I have doubts that the claim about “theoretically optimal” apply to this case.
Now, you have not provided a precise notion of optimality, so the below example might not apply if you come up with another notion of optimality or assume that voters collude with each other, or use a certain decision theory, or make other assumptions…
Also there are some complications because the optimal strategy for each player depends on the strategy of the other players. A typical choice in these cases is to look at Nash-equilibria.
Consider three charities A,B,C and two players X,Y who can donate $100 each.
Player X has utilities 1, 0.9, 0 for the charities A,B,C.
Player Y has utilities 0, 0.9, 1 for the charities A,B,C.
The optimal (as in most overall utility) outcome would be to give everything to charity B.
This would require that both players donate everything to charity B.
However, this is not a Nash-equilibrium, as player X has an incentive to defect by giving to A instead of B
and getting more utility.
This specific issue is like the prisoners dilemma and could be solved with other assumptions/decision theories.
The difference between this scenario and the claims in the literature might be that public goods is not the same as charity, or that the players cannot decide to keep the funds for themselves.
But I am not sure about the precise reasons.
Now, I do not have an alternative distribution mechanism ready, so please do not interpret this argument as serious criticism of the overall initiative.
I have doubts that the claim about “theoretically optimal” apply to this case.
Now, you have not provided a precise notion of optimality, so the below example might not apply if you come up with another notion of optimality or assume that voters collude with each other, or use a certain decision theory, or make other assumptions… Also there are some complications because the optimal strategy for each player depends on the strategy of the other players. A typical choice in these cases is to look at Nash-equilibria.
Consider three charities A,B,C and two players X,Y who can donate $100 each. Player X has utilities 1, 0.9, 0 for the charities A,B,C. Player Y has utilities 0, 0.9, 1 for the charities A,B,C.
The optimal (as in most overall utility) outcome would be to give everything to charity B. This would require that both players donate everything to charity B. However, this is not a Nash-equilibrium, as player X has an incentive to defect by giving to A instead of B and getting more utility.
This specific issue is like the prisoners dilemma and could be solved with other assumptions/decision theories.
The difference between this scenario and the claims in the literature might be that public goods is not the same as charity, or that the players cannot decide to keep the funds for themselves. But I am not sure about the precise reasons.
Now, I do not have an alternative distribution mechanism ready, so please do not interpret this argument as serious criticism of the overall initiative.