I just finished a post about QF (quadratic finance) which some are pushing as the "mathematically optimal" way to fund open source.

mattwthomas.com/blog/fund-open

I hope to clear up some of the confusion that I've heard about it and point out some problems with the way that people outside of Economics are interpreting the original paper.

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@mwt This sounds very interesting but I'm afraid it was not very clear to me...
Am I correct in expecting that QF for each project p would lead to a budget:
X_p = (\sum_p \sum_i c_{p, i}) * (\sum_i \sqrt{c_{p, i}})^2 / (\sum_p \sum_i \sqrt{c_{p, i}})^2)

So that the whole donations are used?

@tfardet I should probably make some edits. QF gives this funding:

$$x_p = (\sum_i \sqrt{c_{p, i}} )^2$$

You never sum over p and you always run an (unknown) deficit that you hope to have enough funds to cover.

The implementation is something completely different with

$$\tilde{x}_p = \left[ \sum_i c_i^p \right] + G \frac{\left( \sum_i \sqrt{c_{p, i}} \right)^2}{ \sum_p \left( \sum_i \sqrt{c_{p, i}} \right)^2}$$

where they force the deficit to equal G. Does that make sense?

@mwt I'm still not getting the logic: suppose that c_{p, i} are greater than 1 (expressed in euros for instance), then x_p is lower than sum of donations, right? (square of sum lower than sum of squares)
So what do you do with the remaining money?
Why not renormalize so that each project get a fraction of the total donations given by x_p / sum_p x_p?
I'm probably missing something very basic but I do not understand the logic (what are the authors/implementers trying to achieve)

@mwt
Forget what I said, must be tired, Friday evening...
OK, so we're actually missing money.
But same issue, why not renormalize?

@tfardet Got it. This is a good question. The simple answer is that we are only interested in QF because it has certain properties. Re-normalizing gets rid of these properties.

I haven't looked too closely at this particular re-normalization, but I believe the quadratic part for the project that you want cancels out. So you are left with the private donations outcome divided by some junk that depends only on other projects. This isn't going to be efficient.

@tfardet another way of looking at it is that VCG and QF aren't optimal ways of fundraising. They are systems where people vote with their wallets to allocate a large pool of funds that was already raised.

The funds raised by the mechanism itself are just a nice bonus.

@mwt
So the fund to distribute is not \sum_p \sum_I c_{p, i} ?
I thought the idea was to get small projects to benefit from people giving to popular projects so that you remove the whole "I will stop giving to this big project that must get enough to give to small projects instead".
In that case, just having the square root to compute x_p would mean that small projects benefit from any donation increase (more money anywhere means more money for them).

@mwt
On the other hand, big projects would get potentially a lot less...

@tfardet Exactly. The fund to distribute is raised externally. You also distribute the contributions, but every project gets more[1] than was contributed to them. You are not redistributing money from one project to another.

If you did, then projects you take money from would not choose to participate.

[^1]: Unless only one person contributes. In that case, the sqrt and sq cancel and you just get that one contribution.

@mwt
OK, got it.
Though for your remark, you never really take from projects in what I proposed since the money comes from donations (as for tax, the more money you get the more money you have)
So it would be a balance for them whether they expect more people to contribute to this system compared to what they would get if they tried raising money on their own.

@tfardet that's true. It's not impossible that everyone would stay in even if you redistributed the bids.

@mwt wow, great!

You mention collusion in *QF as an issue. I had conceived of it as a feature: this gives value to social capital, balancing the influence of those who are financially super-wealthy (often through antisocial activity). What do you think about that?

(Mention @tfardet)

@douginamug @tfardet I should probably define collusion. It's not collusion for many people genuinely value a project to fund it. That's the point of the mechanism and, as you say, it is good.

It is collusion for one wealthy person to further increase his influence by paying thousands of people to donate on his behalf. In doing so, he receives a subsidy that he does not deserve.

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