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

19 Pages Posted: 15 Nov 2019

See all articles by Jacob Leshno

Jacob Leshno

Chicago Booth

Philipp Strack

Yale, Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: October 2019


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

Suggested Citation

Leshno, Jacob and Strack, Philipp, Bitcoin: An Impossibility Theorem for Proof-of-Work Based Protocols (October 2019). Cowles Foundation Discussion Paper No. 2204R, 2019, Available at SSRN: or

Jacob Leshno

Chicago Booth ( email )

5807 S. Woodlawn Ave
Chicago, IL 60610
United States

Philipp Strack (Contact Author)

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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