SoK: Measuring Blockchain Decentralization

Aggelos Kiayias; Christina Ovezik; Daniel W. Woods; Dimitris Karakostas; Mary Milad

REVIEW 3 major objections 5 minor 70 references

SoK: Measuring Blockchain Decentralization

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read In proof-of-work blockchains, the number of active miners does not measure decentralization.

desk verdict Solid systematization of blockchain decentralization measurement, but the headline PoW participation/decentralization split rests on a single population-window choice that the paper itself advises against. read the letter →

arxiv 2501.18279 v2 pith:CNS3LOJA submitted 2025-01-30 cs.CR

Christina Ovezik , Dimitris Karakostas , Mary Milad , Aggelos Kiayias , Daniel W. Woods This is my paper · ORCID

classification cs.CR

keywords blockchaindecentralizationproof-of-workproof-of-stakeexploratoryfactoranalysismetricsconsensuslayerpopulationestimationtokenomics

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Blockchain decentralization is widely invoked but measured in inconsistent ways. This paper builds a framework that separates the choices involved—which resource to look at, how to extract its distribution, and which metric to apply—and then tests, on data from six live systems, whether the common metrics actually track the same underlying property. The central finding is that in proof-of-work blockchains the number of active participants and the concentration of power are statistically distinct signals, so counting participants is not a proxy for decentralization. In proof-of-stake systems the two align. The paper also shows that pre-processing decisions such as the population estimation window and the choice of inclusion thresholds can change decentralization estimates enough to matter.

What carries the argument

The central object is the measurement workflow framework: a three-step pipeline that selects a layer and resource, pre-processes raw ledger data through clustering, resource estimation, population estimation, sampling frequency, and inclusion thresholds, and finally applies a metric function. The argument's carrying tool is exploratory factor analysis, which finds latent variables behind observed metrics; one factor means the metrics measure a single concept, and a second factor means a separate signal. The appearance of a second factor, with the number of parties loading onto it in PoW systems, is the observation that supports the participation-versus-decentralization claim.

What would settle it

Recompute the factor analysis for Bitcoin, Ethereum PoW, and Litecoin with the population of active miners defined by the same 7-day window used for resource estimation; if the number of parties then loads on the same factor as the concentration metrics, the claimed separation collapses.

Watch

Extended reading notes

Core claim

The paper's central claim is that, in Proof-of-Work blockchains, participation on the consensus layer is not correlated with decentralization but captures a distinct signal. The evidence is an exploratory factor analysis of seven metrics—Gini, HHI, CR3, entropy, Nakamoto coefficient, tau-decentralization index, and number of parties—computed on block-production data from Bitcoin, Ethereum PoW, and Litecoin, which yields two factors, with the number of parties loading strongly on the second factor. The same analysis on Cardano, Ethereum PoS, and Tezos yields a single factor, which the paper interprets as showing that Proof-of-Stake systems align participation with decentralization. The paper further demonstrates that population estimation windows and inclusion thresholds can swing the resulting numbers, and it derives practical recommendations, including avoiding the number of parties as a decentralization metric in PoW systems.

Load-bearing premise

The two-factor split for proof-of-work rests on a single population-estimation choice—using all historical participants—and that choice, the paper itself shows, can shift decentralization estimates substantially.

Editorial extensions

If this is right

Counting participants on the consensus layer of a proof-of-work blockchain should not be used as a decentralization metric, because it tracks a different signal from concentration metrics.
Researchers reporting decentralization of PoW systems should state estimation windows explicitly and prefer windows of at least 7 days, since short windows lack statistical confidence.
The choice of population estimation window is not innocent: all-time windows versus measurement-window populations can produce materially different Gini values.
Protocol designers who want more decentralization in PoW systems cannot rely on increasing participation alone; they need mechanisms that reduce concentration of control.
For PoS systems, the single-factor result means simple participation counts are more informative about decentralization.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The two-factor result for PoW may be sensitive to the all-time population window; a natural test is to re-run the factor analysis with population windows matched to the resource-estimation window (e.g., 7 days) or with sliding windows that distinguish current from historical participants.
If the separation between participation and decentralization holds, regulators and exchanges evaluating decentralization for legal classification would need to weigh concentration metrics rather than user counts, which could change security-commodity determinations.
The same EFA methodology could be applied to other PoW chains (e.g., Dogecoin, Bitcoin Cash, Monero) and to layer-2 sequencer sets to see whether the two-factor pattern is a general property of PoW or an artifact of mining economics.
A testable extension: compute the number-of-parties metric in each 7-day window (rather than all-time) for Bitcoin and check whether its correlation with the Gini coefficient rises above the near-zero values reported.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's what you should know before spending time on this SoK. The framework is genuinely useful: resource → pre-processing (clustering, resource estimation, population estimation, frequency, thresholds) → metrics. Table 1 classifying twenty measurement papers is careful, and the sensitivity results (Figure 4, Table 2) make a real point: arbitrary choices like the population window or top-X threshold materially change measured decentralization. That message—be careful, or your numbers are not comparable—is worth the price of admission alone.

The new empirical bit is the exploratory factor analysis across six ledger configurations. For the three PoW systems, # Parties cleanly separates onto a second factor; for the three PoS systems, it does not. If robust, this would be important: participation and decentralization are not interchangeable. But I don't think it is robust yet. The EFA uses an all-time population estimation window, so # Parties is the cumulative count of every entity that ever mined up to that week, while the other metrics come from the 7-day block distribution. It is mechanically non-decreasing and decoupled from current concentration. The paper itself shows in Figure 4 that this window choice swings Gini, and its own Table 3 recommendation is REW < PEW < study window—which all-time violates. The authors even write 'we use the entire history for population estimation, leaving a thorough evaluation of the optimal choice to future work.' So the central abstract claim—that in PoW, participation is not correlated with decentralization—is built on an untested window. If you rerun the EFA with a 14-day or 1-month PEW, the two factors may collapse, and the claim goes with them.

Smaller issues: the abstract says 'not correlated,' but the consensus correlation tables show # Parties moderately correlated with Gini/Entropy in Bitcoin and Litecoin, only negative in Ethereum PoW; 'distinct signal' would be more accurate. No code or processed data is provided, so the factor analysis cannot be checked. The tokenomics EFA is inconclusive and the paper admits it. The 7-day window recommendation leans on the authors' prior work [46], but that is a real result, so not a problem.

Who is this for? Anyone working on blockchain decentralization measurement. The systematization deserves a serious referee. My recommendation: send it out, and condition acceptance on the authors (a) rerunning the factor analysis under at least two shorter population windows, (b) releasing code and processed data, and (c) softening the PoW/PoS generalization to match the evidence. The paper would then be a standard reference; right now the headline result is a well-motivated hypothesis.

Referee Report

3 major / 5 minor

Summary. This paper proposes a systematization framework for measuring blockchain decentralization, organizing the workflow into resource selection, data pre-processing (clustering, resource estimation, population estimation, measurement frequency, inclusion thresholds), and metric choice. It classifies the empirical decentralization literature in Table 1 and contributes an empirical analysis on six ledger instances (Bitcoin, Cardano, Ethereum PoW, Ethereum PoS, Litecoin, Tezos) using live ledger data. The empirical part demonstrates that pre-processing choices such as estimation windows, thresholds, and clustering materially affect decentralization estimates, and it applies exploratory factor analysis to ask whether commonly used metrics capture the same latent construct. The central claim, stated in the abstract and conclusion, is that in Proof-of-Work systems participation (proxied by the number of parties) is not correlated with decentralization metrics and forms a separate factor, whereas in Proof-of-Stake systems all metrics align on one factor. The paper then derives practical recommendations for measuring decentralization.

Significance. If the central empirical claim survives scrutiny, the paper would be an important contribution: it would challenge the widespread assumption that increasing the number of active participants in PoW systems is a meaningful path to decentralization, and it would support the use of concentration metrics such as the Nakamoto coefficient and HHI over participant counts. The systematization framework itself is useful, and Table 1 is a valuable consolidated map of methodological choices in the literature. The threshold sensitivity analysis (Table 2), the clustering comparison (Figure 3), and the population-window sensitivity illustration (Figure 4) are concrete and well matched to the paper's message that methodological choices are consequential. However, the factor-analysis result that underpins the headline claim is computed under a single population-estimation window (all-time) that the paper's own recommendations discourage; this load-bearing dependence must be addressed before the claim can be accepted.

major comments (3)

[Section 4 (Population Estimation) and Figure 5] The consensus-layer factor analysis is computed with the all-time population estimation window, as stated in Section 4: 'In our analysis, we use the entire history for population estimation.' Under this window, #Parties is a cumulative count of all distinct entities ever observed up to each weekly snapshot, while Gini, HHI, CR3, Entropy, NC, and T0.33 are computed from the 7-day block-production distribution. A cumulative count is mechanically non-decreasing and, for growing PoW systems, largely decoupled from the current concentration of block production. The paper's own Figure 4 shows that the all-time window dramatically changes Gini estimates relative to the measurement-window approach, and Table 3 recommends REW < PEW < study window, which the all-time choice violates. The central PoW-vs-PoS claim therefore needs a robustness check under shorter population windows (e.g., 14-day or one-month PEW) to establish that the two-factor structure is not an artifact of the window choice rather than a true participation/decentralization distinction.
[Section 5 / Table 3 versus Section 4] There is an internal inconsistency between the paper's recommendation and its empirical setup. Table 3 recommends 'REW < PEW < study window' for the population estimation window, but Section 4 says the empirical analysis uses the entire history for population estimation, i.e., PEW equals the study window. Because the factor analysis in Figure 5 is the basis for the abstract's claim that PoW participation captures a distinct signal, the paper should either re-run the factor analysis with a PEW that satisfies its own recommendation or explicitly justify why the all-time window is appropriate for this analysis despite being discouraged for general use.
[Section 4 (Decentralization Metrics) and Appendix A.2] The exploratory factor analysis is applied to long weekly time series with strong autocorrelation and, under the all-time PEW, a cumulative #Parties series. The paper reports outlier treatment and Box-Cox transformation, but it does not address non-stationarity or autocorrelation before factor extraction. A separate factor for #Parties could reflect a trending series rather than a stable latent construct. The authors should report whether the two-factor structure survives when using detrended or differenced metric series, or when using a population window that avoids the cumulative-count property.

minor comments (5)

[Figure 5] The panel labels 'Eth r u# P oW', 'Lit coin', and 'T zos' are garbled in the provided version; they should be rendered as 'Ethereum PoW', 'Litecoin', and 'Tezos' in the final PDF.
[Section 2.3] In the definition of the τ-decentralization Index, the notation should explicitly state that the shares s_i are sorted in descending order before taking the partial sum; otherwise the formula is ambiguous.
[Table 3] The adoption rates in Table 3 are informative, but the paper should clarify how adoption was counted when a single study used multiple options for the same workflow step (e.g., multiple resource estimation windows).
[Section 6] The sentence 'we are confident in our recommendations at the consensus layer' is stronger than the evidence supports, given that the population-estimation window is identified as an open problem and the empirical analysis uses a window configuration that the recommendations discourage.
[Section 4] The empirical analysis relies on BigQuery datasets and community attribution data, but no code or data-release artifact is mentioned; providing one would substantially strengthen the reproducibility of the SoK's empirical claims.

Circularity Check

0 steps flagged · score 2.0 of 10

No derivation-level circularity: the factor-analysis claim is an empirical result on live ledger data, and the only self-citations ([46], [49]) are not load-bearing under the stated rules.

full rationale

The central claim — that in PoW blockchains the number of parties separates from the other decentralization metrics — comes from an exploratory factor analysis of seven metrics computed from on-chain block-production data (Section 4, Figure 5, and Table 6). There is no fitted parameter renamed as a prediction, no metric defined in terms of another, and no uniqueness theorem imported from the authors' prior work. The separation of # Parties from Gini, HHI, CR3, Entropy, NC, and T0.33 is an observed correlation pattern, not a construction: the paper reports, for example, that Bitcoin # Parties correlations with the other metrics range from -0.07 to 0.36 (Table 6), while the other metrics correlate strongly among themselves. The clearest self-citation is the adoption of the 7-day resource estimation window: "Prior research on estimation windows for the consensus layer suggests that short windows ... do not provide enough statistical confidence ... [46]. In contrast, windows of 7 or more days were shown to provide statistical confidence in the results. Therefore, we adopted a 7-day window" (Section 4). This is a self-citation, but [46] is a separate published empirical study on mining-power estimates; it does not, by itself, force the factor result, which is computed from live data and would stand or fall independently of that citation. The framework terminology borrowed from [49] is also non-load-bearing for the empirical claim. The all-time population window making # Parties a cumulative historical count is a measurement-validity concern, not circularity: it affects the inputs but does not reduce an equation or prediction to an input by construction. Accordingly, no circular step meets the required standard, and the score 2 reflects only the presence of minor, non-load-bearing self-citations.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on methodological choices rather than fitted constants. The most consequential choice is the all-time population window, which is used for the factor analysis and which the paper itself shows has a large effect on decentralization estimates. The statistical assumptions of EFA and the completeness of tagging are additional load-bearing premises. No new theoretical entities are introduced.

free parameters (3)

population_estimation_window = all-time (entire observation period per ledger)
Chosen for the main analysis; Figure 4 shows Gini estimates change dramatically with this choice, and the factor analysis (Figure 5) is computed only with this window, so the # Parties factor may be affected.
resource_estimation_window = 7 days
Adopted from the authors' prior work [46] rather than fitted; affects all consensus-layer metrics and could influence factor structure.
measurement_frequency = weekly consensus, monthly tokenomics
Sampling choices determine the number of data points and autocorrelation in the EFA; not varied in sensitivity analysis.

assumptions (4)

domain assumption Exploratory factor analysis on time-series data yields interpretable latent factors without accounting for autocorrelation
EFA assumes independent observations; weekly sampled blockchain metrics are autocorrelated, which can inflate factor stability.
domain assumption Tagging data from blockchain explorers provides sufficiently complete entity attribution
Clustering is essential; the paper acknowledges tagging incompleteness for legacy blocks but still uses it for the main analysis.
domain assumption The reviewed decentralization metrics are valid operationalizations of the latent construct 'decentralization'
Factor labels are assigned by the authors; no external ground truth validates that Factor 1 is decentralization.
standard math Standard statistical adequacy criteria (KMO, Kaiser criterion, Box-Cox transformations) justify the factor solutions
Used in Appendix A.2; standard but not universally decisive.

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Cite this review

Pith. "Pith review of SoK: Measuring Blockchain Decentralization." pith.science (2026). https://pith.science/paper/CNS3LOJA

@misc{pith2026250118279,
  author       = {Pith},
  title        = {Pith review of: SoK: Measuring Blockchain Decentralization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CNS3LOJA}},
  note         = {Machine review of arXiv:2501.18279}
}

read the original abstract

In the context of blockchain systems, the importance of decentralization is undermined by the lack of a widely accepted methodology to measure it. To address this gap, we set out a systematization effort targeting the decentralization measurement workflow. To facilitate our systematization, we put forth a framework that categorizes all measurement techniques used in previous work based on the resource they target, the methods they use to extract resource allocation, and the functions they apply to produce the final measurements. We complement this framework with an empirical analysis designed to evaluate whether the various pre-processing steps and metrics used in prior work capture the same underlying concept of decentralization. Our analysis brings about a number of novel insights and observations. First, the seemingly innocuous choices performed during data extraction, such as the size of estimation windows or the application of thresholds that affect the resource distribution, have important repercussions when calculating the level of decentralization. Second, exploratory factor analysis suggests that in Proof-of-Work (PoW) blockchains, participation on the consensus layer is not correlated with decentralization, but rather captures a distinct signal, unlike in Proof-of-Stake (PoS) systems, where the different metrics align under a single factor. These findings challenge the long-held assumption within the blockchain community that higher participation drives higher decentralization. Finally, we combine the results of our empirical analysis with first-principles reasoning to derive practical recommendations for researchers that set out to measure blockchain decentralization, and we further systematize the existing literature in line with these recommendations.

Figures

Figures reproduced from arXiv: 2501.18279 by the authors.

**Figure 2.** Decentralization measurement pipeline. Decentralization Metrics. Several metrics have been employed in the literature to measure blockchain decentralization on the consensus and tokenomics layers. Starting from concentration ratios [21, 64, 66, 39, 48] — or “mining power ratios” as often referred to in this literature — various metrics were gradually incorporated into the blockchain decentralization toolkit. Overal… view at source ↗

**Figure 3.** Bitcoin tokenomics HHI values with and without clustering (tagging). [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Historical Gini coefficient of Bitcoin using different population estimation [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]

**Figure 5.** Figure 5: Factor analysis results for decentralization metrics on the consensus layer. [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]

**Figure 6.** Figure 6: Factor analysis results for decentralization metrics on the tokenomics [PITH_FULL_IMAGE:figures/full_fig_p029_6.png]

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