Intro
This is a response article to the article, "Towards a Statistic Simulation of Fractal Democracy," by Genesis Fractal member @aguerrido. This article will not provide all of the relevant context for each response, and if you're trying to understand this article, it is necessary to first read the original (linked above).
The original post (OP) is very thoughtful, and defines an interesting mathematical model by which one could begin to model the evolution of a system governed by fractal democracy.
My post only represents my own views, and is simply an individual response I've made after carefully considering the claims in the original post. I freely express disagreement, which I hope doesn't come across as anything other than that - disagreement. I very highly value the contribution by @aguerrido to inject additional mathematical rigor into the design of FD.
Re: the "fair estimate" of member contributions
OP states:
"...when dealing with the Law of Large Numbers, ...it is valid [only] in the limit when the number of measurements goes to infinity. In the case of Fractally, this would require a large number of breakout sessions. ...In the interval between now and that future time when we will have a fair estimate of the actual value of members' contributions, anything can happen."
That "future time" doesn't exist, even as the limit of samples approaches infinity. The reason is because there is no perfectly shared view among members about the goal or ideal end-state of the community. Rather, there are many competing and continually changing ideas for what is the most valuable. Therefore the goal cannot be to arrive at a discrete "fair estimate," but rather to have a system that is roughly correlated to the average opinion of the community, even as goals and membership change over time.
Re: complex systems
OP confuses chaotic systems with complex systems. Chaotic systems have a sensitive dependence on initial conditions, as OP noted. I agree that consensus is a chaotic system. But for something to exhibit chaotic behavior, it is not necessarily complex: a faucet can exhibit aperiodic dripping patterns, the position of three gravitationally-bound bodies is chaotic, etc. So even though consensus is chaotic, an important goal to pursue is to keep the base-layer mechanisms that drive ƒractal democracy as simple as possible. Complexity is hard to define - I like the distinction made by Vitalik on systemic & encapsulated complexity, and think it's best to optimize for minimal systemic complexity. The primary reason to prefer simple mechanisms is to improve it's perceived (and actual) neutrality.
"But, unlike the tossing of the coin, markets are complex systems."
The tossing of a coin is another good example of a simple (non-complex) but chaotic system. The value heads or tails has a sensitive dependence on the initial conditions of the experiment, which is precisely what makes it a reasonably fair proxy for a 50/50 odds event. This example also illustrates that small changes to the input in a chaotic system do not always result in large deviations in the outcome. It depends on the chaotic system. See attractors.
Re: marketcaps
Every second, millions of participants in the cryptospace achieve consensus on the perceived value of crypto projects...
Marketcap is primarily derived from expected future ROI, rather than from evaluations of past work. The value of something as an investment is very different than the value something is perceived to have already had in achieving a goal. That's also related to why FD uses average contribution level over time, rather than the accumulation of the Respect tokens (coin-voting), to form the council.
Therefore, marketcap value is qualitatively different from the value measured by contribution level in FD meetings, and OP's assertion that "the global crypto market should arrive to correct valuations much faster than the Fractally community" is incorrect.
Re: the variance of selfishness
OP states:
"Whatever the case, of all parameters, s(i) seems to be the one that contributes the more noise to the system and, therefore, more likely to generate detrimental butterfly effects."
I agree, and I think there is a systemic bias towards over-valuing contributions from those who are able to convincingly over-sell their own contributions.
"...it would be better to simply minimize [the impact of s(i)] in the protocol."
It's an interesting idea, I am in favor of thinking of ways to minimize the impact of s(i). But I'm not convinced by OP's proposal to prevent people from expressing the opinion that their own contribution is the most valuable. I prefer that everyone can fight for their own contributions, and the consensus process will naturally eliminate groups with an excessive avg(s(i)) by their failure to reach consensus.
Here's an alternative proposal that minimizes s(i): Maximize the number of consensus rounds. This bias effect of s(i) is more relevant when the community is small, because there is only one consensus round. In subsequent rounds, I expect avg(J(i)) to be significantly higher (because both a and g should be higher), and the impact of s(i) to therefore be correspondingly lower.
Conclusion
I disagree with many of OP's philosophical/economical premises, but I agree with the ultimate conclusion to look for ways to minimize the impact of individual "selfishness" (s(i)) and other high-noise variables on the system.
I disagree with OP's proposal to censor the opinions of those who sincerely believe their own contribution is the most valuable, and I offered a counter-proposal to consider in the design of a fractal that should effectively minimize s(i).
It is thoughtful articles like the OP by @aguerrido that help us to have a more rigorous understanding of the systems we are building, and I'm very interested in the outcomes of simulations like this.
I challenge the simulation teams to try to make testable predictions about the future state of fractals, to allow us to evaluate the veracity of the models.