Bitcoin: An Impossibility Theorem for Proof-of-Work Based Protocols

Abstract

Bitcoin’s main innovation lies in allowing a decentralized system that relies on anonymous, profit driven miners who can freely join the system. We formalize these properties in three axioms: anonymity of miners, no incentives for miners to consolidate, and no incentive to assuming multiple fake identities. This novel axiomatic formalization allows us to characterize which other protocols are feasible: Every protocol with these properties must have the same reward scheme as Bitcoin. This implies an impossibility result for risk-averse miners: no protocol satisfies the aforementioned constraints simultaneously without giving miners a strict incentive to merge. Furthermore, any protocol either gives up on some degree of decentralization or its reward scheme is equivalent to Bitcoin’s.

Keywords: Bitcoin, Random Selection, Proportional Selection Rule, Impossibility Theorem

JEL Classification: C72, D02, D47