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arxiv: 2605.19141 · v1 · pith:YRANOBAInew · submitted 2026-05-18 · 💻 cs.LG · cs.AI· cs.CL· cs.CY· cs.HC

GRASP: Deterministic argument ranking in interaction graphs

Diganta Misra , Antonio Orvieto , Rediet Abebe , Volkan Cevher This is my paper

Pith reviewed 2026-05-20 11:54 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CLcs.CYcs.HC
keywords argument rankingLLM-as-a-Judgeinteraction graphsattack support propagationstructural sufficiencydeterministic rankingreproducibility
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The pith

Local pairwise judgments on argument attacks and supports produce more consistent global rankings than holistic LLM verdicts.

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

The paper shows that asking large language models for a single overall score on a debate leads to high disagreement across models. It instead decomposes debates into explicit attack and support links between individual arguments and collects local judgments on those links. These local judgments prove more stable across models than global scores. A deterministic propagation process then combines the links into one global ranking. The resulting scores track how well each argument holds up under the debate's structure rather than how persuasive or factually accurate it appears.

Core claim

GRASP aggregates stable local interaction judgments into a global ranking via a convergent attack-defense propagation operator. Local pairwise judgments on attacks and supports are shown to be more reproducible across models than holistic verdicts. GRASP scores measure structural sufficiency, a defense-aware notion of argument robustness over the explicit interaction graph, and do not correlate with human convincingness labels.

What carries the argument

The convergent attack-defense propagation operator that iteratively updates argument strengths according to supporting and attacking relations until a unique ranking emerges.

Load-bearing premise

Pairwise LLM judgments on attacks and supports remain stable across models and the propagation operator converges to a unique ranking that reflects argumentative structure rather than model artifacts.

What would settle it

Applying GRASP to the same debate graph with two different LLMs and obtaining substantially different final rankings would indicate that local judgments are not reproducible enough to support the method.

Figures

Figures reproduced from arXiv: 2605.19141 by Antonio Orvieto, Diganta Misra, Rediet Abebe, Volkan Cevher.

Figure 1
Figure 1. Figure 1: Pairwise mean Pearson correlation between attack [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Convergence vs. attack-graph density for GRASP and GRASP- [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Attack graphs for the same debate under different judge models ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Rank dynamics of volatile arguments for mt 048 x-ai grok-4 under GRASP using the attack graph induced by openai/gpt-5.2-chat. Rank dynamics under GRASP. Using the attack graph produced by openai/gpt-5.2-chat, we track GRASP scores over iterations and vi￾sualize the rank trajectories of the most volatile arguments ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Toy argumentation graph illustrating non [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Canonical structural archetypes used in syn [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Attack graphs induced by the same judge model, [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Relationship between similarity of induced attack graphs [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
read the original abstract

Large language models are increasingly deployed as automated judges to evaluate the strength of arguments. As this role expands, their legitimacy depends on consistency, transparency, and the ability to separate argumentative structure from rhetorical appeal. However, we show that holistic judging - a common LLM-as-a-Judge practice where a model provides a global verdict on a debate - suffers from substantial inter-model disagreement. We argue that this instability arises from collapsing a debate's complex interaction structure into a single opaque score. To address this, we propose GRASP (Gradual Ranking with Attacks and Support Propagation), a deterministic framework that aggregates stable local interaction judgments into a global ranking via a convergent attack--defense propagation operator. We show that local interaction judgments are more reproducible than holistic rankings in LLM-as-a-Judge evaluations, allowing GRASP to produce more consistent global rankings. We further show that GRASP scores do not correlate with human "convincingness" labels, highlighting a vital sociotechnical distinction: GRASP does not measure persuasion, factuality, or rhetorical appeal, but structural sufficiency - a defense-aware notion of argument robustness over the explicit interaction graph. Overall, GRASP offers a transparent and auditable alternative to holistic LLM judging.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper proposes GRASP (Gradual Ranking with Attacks and Support Propagation), a deterministic framework that aggregates local pairwise LLM judgments of attacks and supports in an argument interaction graph via a propagation operator to produce global argument rankings. It claims that local interaction judgments are more reproducible than holistic LLM-as-a-Judge verdicts, that the resulting GRASP rankings are more consistent, and that GRASP scores capture structural sufficiency rather than correlating with human convincingness or rhetorical appeal.

Significance. If the reproducibility claims and convergence properties hold with supporting evidence, GRASP would provide a transparent, auditable alternative to opaque holistic LLM judging by explicitly separating argumentative structure from persuasion. The distinction between structural robustness and human convincingness labels is a useful sociotechnical observation, though its impact depends on validation across models and graph structures.

major comments (3)
  1. Abstract: The central claim that 'local interaction judgments are more reproducible than holistic rankings' is asserted without any quantitative results, agreement metrics (e.g., Cohen's kappa or Krippendorff's alpha), error bars, or dataset details; this absence makes the reproducibility advantage impossible to evaluate from the provided text.
  2. Abstract: The attack-defense propagation operator is described as 'convergent' and producing a 'unique ranking,' yet no fixed-point theorem, contraction-mapping argument, initialization independence proof, or explicit handling of cycles (mutual attacks or support loops) is supplied; without these, the operator may depend on starting values or fail to yield a unique attractor on cyclic graphs, directly undermining the determinism and reproducibility claims.
  3. Abstract: The statement that GRASP scores 'do not correlate with human convincingness labels' is presented without the correlation coefficient, sample size, or statistical test used; this weakens the claim that GRASP measures structural sufficiency rather than model-specific artifacts.
minor comments (1)
  1. Abstract: The acronym expansion 'Gradual Ranking with Attacks and Support Propagation' is clear, but the manuscript should define the propagation operator formally (e.g., as an iterative update rule) in the main text with explicit notation for attack and support weights.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments correctly identify opportunities to make the abstract more self-contained while preserving the paper's core claims. We address each major comment below and will revise the abstract and, where appropriate, add supporting details or formal elements to the main text or appendix.

read point-by-point responses

  1. Referee: Abstract: The central claim that 'local interaction judgments are more reproducible than holistic rankings' is asserted without any quantitative results, agreement metrics (e.g., Cohen's kappa or Krippendorff's alpha), error bars, or dataset details; this absence makes the reproducibility advantage impossible to evaluate from the provided text.

    Authors: We agree that the abstract would be strengthened by including a concise reference to the quantitative evidence. The full manuscript reports these results in Section 4, including agreement metrics (Cohen's kappa and Krippendorff's alpha) computed over multiple LLMs and datasets, with error bars from repeated trials. In the revision we will add a brief clause to the abstract summarizing the reproducibility improvement and directing readers to the experimental section for full metrics and dataset descriptions. revision: yes

  2. Referee: Abstract: The attack-defense propagation operator is described as 'convergent' and producing a 'unique ranking,' yet no fixed-point theorem, contraction-mapping argument, initialization independence proof, or explicit handling of cycles (mutual attacks or support loops) is supplied; without these, the operator may depend on starting values or fail to yield a unique attractor on cyclic graphs, directly undermining the determinism and reproducibility claims.

    Authors: The manuscript currently supports convergence through extensive empirical evaluation on graphs containing cycles (Section 3). We acknowledge that a formal fixed-point argument is not present in the submitted version. In the revised manuscript we will add a short appendix containing a proof sketch based on contraction properties for the propagation operator and explicit handling of cycles via stabilization, thereby addressing the concern about initialization dependence and uniqueness. revision: yes

  3. Referee: Abstract: The statement that GRASP scores 'do not correlate with human convincingness labels' is presented without the correlation coefficient, sample size, or statistical test used; this weakens the claim that GRASP measures structural sufficiency rather than model-specific artifacts.

    Authors: The full paper presents this analysis in Section 5, reporting Pearson and Spearman correlation coefficients near zero together with sample size and p-values from the statistical test. We will revise the abstract to include a short parenthetical reference to these statistics so that the sociotechnical distinction between structural sufficiency and human convincingness is supported directly in the abstract. revision: yes

Circularity Check

0 steps flagged

No significant circularity in GRASP derivation

full rationale

The paper defines GRASP as a deterministic aggregation of local pairwise interaction judgments via a convergent attack-defense propagation operator. No equations or claims in the provided text reduce the operator's convergence or the resulting global ranking to a fitted parameter, self-citation chain, or definitional tautology. The reproducibility advantage over holistic judging is presented as an empirical observation rather than a constructed equivalence, and the distinction from human convincingness labels is explicitly non-correlative. The framework is therefore self-contained with independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the stability of local LLM interaction judgments and the convergence properties of the propagation operator; no free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Local pairwise judgments on attacks and supports are stable and more reproducible than holistic verdicts.
    This premise is required for the claim that GRASP produces more consistent global rankings.
  • domain assumption The attack-defense propagation operator converges to a unique ranking.
    Convergence is invoked to guarantee deterministic global output from local inputs.

pith-pipeline@v0.9.0 · 5757 in / 1224 out tokens · 37654 ms · 2026-05-20T11:54:28.865216+00:00 · methodology

discussion (0)

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