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.
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.