Adjusting dynamically the roll size to reach a static 0.5 Gini coefficient

Making sure the Tezos blockchain is decentralized for ever.

Similarly to bitcoin’s difficulty adjustment, you could imagine decreasing the roll size as long as the Tezos Gini coefficient is above 0.5 and vice-versa.

This would deliver mathematical promise that “Richs won’t get that richer” while guaranteeing a number of bakers low enough to allow transaction volumes.

[The Gini coefficient is a measure of statistical dispersion ranging from 0 to 1. A coefficient of 0 would indicate an equal allocation to every wallet, while a coefficient of 1 would describe a dataset where the entire allocation goes to a single contributor. The Gini coefficient is easily computable with the Lorenz Curve.]

In 2017, the Tezos Gini coefficient of was 0.878 , which was higher than the Gini coefficient of the Ethereum crowdsale (0.832), or wealth in the world (0.804), the United States (0.801), and Switzerland (0.803).

0.5 is a random, but symbolic number. Feel free to own this idea and to compute an optimum static Gini coefficient.

That doesn’t work for a few reasons.

  1. The size of the roll is not an arbitrary number, it reflects memory and efficiency concerns when tracking baking rights. Either that number is too conservative for the vast majority of nodes and it should be lowered or it’s already the lowest it can be and any considerations regarding the “Gini” coefficient of baking is irrelevant.

  2. It’s dubious that lowering the roll size would have much of an effect on the Gini coefficient. In fact, quite perversely it might increase the Gini coefficient by encouraging more solo bakers. This is because the “Gini” coefficient is not a very robust metric. Consider a situation with 10 baker with 10% of the rolls each: the Gini coefficient is 0. Consider now 10 bakers with 9% each and 100 bakers with 0.1% each, the Gini coefficient is now 0.4! Of course that doesn’t mean solo baking is bad, it’s great, it means the Gini coefficient is a pretty flawed metric.

  3. Using number of roll per baker is not Sybil resistant, no part of the design should rely on the idea that a baker only has one key because it is a fundamentally brittle hypothesis.


If the roll size was 1000 Tez, 1 roll would get you on average:

  • one endorsement every 4.8 cycles (14 days).
  • one block every 153 cycles (429 days).
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