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5. Optimisable Proof-of-Work
Optimisable proof-of-work (OPoW) distinctively requires multiple proof-of-works to be featured, "binding" them in such a way that optimisations to the proof-of-work algorithms do not cause instability/centralisation. This binding is embodied in the calculation of influence for Benchmarkers. The adoption of an algorithm is then calculated using each Benchmarker's influence and the fraction of qualifiers they computed using that algorithm.
5.1. Influence
OPoW introduces a novel metric, imbalance, aimed at quantifying the degree to which a Benchmarker contributes to centralization by leveraging statistical measures. This is only possible when there are multiple proof-of-works.
The metric is defined as imbalance = \frac{CV(\%qualifiers)^2}{N - 1} where CV is coefficient of variation, %qualifiers is the fraction of qualifiers found by a Benchmarker across challenges, and N is the number of active challenges. This metric ranges from 0 to 1, where lower values signify less centralisation.
Penalising imbalance is achieved through imbalance\_penalty = 1 - \frac{1}{1 + k \cdot imbalance}, where k is a multiplier (currently set to 1.5). The penalty ranges from 0 to 1, where zero signifies no penalty.
When block rewards are distributed pro-rata amongst Benchmarkers based on influence, where influence has imbalance penalty applied, the result is that Benchmarkers are incentivised to minimise their imbalance as to maximise their earnings:
weight = mean(\%qualifiers) \cdot (1 - imbalance\_penalty)influence = normalise(weights\ across\ benchmarkers)Notes:
-
A Benchmarker focusing solely on a single challenge will exhibit a maximum imbalance value of
1. -
Conversely, a Benchmarker with an equal fraction of qualifiers across all challenges will demonstrate a minimum imbalance value of
0.
5.2. Adoption
Any active solution can be assumed to already have undergone verification of the algorithm used. This allows the straightforward use of Benchmarkers' influence for calculating algorithm adoption:
weight = sum(influence \cdot \%qualifiers) \cdot (1 - imbalance\_penalty)adoption = normalise(weights\ across\ algorithms\ for\ a\ challenge)By integrating influence into the adoption calculation, TIG effectively guards against potential manipulation by Benchmarkers.