So exciting! Can community members donate to more than one project? I understood so from the post. And if they do, then there is probably some beautiful optimum(s?) of how much they should diversify, as a vote can be a lot more powerful than the size of the donation when it is matched. Maybe that math is explained in one of the links on quadratic funding. I haven’t checked them out yet :)
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.
Yes, community members can donate in any proportion to the projects in this round. The math of quadratic funding roughly means that your first $1 to a project receives the largest match, then the next $3, then the next $5, $7, etc. Or: your match to a project is proportional to the square root of how much you’ve donated.
You can get some intuition by playing with the linked simulator; we’ll also show calculations about current match rates directly on our website. But you also don’t have to worry very much about the quadratic funding equation if you don’t want to, and you can just send money to whatever projects you like!
So exciting! Can community members donate to more than one project? I understood so from the post. And if they do, then there is probably some beautiful optimum(s?) of how much they should diversify, as a vote can be a lot more powerful than the size of the donation when it is matched. Maybe that math is explained in one of the links on quadratic funding. I haven’t checked them out yet :)
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.
Yes, community members can donate in any proportion to the projects in this round. The math of quadratic funding roughly means that your first $1 to a project receives the largest match, then the next $3, then the next $5, $7, etc. Or: your match to a project is proportional to the square root of how much you’ve donated.
You can get some intuition by playing with the linked simulator; we’ll also show calculations about current match rates directly on our website. But you also don’t have to worry very much about the quadratic funding equation if you don’t want to, and you can just send money to whatever projects you like!