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REVIEW 3 major objections 5 minor 17 references

Balancing incentives in committee-based blockchains

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper proves that in committee-based blockchains the costs of vote omission and vote delay attacks are reciprocal, making reward design a balancing problem.

desk verdict Useful framework, clean inverse-cost theorem under a cause-blind reward model; real penalties break the symmetry, so the systems conclusions need revision. read the letter →

arxiv 2505.24482 v1 pith:FIWYPVH7 submitted 2025-05-30 cs.GT cs.DC

Arian Baloochestani , Leander Jehl This is my paper
classification cs.GTcs.DC MSC 91A1091A8068M14
keywords committee-basedblockchainsdenialofprofitattacksvoteomissionattackdelaycostandeffectivenessrewardmechanismbalancingEthereumvalidatorrewardsCosmos
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

Vote collection in committee-based blockchains is a collaboration between a leader who includes signatures and validators who supply them, and each party can unilaterally deny the other's profit: the leader can omit a validator's signature, and a validator can delay its own signature when that player leads. This paper proves that for any reward function that depends only on whether a signature is included, the cost of the omission attack and the cost of the delay attack are exact reciprocals, so a designer cannot make both attacks expensive at once and must instead balance them. It introduces two metrics, effectiveness (victim loss normalized by attacker power) and cost (attacker loss relative to the worst victim loss), and shows how common protections—bonus thresholds, scaling rewards, inclusion windows, base rewards, aggregation—shift that balance. Applied to real systems, the framework finds that Cosmos parameters make vote omission profitable for attackers with more than about 14% of stake, while Ethereum is better balanced but still lets a 15% attacker cost a victim up to 3% of its reward. The practical point is that reward tuning is a balancing problem, with concrete parameter targets such as a Cosmos proposer bonus near 0.141 and an Ethereum bonus near 0.183.

What carries the argument

The machinery is the vote collection normal-form game, where a player's utility is an expected reward $R(\delta_l, \delta_i, P[i], \Sigma P)$ depending on whether the player is leader, whether the player's signature is included, the player's power, and the total included power. The load-bearing identity is Lemma 5, $U(p_r, S^l_{j\to i}) = U(p_r, S^v_{i\to j})$, which turns a missing signature into a single economic event and yields the reciprocal cost relation of Theorem 6 and the effectiveness relation of Theorem 8. The paper also models practical protection mechanisms as modifications of $R$: bonus threshold, scaling rewards, inclusion window, base reward, and aggregation, and catalogs how each one changes cost and effectiveness rather than the attacker's ability to attack.

What would settle it

Compute $\operatorname{cost}(S^l_{j\to i})$ and $\operatorname{cost}(S^v_{i\to j})$ from the paper's definitions for any reward function of the stated form and find one parameter set where their product is not 1; alternatively, an empirical study of Cosmos blocks showing that an attacker with more than 14% of stake does not increase its reward by omitting a victim's vote would refute the claimed Cosmos calibration.

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Extended reading notes

Core claim

The central claim is Theorem 6: in the vote collection game with the stated reward function $R(\delta_l, \delta_i, P[i], \Sigma P)$, the attack costs satisfy $\operatorname{cost}(S^l_{j\to i}) = 1 / \operatorname{cost}(S^v_{i\to j})$. The argument rests on Lemma 5, which shows that every player's utility is identical whether the leader $p_j$ omitted $p_i$'s signature or the validator $p_i$ delayed its own signature under leader $p_j$; the two attacks are the same missing-signature event seen from opposite sides. As a consequence, disincentivizing one denial-of-profit attack automatically makes the other cheaper or more damaging, and the best a designer can do is to balance the attack costs at 1. The paper uses the framework to quantify concrete systems and proposes alternative parameters, $b^* \approx 0.141$ for Cosmos and $b^* \approx 0.183$ for Ethereum, that bring the attack costs closer to balanced.

Load-bearing premise

The load-bearing assumption is that a missing signature looks identical to the reward function whether the leader omitted it or the validator delayed it, so protocols that punish the two causes differently can escape the inverse-cost relation.

Editorial extensions

If this is right

  • A protocol designer using a reward function of the stated form cannot make both vote omission and vote delay expensive; the attainable goal is balanced cost 1, where the attacker loses the same amount as the most harmed victim.
  • Under the analyzed Cosmos parameters ($a=0.9$, $t=2/3$, $b=0.05$), vote omission is profitable for attackers with more than roughly 14% of the stake, meaning honest behavior is not a Nash equilibrium; raising the proposer bonus to $b^*\approx 0.141$ restores equilibrium.
  • In Ethereum's current reward scheme, an attacker with 15% of the stake can deny any victim up to 3% of its total reward; raising the proposer bonus to $b^*\approx 0.183$ keeps both attack costs inside $[0.8, 1.2]$ for almost all attacker and victim powers.
  • Mechanisms that change the reward function itself—bonus threshold, scaling rewards, inclusion window, base reward—are all subject to the inverse-cost trade-off, whereas aggregation reduces vote omission effectiveness without making vote delay cheaper, because it changes the attacker's ability rather than the reward for a missing signature.

Reading between the lines

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

  • My inference: the inverse-cost theorem extends to any reward scheme where the only observable is whether the signature is present; protocols that add an observable cause—for example slashing a leader who omits differently from a validator who delays—can break the symmetry and escape the trade-off.
  • My inference: the framework implies a practical on-chain audit: measure, per validator, the lost reward when its votes are missing and the lost reward of leaders whose votes it withholds, and compare the ratio to 1; ratios far from 1 identify which direction of denial-of-profit attack the protocol secretly favors.
  • My inference: the paper's aggregation result suggests a general design principle—inserting an additional role between proposer and voters, such as aggregators or relayers, can weaken or break the two-party balance constraint that Theorem 6 imposes on direct leader-validator reward functions.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes a game-theoretic framework for denial-of-profit attacks in committee-based blockchains. It defines effectiveness and cost metrics, models vote collection as a normal-form game with a reward function R(δ_l, δ_i, P[i], ΣP) that depends only on whether a player's signature is included and on the total included power, and proves that the costs of vote omission and vote delay attacks are inverse (Theorem 6) and that their effectiveness values are related (Theorem 8). It then catalogues protection mechanisms, applies the framework to Cosmos and Ethereum, reports that the current Cosmos parameters make vote omission profitable, and proposes alternative bonus parameters b* for both systems.

Significance. The formal core is clean and the inverse-cost statement is a useful design principle for the restricted class of cause-blind reward functions considered. The paper gives transparent formulas, checks its claims in figures and tables, and presents concrete parameter recommendations (b*≈0.141 for Cosmos, b*≈0.183 for Ethereum) that a reader can reproduce. The main value is the framework and the structural warning that balancing the two attacks is constrained by the reward model; this justifies publication if the applicability gaps identified below are addressed.

major comments (3)
  1. [§4 / Theorem 6 and §5] Theorem 6's inverse-cost relation is derived for the Section 4 utility function R(δ_l, δ_i, P[i], ΣP), which depends only on whether the target's signature is included and not on who caused its absence. Real systems analyzed in Section 5 include cause-dependent penalties: Ethereum's inactivity leak penalizes validators who fail to attest, and Cosmos jails validators for missing votes, while proposers who omit submitted attestations are not penalized in the same way. Once utility includes such a term, the equality U(p_r, S^l_{j→i}) = U(p_r, S^v_{i→j}) in Lemma 5 can fail, and the conclusion that the two attacks 'have to be balanced' is no longer forced. The paper should either extend the model to cause-dependent penalties and re-derive the relevant conditions, or explicitly restrict Theorem 6's scope and soften the corresponding claims in the abstract and Section 4.1.
  2. [§5.2.2 vs §5.2.3.1] Section 5.2.2 states and Figure 5 uses b = 1/8 for Ethereum, whereas Section 5.2.3.1 says 'The current value of b = 0.05 is therefore not balanced' and Corollary 11 builds on b*≈0.183. I cannot reproduce the stated cost range [0.2,1.8] from either parameter choice using Eqs. (15)-(17). The authors must decide on the actual current Ethereum proposer bonus, correct the figure and text, and recompute the minimal b* and cost ranges, since the parameter recommendation depends on this value.
  3. [§5.2.1 / Eqs. (14)-(17)] The Ethereum effectiveness formula (14) multiplies by the aggregator probability p_agg(i), while the cost formula (15) does not, although both are derived from the same attack profile. This is consistent only if cost is interpreted as the ratio of expected losses over the random aggregator selection, an extension of Definitions 1-2 that is not stated. Since Theorem 6 is proved for deterministic normal-form profiles, the paper should formally define the game with random aggregator and inclusion-window mechanisms and state which theorems survive, or clarify that Eqs. (14)-(17) are an approximate application of the framework. As written, the applicability of the central balance theorem to Ethereum is incompletely specified.
minor comments (5)
  1. [§4.1 / Lemma 5] The proof of Lemma 5 is only sketched ('It can be proven by considering Equation (4) and (5) and setting up similar equations...'); since Theorems 6 and 8 rest on this lemma, a full derivation of the utility equality for all p_r would make the paper easier to verify.
  2. [§4.1] The statement that the targeted victim has the maximum loss for all reward functions considered is asserted without proof; because the subsequent formulas drop the max operator, a short justification or an explicit assumption should be added.
  3. [Throughout] There are several wording and typographical issues: 'disrespect of wether' in the Lemma 5 proof should be 'regardless of whether', 'loose' should be 'lose' in Section 3.2, and 'efficiency' should be 'effectiveness' in the bonus-threshold paragraph of Section 4.2.
  4. [§5.1.3 and §5.2.3.1] Corollaries 10 and 11 are numerical results rather than corollaries of the preceding theorems; renaming them 'Numerical result' and specifying the numerical method or grid search used would avoid confusion.
  5. [Figure 5] The top-left panel of Figure 5 has no legend, and the text does not identify which curve corresponds to vote-omission cost; adding a legend or a clear description would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Theorem 6 is an algebraic consequence of an explicit cause-blind reward model, not a restatement of its input.

full rationale

The paper's derivation chain is theorem-from-model. Definitions 1 and 2 define effectiveness and cost from utility differences (Eqs. 1-2). Section 4 defines the vote collection game with utility function R(δ_l, δ_i, P[i], ΣP) (Eqs. 3-5). The reward function is cause-blind by explicit modeling declaration, not because the theorem requires it: Lemma 5 then derives equality of utilities by checking that the two attack profiles produce the same (δ_l, δ_i, ΣP) outcomes. Theorem 6 is a direct algebraic consequence of Lemma 5 and the definitions of cost. Nothing in Lemma 5 or Theorem 6 is used to define the reward function or the attack profiles, and no parameter is fitted to the conclusion. The applications to Cosmos and Ethereum translate protocol specifications into explicit reward functions (Eqs. 10 and 13) and compute metrics from those formulas; Corollaries 10 and 11 are numerical consequences, not inverse-engineered to match Theorem 6. The self-citations to prior work (e.g., Rebop, Iniva, Eiffel) appear in related-work discussion and as additional support for the known non-Nash result in Cosmos, but the paper also independently derives negative cost for vote omission under the Cosmos parameters. There is no uniqueness theorem imported from the authors, no ansatz concealed behind a citation, and no renaming of a known result as a new derivation. The only caveat is the cause-blindness of R, which is a modeling assumption and an applicability limitation for real systems with cause-dependent penalties such as slashing or jailing; that is not circularity in the paper's own derivation.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The analysis is a mathematical model of two real protocols. It introduces no new entities. It relies on protocol parameters (b, a, t, ρ, k) taken from the cited systems and on stated simplifying assumptions (proportional leader election, 1/3 stake cap, votes always included within the window, negligible probability of controlling all aggregators or consecutive proposers, constant transaction fees). The proposed b* values are obtained by numerical search over these parameters.

free parameters (6)
  • Proposer bonus fraction b (Cosmos) = current 0.05, proposed b*≈0.141
    Parameter in the reward function that trades off cost of vote omission vs vote delay; b* chosen numerically to make both attacks unprofitable.
  • Proposer bonus fraction b (Ethereum) = current 1/8 (text also says 0.05, inconsistent), proposed b*≈0.183
    Same role; b* chosen numerically to keep both attack costs in [0.8,1.2] for a given range.
  • Base reward fraction a (Cosmos) = 0.9
    Fraction of reward paid unconditionally; based on claim that transaction fees are ~10% of validator reward.
  • Bonus threshold t (Cosmos) = 2/3
    Protocol parameter, leader must collect 2/3 signatures for bonus.
  • Inclusion window reduction ρ (Ethereum) = 0.781
    Protocol parameter, fraction of reward received for late inclusion.
  • Number of aggregators k (Ethereum) = 16 on average
    Protocol parameter; paper explores k=8 as alternative.
assumptions (6)
  • domain assumption A designated Nash equilibrium strategy profile se exists and utilities in se are proportional to power.
    Section 3.1: 'We assume that a designated nash-equilibrium strategy profile for G exists... We assume that in se the utilities of players are relative to their power.'
  • domain assumption Leader election probability is proportional to power: P_l(p_i)=P[i].
    Section 4: 'we assume that the chance for a player to be elected as leader is proportional to its power.'
  • domain assumption No player controls more than 1/3 of total stake.
    Section 4: 'We assume that no player controls more than 1/3 of the total stake in the system.'
  • domain assumption Every omitted or delayed vote is included in a later block within the inclusion window (for Ethereum analysis).
    Section 4.2, Eq (9): 'If we assume that w is large enough, such that a delayed or omitted vote always is included in a later block...' and Section 5.2.1: 'Since we assume all votes are included within the window, this term is not scaled.'
  • domain assumption Probability that an attacker controls all aggregators is negligible, and probability of controlling w+1 consecutive proposers is negligible (for Ethereum).
    Section 5.2: 'The probability that all k aggregators are controlled by p_i is negligible (P[i])^k ≈ 0... We ignore the chance that p_i controls w+1 consecutive proposers.'
  • domain assumption Transaction fees are constant (for Cosmos analysis).
    Section 5.1: 'To simplify the analysis, we assume that transaction fees are constant.'

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Cite this review

Pith. "Pith review of Balancing incentives in committee-based blockchains." pith.science (2026). https://pith.science/paper/FIWYPVH7

@misc{pith2026250524482,
  author       = {Pith},
  title        = {Pith review of: Balancing incentives in committee-based blockchains},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FIWYPVH7}},
  note         = {Machine review of arXiv:2505.24482}
}
read the original abstract

Blockchain protocols incentivize participation through monetary rewards, assuming rational actors behave honestly to maximize their gains. However, attackers may attempt to harm others even at personal cost. These denial of profit attacks aim to reduce the rewards of honest participants, potentially forcing them out of the system. While existing work has largely focused on the profitability of attacks, they often neglect the potential harm inflicted on the victim, which can be significant even when the attacker gains little or nothing. This paper introduces a framework to quantify denial of profit attacks by measuring both attacker cost and victim loss. We model these attacks as a game and introduce relevant metrics to quantify these attacks. We then focus on committee-based blockchains and model vote collection as a game. We show that in the vote collection game, disincentivizing one denial of profit attack will make another attack more appealing, and therefore, attacks have to be balanced. We apply our framework to analyze real-world reward mechanisms in Ethereum and Cosmos. Our framework reveals imbalances in Cosmos that can make correct behavior suboptimal in practice. While Ethereum provides stronger protections, our framework shows that it is also not complete, and we propose alternative parameter settings to improve the balance between attacks. Our findings highlight the need for better-balanced reward designs to defend against denial of profit attacks.

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Reference graph

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