Hi everyone, Joel from the Q.E.D. program here. Today marks two weeks into the program, so itâ€™s time to update you all on our progress. Iâ€™m going to focus on two big lessons weâ€™ve learned so far, and then give two brief technical updates.

**Lesson 1: translation isnâ€™t just technical**

Our goal with the Q.E.D. program, in a nutshell, is to adapt state-of-the-art QF research for use at Gitcoin. But you canâ€™t just immediately take the mechanisms from research papers, plop them into python, and then call it a day (although I did do that, if anyoneâ€™s interested): translating between the world of pure math (where QF whitepapers live) and the real world requires a lot of technical adjustments. We were expecting this.

What I wasnâ€™t expecting, however, is that QF isnâ€™t just an algorithm that web3 communities like because it has appealing mathematical properties. It does have nice properties, of course, but in my time reading forum posts and talking to community members, Iâ€™ve gotten the impression that folks also like QF for more intuitive reasons. Iâ€™ve heard people say they like QF because itâ€™s egalitarian, democratic, empoweringâ€¦ Based on the qualitative research on the topic, it seems to me that QF serves as a mirror for the communityâ€™s values: the community co-creates an implementation of QF, sees if the outcome matches their intuitive idea of what should be happening, and then adjusts accordingly for the next grants round.

Because of all of the intangible value propositions, translation canâ€™t just be about the technical details. We have to also make sure that our work syncs up with the Gitcoin communityâ€™s idea of what QF should be. To that end, Iâ€™m requesting community input so that we can really flesh out our understanding of how the community intuitively thinks about QF and make sure the Q.E.D. program provides the maximum possible value. If you have time, please visit this polis conversation and let us know what you think. Additionally, Iâ€™d love to have one-on-one meetings with anybody whoâ€™s interesting in taking a deeper dive â€“ to set one up, email me at joeldmiller73@gmail.com.

**Lesson 2: collusion resistance can be private or public**

Iâ€™ve learned that Gitcoin has a few cool ways of dealing with sybil networks. Previously, Gitcoinâ€™s fraud defense team implemented sybil defense measures that were kept relatively private, in order to keep bad actors from adjusting their behaviors to avoid censure. On the other hand, Gitcoin Passport provides what I would call a more â€śpublic-facingâ€ť approach to sybil resistance, where rules are out in the open. Both approaches have advantages, and as we try to understand how to implement anti-collusive QF, this distinction presents the first obvious crossroads. Do we want to keep the rules of our implementation relatively private, or make them public? While weâ€™re open to re-negotiating this issue, right now I strongly feel that our implementation should be public. A public implementation will allow for much easier integration with Passport and other like-minded products in the web3 space, and on a more fundamental level, it better aligns with my belief that social diversity (the backbone of anti-collusive QF) is something to be celebrated and encouraged, rather than something to be hidden away.

**Technical update 1: Metrics for assessing outcomes**

Assessing the differences between outcomes from different QF rounds will be an important part of our analysis. Based on some conversations with members of the data guild, it looks like a metric inspired by earth-mover distance (EMD) will work well. For our purposes, we can think of EMD as a measure of distance between two different sets of funding amounts: intuitively, the EMD is the total amount of money one would need to move around between various projects to get from one set of funding amounts to the other.

For example, suppose that in a world with only two projects competing for grants funds, I could run algorithm A, which gives both projects $100, or algorithm B, which gives one project $50 and the other $150. Then the EMD between these two outcomes is 50 â€“ since if you start with the outcome specified by algorithm B, then move $50 from one project to the other, you get the outcome specified by algorithm A.

The most general definition of EMD is a little complicated, but for our special case, itâ€™s easier to define. Let f(*p*,A) be the amount of funding given to project *p* in outcome A. Then our EMD-inspired metric can be defined more simply as

EMD(A,B) = Â˝ ÎŁ*â‚š* f(*p*, A) - f(*p*, B)

where â€śÎŁ*â‚š*â€ť denotes a sum over all projects *p*.

EMD becomes useful when you have some approximate idea of what â€śshouldâ€ť happen â€“ in this case, some idea of the socially optimal allocation. If you can estimate that, then the EMD between algorithm Xâ€™s allocation and the socially optimal allocation is a great metric for evaluating algorithm X. Iâ€™ll talk more about how we can estimate socially optimal allocations in the next update.

*Extra info for nerds: if you think of an allocation outcome over n projects as a point in n-dimensional space, then the EMD between outcomes A and B is closely related to the L1 distance (or â€śmanhattan distanceâ€ť) between the â€śpointâ€ť versions of outcomes A and B. But thinking of outcomes as points opens you up to many more distance metrics, for example, L2 (euclidean) distance. So really, there are many closely related metrics to choose from.*

**Technical update 2: Python tool for minimum distance on the Ethereum network**

As I began to dive into the Ethereum data, I found it useful to whip up a simple python tool to query the â€śdistanceâ€ť between two wallets, where distance is measured in degrees of separation between wallets â€“ i.e., if wallet P transacted directly with wallet Q, the distance between P and Q is one. If wallets Q and R also transacted, but wallets P and R never transacted, then the distance between P and R is 2. Iâ€™m sure many have already coded up similar tools, but if anyone is looking for a simple implementation, you can find my code in a google Colab notebook or on GitHub.

Thatâ€™s all for now. If you have any feedback please let us know in the replies, and if you want to chat one-on-one about QF, please reach out to me via email (joeldmiller73@gmail.com). Thanks!