A Note on the Non-Proportionality of Winning Probabilities in Bitcoin

18 Pages Posted: 17 Jun 2019 Last revised: 19 Feb 2021

See all articles by José Parra-Moyano

José Parra-Moyano

Copenhagen Business School

Gregor Reich

Tsumcor Research AG

Karl Schmedders

IMD Lausanne

Date Written: October 1, 2020


It is widely assumed that the selection process in a blockchain is based on proportional winning probabilities. The reliability and security of any blockchain is based upon this assumption. However, making an analogy between the Bitcoin protocol and the classical statistical urn problem, we argue that, at least on a theoretical level, the selection process in several blockchains is based on nonproportional winning probabilities. This reveals a misconception regarding the incentive structure of many blockchain protocols. We develop an empirical approach to testing for nonproportional winning probabilities in any blockchain, and offer a solution to this problem.

Keywords: Bitcoin, Blockchain, Choice Models

JEL Classification: C25, C44

Suggested Citation

Parra-Moyano, José and Reich, Gregor and Schmedders, Karl, A Note on the Non-Proportionality of Winning Probabilities in Bitcoin (October 1, 2020). Available at SSRN: https://ssrn.com/abstract=3399742 or http://dx.doi.org/10.2139/ssrn.3399742

José Parra-Moyano (Contact Author)

Copenhagen Business School ( email )

Solbjerg Plads 3
Frederiksberg C, DK - 2000

Gregor Reich

Tsumcor Research AG ( email )


Karl Schmedders

IMD Lausanne ( email )

Lausanne, CH-1003
+41 (0)79 596 8956 (Phone)

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