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I've heard that the Theseus criterion can be used to evaluate how decentralized an organisation is. But what is it, and what happens when we evaluate Ethereum according to it?

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    Can you provide some more context to your question, perhaps through a link to supporting information? – Taylor Gerring Jan 22 '16 at 14:24
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(moved out of the question, since it describes part of the answer)

From the Ethereum wiki:

Theseus criterion: a test for determining how decentralized an organization is. The test is as follows: suppose the organization has N people, and aliens try to pick K people in the organization at a time (eg. once per week) and zap them out of existence, replacing each group with K new people who know nothing about the organization. For how high K can the organization function?

A stricter test, the Byzantine Theseus criterion, involves randomly substituting K users at a time with malicious actors for some time before replacing them with new users.

(added by me)

Measured against the Theseus criterion, Ethereum the project (it's not really an organisation) would not fair especially well against high K. This is because Ethereum is still in a highly formative state and there are many people whose technical skills and expertise are critical to the project's continued development. However, for low K the fact that the project is open and clearly documented would probably allow it to fair better than most centralised projects that rely explicitly on a few key individuals, because other people would be able to join the project and take their place.

Applying the idea more generally within the Ethereum ecosystem, the promise of organisations whose structure is decentralised via the blockchain suggests that we can build Ethereum-based companies and projects who have a tolerance for higher K according to the criterion than has historically been possible.

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