The nice thing about the quadratic voting /​ quadratic funding formula (and the reason that so many people are huge nerds about it) is that the optional diversification is really easy to state:
You should donate in a $X : $1 ratio of org A to org B if you believe that org A is X times as effective as org B (in their marginal use of funding).
One explanation for this is, if you’re donating $X to A and $1 to B, then adding one more cent to A increases A’s total match by 1/​X the amount that B would get if you gave it to B. So the point where your marginal next-dollar is equal is the point where your funding /​ votes are proportional to impact.
Consider three charities A,B,C and three voters X,Y,Z, who can donate $1 each. The matching funds are $3.
Voter Z likes charity C and thinks A and B are useless, and gives everything to C.
Voter Y likes charity B and thinks A and C are useless, and gives everything to B.
Voter X likes charities A and B equally and thinks C is useless.
Then voter X can get more utility by giving everything to charity B,
rather than splitting equally between A and B:
If voter X gives everything to charity B, the proportions for charities A,B,C are
02:(1+1)2:12
If voter X splits between A and B, the proportions are
√1/22:(1+√1/2)2:12
The latter gives less utility according to voter X.
The quadratic-proportional lemma works in the setting where there’s an unbounded total pool; if one project’s finding necessarily pulls from another, then I agree it doesn’t work to the extent that that tradeoff is in play.
In this case, I’m modeling each cause as small relative to the total pool, in which case the error should be correspondingly small.
The nice thing about the quadratic voting /​ quadratic funding formula (and the reason that so many people are huge nerds about it) is that the optional diversification is really easy to state:
You should donate in a $X : $1 ratio of org A to org B if you believe that org A is X times as effective as org B (in their marginal use of funding).
One explanation for this is, if you’re donating $X to A and $1 to B, then adding one more cent to A increases A’s total match by 1/​X the amount that B would get if you gave it to B. So the point where your marginal next-dollar is equal is the point where your funding /​ votes are proportional to impact.
This seems false.
Consider three charities A,B,C and three voters X,Y,Z, who can donate $1 each. The matching funds are $3. Voter Z likes charity C and thinks A and B are useless, and gives everything to C. Voter Y likes charity B and thinks A and C are useless, and gives everything to B. Voter X likes charities A and B equally and thinks C is useless.
Then voter X can get more utility by giving everything to charity B, rather than splitting equally between A and B: If voter X gives everything to charity B, the proportions for charities A,B,C are 02:(1+1)2:12 If voter X splits between A and B, the proportions are √1/22:(1+√1/2)2:12 The latter gives less utility according to voter X.
The quadratic-proportional lemma works in the setting where there’s an unbounded total pool; if one project’s finding necessarily pulls from another, then I agree it doesn’t work to the extent that that tradeoff is in play.
In this case, I’m modeling each cause as small relative to the total pool, in which case the error should be correspondingly small.