Replication or Corroboration? An Axiomatic Framework for Evidential Dependence in Multi-Agent Debate

Hoang-Loc Cao; Truong Thanh Hung Nguyen; Phuc Truong Loc Nguyen; Vo Thanh Khang Nguyen; Phuc Ho; Hung Nguyen; Duc Pham; Long Tran-Thanh

cs.MAOct 26, 2026

Replication or Corroboration? An Axiomatic Framework for Evidential Dependence in Multi-Agent Debate

Authors: Hoang-Loc Cao, Truong Thanh Hung Nguyen, Phuc Truong Loc Nguyen, Vo Thanh Khang Nguyen, Phuc Ho, Hung Nguyen, Duc Pham, Long Tran-Thanh,

Organizations: University of New Brunswick Canada · FAU Erlangen-Nürnberg Germany · FPT Software Vietnam · Vietnamese-German University Vietnam ·

Abstract

In multi-agent debates, matching reports can arise for two different reasons: agents may repeat the same evidence (replication), or they may provide separate evidential roots that support the same claim (corroboration). A judge must distinguish these two cases. Counting report occurrences gives extra weight to relays, paraphrases, alias resubmissions, and excerpt splits, while merging all matching content avoids this only by also removing genuine corroboration. We formalize this tension as a minimal judgment game in which acquiring new evidence is costly, but replication is cheap. We show that root replication invariance (RRI) is exactly threshold-uniform replication immunity. Under RRI, replication-only deviations cannot change the verdict, and positive-cost replication is strictly dominated, whereas occurrence-sensitive and content-keyed judges admit profitable deviations. We also establish an information boundary: if a judge's observation interface cannot distinguish a replica from a matched fresh root, no judge can both ignore the replica and respond strictly to the fresh root. To preserve this distinction, we introduce the lineage quotient, which removes wording, identity, occurrence multiplicity, and arbitrary root names while keeping distinct roots separate. On orbit-connected domains, it is the coarsest representation sufficient for every deterministic judge invariant to replication and root-label renaming. We further lift this construction to quantitative bipolar argumentation frameworks (QBAFs), characterize strict fresh-root response, prove its propagation along sign-consistent paths under DF-QuAD, and derive a tight closed-form response modulus. Exhaustive audits over 28,224 direct-star profiles, 2,052 multi-layer DAGs, with matched interventions on 277 AVeriTeC-derived profiles, show the predicted separation between replication and corroboration under a supplied partition.

Figures & tables

Panel of Figure 1 — Figure 1. Method overview. (a) Replication and corroboration become indistinguishable once root labels are dropped (Thm. 5 ). (b) Only the lineage quotient $q_{L}$ ignores replicas and excerpt splits yet counts fresh roots, and it is the coarsest such key (Thms. 3 – 4 ). (c) Lifting $q_{L}$ to QBAFs preserves these guarantees for any semantics (Thm. 1 ), making replication strictly dominated while fresh roots still propagate. Color denotes evidential root.

Representation (key)	Replica	Excerpt split	Fresh root
Occurrence multiset	2	2	2
Content quotient $q_{\!C}$ $(\kappa,p,s)$	1	2	1
Content-keyed $q_{\!K}$ $(\kappa,\lambda,p,s)$	1	2	2
Lineage quotient $q_{\!L}$ $(\lambda,p,s)$	1	1	2

Table 1. Units retained by four representations under three interventions on a role already in the profile.

Panel of Figure 2 — Figure 2. Only the lineage quotient separates replicas from fresh roots. Toy debate of Ex. 8 under DF-QuAD ( $v_{0}=.5$ , $\tau=.2$ , $\theta=.5$ ), one added report per column. Cells give the topic score, colored by whether the judge meets the target (replicas neutral, fresh roots move the score in their sign). An argumentation graph with one supporter and one attacker of a claim, beside a table of topic scores for six judges under four single-report interventions: relay, excerpt, fresh attacker, and fresh supporter.

Judge	CD	RSS 8	RFR 8	FLG	MinG	FASR
Vote	.1818	.2723	.4582	.0752	.0500	1.0000
Occurrence DF-QuAD	.0000	.0677	.0932	.0298	.0013	.1922
Max-QuAD	.0448	.0000	.0000	.0000	.0000	.0000
Content quotient	.0000	.0000	.0000	.0000	.0000	.0000
Lineage quotient	.0000	.0000	.0000	.0298	.0013	.0000

Table 2. Exhaustive structural audit. Target:

\mathrm{CD}=\mathrm{RSS}_{8}=\mathrm{RFR}_{8}=\mathrm{FASR}=0

and

\mathrm{MinG}>0

. Bold marks joint satisfaction.

Judge	CD	RSS 8	RFR 8	FLG	MinG	FASR
Vote	.0187	.0572	.0703	.0219	.0000	1.0000
Occurrence DF-QuAD	.0000	.0114	.0689	.0088	$1.1\!\times\!10^{-8}$	.9800
Max-QuAD	.0278	.0000	.0000	.0000	.0000	.0000
Content quotient	.0003	.0000	.0000	.0000	.0000	.0000
URL quotient	.0002	.0000	.0000	.0000	.0000	.0000
Lineage quotient	.0000	.0000	.0000	.0088	$1.1\!\times\!10^{-8}$	.0000

Table 3. Matched audit on 277 AVeriTeC-derived profiles. Same target as Table 2 .

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Judge	CD	RSS 8	RFR 8	FLG	MinG	FASR	$n_{F}$
Vote	.01867 [.01408,.02373]	.05724 [.04294,.07196]	.07032 [.05292,.08873]	.02194 [.01648,.02766]	.00000	1.000 [1.000,1.000]	50
Occurrence DF-QuAD	.00000 [.00000,.00000]	.01137 [.00894,.01399]	.06892 [.05114,.08733]	.00880 [.00710,.01069]	$1.13\!\times\!10^{-8}$	.980 [.933,1.000]	50
Max-QuAD	.02785 [.02546,.03035]	.00000 [.00000,.00000]	.00000 [.00000,.00000]	.00000 [.00000,.00000]	.00000	.000 [.000,.000]	61
Content quotient	.00028 [.00000,.00075]	.00000 [.00000,.00000]	.00000 [.00000,.00000]	.00000 [.00000,.00000]	.00000	.000 [.000,.000]	50
URL quotient	.00020 [.00000,.00060]	.00000 [.00000,.00000]	.00000 [.00000,.00000]	.00000 [.00000,.00000]	.00000	.000 [.000,.000]	50
Lineage quotient	.00000 [.00000,.00000]	.00000 [.00000,.00000]	.00000 [.00000,.00000]	.00880 [.00710,.01066]	$1.13\!\times\!10^{-8}$	.000 [.000,.000]	50

Appendix

Table 4. AVeriTeC audit with claim-clustered 95% bootstrap intervals. MinG is the observed finite-position minimum, and

n_{F}

is the judge-specific FASR denominator.

Statistic	Value	Statistic	Value
Claims	277	Supported / Refuted	127 / 150
Reports	711	Support / attack	152 / 559
Reports per claim	2.57	Mixed-sign claims	47
Content-Q changed	3	URL-Q changed	2
Fresh positions	711	FASR-eligible claims	47

Appendix

Table 5. AVeriTeC profile statistics after the stated filters.

Condition	Claims	Pos.	FLG [95% CI]	MinG
NLI thr. .50	277	737	.00833 [.00670,.01018]	$1.13{\times}10^{-8}$
NLI thr. .60	277	711	.00880 [.00710,.01066]	$1.13{\times}10^{-8}$
NLI thr. .70	237	601	.00655 [.00510,.00819]	$1.36{\times}10^{-8}$
Fixed str. .50	277	711	.05132 [.04746,.05526]	.001953

Appendix

Table 6. Sensitivity of the AVeriTeC lineage-quotient audit. FLG is reported with a claim-clustered 95% bootstrap interval.

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Multi-Agent Debate studies how language-model agents exchange arguments, critique answers, and combine judgments for collective reasoning.

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Epistemic Sybil Resistance: Multiplying AI Agents Without Multiplying Evidence

Marc Bara

Universitat Oberta de Catalunya (UOC), Barcelona, Spain

AI Agent Reliability Multi-Agent LLM Systems Multi-Agent Reasoning

Open paper AskPDF arXiv

Multi-agent AI systems improve inference by spawning agents and synthesizing reports. But another agent is not another observation: apparently independent reports may descend from the same evidence, and genuinely independent evidence can produce nearly identical reports. We formalize this as an epistemic Sybil problem. A report Z is an epistemic Sybil extension relative to reports R when I(Theta; Z | R) = 0. No report-only aggregator can generally distinguish replication from independent corroboration: identical reports can warrant different posteriors under unobserved ancestry. A Gaussian shared-root model shows common ancestry does not imply complete redundancy. Repeated extraction adds information toward a source-level ceiling, and correlated extraction errors, which a shared base model can induce among independent agents, lower that ceiling further. We test these predictions with more than 20,000 controlled LLM-agent report and extraction calls on synthetic evidentiary documents. Holding one evidence root fixed while report multiplicity rises from 1 to 32 collapses naive posterior coverage from 0.940 to 0.263. Holding report count fixed while evidence-root multiplicity rises from 1 to 16 closes the gap, and the aggregators are statistically indistinguishable at k = 16. The agent's replicate extraction errors are correlated (gamma_cal = 0.719, estimated out of sample), and a correlated-extraction aggregator restores calibration accordingly. A controlled manipulation isolates representation similarity from evidential ancestry. It changes a report-space deduplication mechanism's mean inferred cluster count by 1.425 (95% CI [1.363, 1.485]), whereas a fourfold change in true ancestry changes it by only 0.040 ([-0.045, 0.120]). Collective inference should therefore track evidential ancestry and dependence, not agent or report multiplicity or similarity.

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