of winning) * (total pool)² = (1/total pool) * (total pool)² = total pool.
Obviously that exact model is a bit contrived, but it points at why non-report-writing people still bring value in a lottery
Except that the pot size isn’t constrained by the participation of small donors: the CEA donor lottery has fixed pot sizes guaranteed by large donors, and the largest donors could be ~risk-neutral over lotteries with pots of many millions of donors. So there is no effect of this kind, and there is unlikely to ever be one except at ludicrously large scales (where one could use derivatives or the like to get similar effects).
I guess it depends on the details of the returns to scale for donors. If there are returns to scale across the whole range of possible values of the donor lottery, as long as one person who would do lots of work/has good judgment joins the donor lottery, we should be excited about less conscientious people joining as well.
To be more concrete, imagine the amount of good you can do with a donation goes with the square of the donation. Let’s suppose one person who will be a good donor joins the lottery with $1. Everyone else in the lottery will make a neutral donation if they win. The expected value of the lottery is (good person’s chance of winning) * (total pool)² = (1/total pool) * (total pool)² = total pool.
Obviously that exact model is a bit contrived, but it points at why non-report-writing people still bring value in a lottery
Except that the pot size isn’t constrained by the participation of small donors: the CEA donor lottery has fixed pot sizes guaranteed by large donors, and the largest donors could be ~risk-neutral over lotteries with pots of many millions of donors. So there is no effect of this kind, and there is unlikely to ever be one except at ludicrously large scales (where one could use derivatives or the like to get similar effects).