user1063: 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.).

user1655: 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

user1714: 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:

The Bitcoin Backbone Protocol with Chains of Variable Difficulty
But Why Does It Work? A Rational Protocol Design Treatment of Bitcoin
Full Analysis of Nakamoto Consensus in Bounded-Delay Networks
Comparison of Block Expectation Time for 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.

IOG Research Library (has all the Ouroboros Papers)

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.

Algorand Research Library

Polkadot Research Library



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.

user281: 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"

1063: <p>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 <em>specific</em> coin's virtues and defects (which are, more often than not, tangential to the formal properties of its consensus protocol).</p>
<p>What I would like to find is a <em>formal</em> 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.</p>
<p>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.</p>
<p>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.</p>
<p>I would appreciate any pointers (to papers, books, individual researchers, etc.).</p>
 1655: <p>This article contains some references to more &quot;technical&quot; papers, although I agree with the general view that a more formal comparison is required:
<a href="https://hackernoon.com/consensus-mechanisms-explained-pow-vs-pos-89951c66ae10" rel="nofollow noreferrer">Consensus Mechanisms Explained: PoW vs. PoS</a></p>
 1714: <p>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:</p>
<ul>
<li><a href="http://eprint.iacr.org/2016/1048" rel="nofollow noreferrer">The Bitcoin Backbone Protocol with Chains of Variable Difficulty</a></li>
<li><a href="https://eprint.iacr.org/2018/138" rel="nofollow noreferrer">But Why Does It Work? A Rational Protocol Design Treatment of Bitcoin</a></li>
<li><a href="https://eprint.iacr.org/2020/277" rel="nofollow noreferrer">Full Analysis of Nakamoto Consensus in Bounded-Delay Networks</a></li>
<li><a href="https://doi.org/10.15588/1607-3274-2018-4-15" rel="nofollow noreferrer">Comparison of Block Expectation Time for Various Consensus Algorithms</a></li>
</ul>
<p>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.</p>
<ul>
<li><a href="https://iohk.io/en/research/library/" rel="nofollow noreferrer">IOG Research Library (has all the Ouroboros Papers)</a></li>
</ul>
<p>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.</p>
<ul>
<li><p><a href="https://www.algorand.com/technology/research-innovation/research-papers" rel="nofollow noreferrer">Algorand Research Library</a></p>
</li>
<li><p><a href="https://research.web3.foundation/en/latest/Publications.html" rel="nofollow noreferrer">Polkadot Research Library</a></p>
</li>
</ul>
<hr />
<p>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.</p>
 281: <p>There are many variations on proof of work and proof of stake.  It is unlikely that there will be a <em>formal</em> comparison of these broad concepts.</p>
<p>The closest you are likely to find are <em>informal</em> comparisons such as Charles Hoskinson's video <a href="https://www.youtube.com/watch?v=lMZ1xQzWtl4" rel="noreferrer">&quot;Video for Jack: PoW versus PoS&quot;</a></p>
