For some time now I have been trying to find some clear and objective comparison of proof-of-stake (PoS) and proof-of-work-based (PoW) consensus protocols. Unfortunately, pretty much every comparison I have found has been written by a partisan of one or another coin, and has been strongly colored by the writer's opinions of each specific coin's virtues and defects (which are, more often than not, tangential to the formal properties of its consensus protocol).

What I would like to find is a formal comparison of PoS and PoW. By this I mean a comparison that models each protocol (including their possible variations) formally, in idealized forms that are independent of any real-world coin, and in such a way that it becomes possible to characterize objectively the relative strengths and weaknesses of these idealizations. Such characterizations may include, for example, expressions for cost per transaction, or the probability of success a particular type of attack, in terms of the values of various model parameters.

I realize that such work is difficult to do, and that it is rarely definitive, as there is always a gap, often a considerable one, between theory and practice. In other words, factors that cannot be adequately captured by the models may ultimately be decisive in practice.

Still, even with these caveats, such formal work can still help to identify and clarify the main structural features of the real-world problem that impinge on the comparison.

I would appreciate any pointers (to papers, books, individual researchers, etc.).

  • 3
    I will provide one paper as a comment as I dont believe that this question allows a "correct" reply. However, after a quick search on google scholar, I believe that this paper in part discusses what you are looking for: elit.lnu.edu.ua/pdf/9_10.pdf - there are many papers exploring proof of work or proof of stake. You could invest some work to create a comparison of these papers by yourself. Many blogs and articles do what you request, but I would not label them "formal".
    – Peter1807
    Commented May 10, 2021 at 14:12
  • 2
    Hey @Peter1807 , I think you should post the link to this paper with some snippet of it pulled out and an explanation of why you think it would be helpful to the asker. In my opinion that would suffice as a "correct" answer, given that the publication is in my opinion "formal". If that is not a "correct" answer to kjo's question then maybe the question needs to be closed for being unanswerable.
    – Cavenfish
    Commented May 11, 2021 at 22:02

3 Answers 3


There are many variations on proof of work and proof of stake. It is unlikely that there will be a formal comparison of these broad concepts.

The closest you are likely to find are informal comparisons such as Charles Hoskinson's video "Video for Jack: PoW versus PoS"


This article contains some references to more "technical" papers, although I agree with the general view that a more formal comparison is required: Consensus Mechanisms Explained: PoW vs. PoS


I don't think this is by any means a complete answer however I know that IOG has a number of papers going into the formal properties of various consensus algorithms. Here are some papers that do formal analysis of and comparison between various consensus algorithms:

You might also want to look at the various papers for the Ouroboros protocol as those reason about the formal properties of the Ouroboros protocol specifically and compare performance and security guarantees against Proof of Work and ideal BFT consensus.

The some of the other Proof of Stake consensus protocols have a decent bit of academic work reasoning about the properties of their protocols. These papers (and research libraries in general) should also be considered as they have a wealth of knowledge as well.

By no means is this all of the research out there on the subject, this is just what I know of off the top of my head.

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