Beyond Final Outcomes: Quantifying Claim-Level Information Dynamics in Multi-Agent LLM Interaction
Organizations: Xi’an Jiaotong University
Abstract
When LLM-powered agents interact, information is repeatedly shared, expanded, and forgotten, yet multi-agent evaluation typically focuses on final task outcomes. We study such interaction as claim-level information dynamics and propose RIVER, which decomposes agent outputs into atomic claims and evaluates three complementary dimensions: convergence, exploration, and retention. Convergence captures cross-agent claim correspondence and stance alignment; exploration captures semantic breadth and extension beyond the source; and retention tracks source preservation and the persistence of new claims across stages and lineages. We evaluate five interaction strategies on 40 controlled news-generation cases. Repeatedly pooled interaction promotes convergence but narrows the information space, whereas distributed relay yields broader, less shared information. Further comparisons show that method-specific constraints increase exploration while weakening convergence and retention. Our findings suggest that collective information dynamics are better explained by underlying information-flow mechanisms than by simple downstream performance.
Figures & tables
| Dataset | Pearson | Spearman | |
|---|---|---|---|
| DBS-eval | 10 | 0.641 | 0.638 |
| DELPHISTAR | 33 | 0.729 | 0.689 |
| Polis | 16 | 0.994 | 0.840 |
| Model | Unity | Simple | |
|---|---|---|---|
| Gemini 2.5 Flash Lite | 0.641 | -0.110 | +0.751 |
| Gemini 2.5 Flash | 0.588 | -0.031 | +0.619 |
| Gemini 3.8 Flash | 0.678 | 0.620 | +0.058 |
| Evaluator pair | Pearson | Spearman |
|---|---|---|
| 2.5 Flash Lite / 2.5 Flash | 0.971 | 0.939 |
| 3.8 Flash / 2.5 Flash Lite | 0.765 | 0.770 |
| 3.8 Flash / 2.5 Flash | 0.807 | 0.842 |
| Strategies | Setting | Convergence | Exploration | Retention | |||
|---|---|---|---|---|---|---|---|
| U | CC | ER | OR | SR | SL | ||
| Free | Control | 0.371 | 13.46 | 0.892 | 0.713 | 0.680 | 1.521 |
| NGT | Full | 0.323 | 13.24 | 0.943 | 0.513 | 0.643 | 1.391 |
| Framework | 0.518 +60.6% | 10.41 -21.4% | 0.889 -5.7% | 0.766 +49.3% | 0.721 +12.1% | 1.616 +16.2% | |
| Delphi | Full | 0.275 | 14.92 | 0.920 | 0.630 | 0.635 | 1.419 |
| Framework | 0.497 +80.4% | 10.88 -27.1% | 0.887 -3.6% | 0.750 +19.0% | 0.703 +10.8% | 1.544 +8.8% | |
Appendix figures & tables11 assets
Supplementary material from the paper’s appendix.
Appendix
| Cycle | Stages | Discussion focus |
|---|---|---|
| 1 | 1–4 | Possible causes and problem framing |
| 2 | 5–8 | Direct and indirect consequences |
| 3 | 9–12 | Stakeholder reactions and risks |
| 4 | 13–16 | Responses or policy options |
| Agent ID | Name | Role | Persona | Qualification |
|---|---|---|---|---|
| 0 | James | Commentator | analytical, outspoken, cooperative | Bachelor’s Degree |
| 1 | Mary | Verifier | precise, skeptical, patient | Master’s Degree |
| 2 | Robert | Spreader | gregarious, quick, optimistic | High School Diploma |
| 3 | Patricia | Bystander | reserved, empathetic, cautious | Associate Degree |
| 4 | John | Commentator | independent, insightful, stubborn | PhD |
| Strategy | Core interaction structure | Additional constraints in Full |
|---|---|---|
| Free | Open discussion without a prescribed interaction procedure | None |
| NGT | Independent generation; anonymous sharing; clarification; private synthesis | Equal extension sharing; protection of low-frequency views |
| Delphi | Anonymous feedback; private multi-round revision | Coverage; minority views; pro/con reasons; and uncertainty requirements |
| Policy Delphi | Anonymous presentation of stances and reasons; responses; private disagreement summary | Pro/con; alternatives; strongest opposing views; and self-criticism |
| Brainwriting | Anonymous relay; distributed lineage; private lineage review | Risk; counterfactual; consequence; and causal-chain elaboration |
| Setting | Local Stage 1 | Local Stage 2 | Local Stage 3 | Local Stage 4 |
|---|---|---|---|---|
| Free | Start independently. | Interact freely. | Interact freely. | Choose any useful action; consensus is optional. |
| NGT Full | Work silently and independently. | Read the balanced idea bank; restate and clarify before judging. | Clarify, support, challenge, revise, or combine shared claims. | Privately synthesize retained, rejected, and uncertain claims. |
| NGT Framework | Work silently and independently. Only this Stage permits new extension claims. | Read the complete, balanced Stage-1 idea bank. Restate, compare, support, challenge, or clarify existing ideas without adding new claims. | Discuss the Stage-1 idea bank and preceding sharing outputs. Select, support, challenge, clarify, revise wording, or combine existing claims without introducing new propositions. | Privately synthesize only Stage-1 claims. Retain, reject, or express uncertainty without adding new propositions. Other Stage-4 outputs are hidden. |
| Delphi Full | Answer privately and independently. | Use anonymous controlled feedback without treating frequency as truth. | Revise privately. | Use second feedback for a final private revision. |
| Delphi Framework | Generate independently. | Review the anonymous compilation and respond freely. | Privately reconsider it. | Use the second compilation for final revision. |
| Policy Delphi Full | Generate positions, pro/con reasons, alternatives, and uncertainty. | Use the anonymous pro-con matrix and preserve minority positions. | Develop counterarguments and alternatives. | Map accepted, rejected, uncertain, and disputed claims. |
| Strategy | Setting | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| Free | Control | 0.269 | 0.308 | 0.385 | 0.456 | 0.256 | 0.345 | 0.418 | 0.488 |
| NGT | Full | 0.329 | 0.230 | 0.300 | 0.412 | 0.263 | 0.238 | 0.337 | 0.456 |
| NGT | Framework | 0.417 | 0.458 | 0.535 | 0.606 | 0.387 | 0.504 | 0.631 | 0.670 |
| Delphi | Full | 0.352 | 0.273 | 0.309 | 0.311 | 0.291 | 0.312 | 0.330 | 0.303 |
| Delphi | Framework | 0.443 | 0.485 | 0.490 | 0.574 | 0.419 | 0.588 | 0.599 | 0.651 |
| Policy Delphi | Full | 0.271 | 0.118 | 0.269 | 0.387 | 0.258 | 0.095 | 0.259 | 0.418 |
| Strategy | Setting | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| Free | Control | 13.65 | 14.38 | 12.32 | 11.05 | 15.43 | 14.55 | 12.40 | 11.32 |
| NGT | Full | 12.00 | 13.75 | 12.95 | 11.10 | 15.05 | 14.93 | 12.78 | 10.40 |
| NGT | Framework | 10.97 | 11.05 | 10.28 | 8.88 | 12.43 | 10.95 | 8.62 | 7.62 |
| Delphi | Full | 11.55 | 14.70 | 13.43 | 13.78 | 14.65 | 14.88 | 14.15 | 14.38 |
| Delphi | Framework | 10.65 | 10.93 | 10.35 | 9.03 | 12.72 | 9.78 | 9.32 | 8.18 |
| Policy Delphi | Full | 18.38 | 17.48 | 14.95 | 11.93 | 17.95 | 19.10 | 15.78 | 12.20 |
| Strategy | Setting | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| Free | Control | 0.799 | 0.855 | 0.871 | 0.880 | 0.855 | 0.875 | 0.896 | 0.889 |
| NGT | Full | 0.766 | 0.969 | 0.955 | 0.956 | 0.841 | 0.988 | 0.978 | 0.964 |
| NGT | Framework | 0.805 | 0.845 | 0.860 | 0.841 | 0.868 | 0.884 | 0.894 | 0.896 |
| Delphi | Full | 0.781 | 0.919 | 0.914 | 0.930 | 0.857 | 0.915 | 0.919 | 0.930 |
| Delphi | Framework | 0.760 | 0.826 | 0.836 | 0.863 | 0.836 | 0.887 | 0.886 | 0.878 |
| Policy Delphi | Full | 0.870 | 0.950 | 0.950 | 0.941 | 0.874 | 0.962 | 0.959 | 0.954 |
| Strategy | Setting | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| Free | Control | 0.815 | 0.794 | 0.767 | 0.760 | 0.789 | 0.759 | 0.731 | 0.723 |
| NGT | Full | 0.841 | 0.432 | 0.557 | 0.575 | 0.804 | 0.366 | 0.451 | 0.448 |
| NGT | Framework | 0.823 | 0.817 | 0.818 | 0.809 | 0.783 | 0.770 | 0.779 | 0.777 |
| Delphi | Full | 0.848 | 0.692 | 0.694 | 0.640 | 0.787 | 0.673 | 0.669 | 0.665 |
| Delphi | Framework | 0.851 | 0.819 | 0.817 | 0.788 | 0.812 | 0.771 | 0.763 | 0.762 |
| Policy Delphi | Full | 0.816 | 0.512 | 0.564 | 0.576 | 0.818 | 0.442 | 0.533 | 0.558 |
| Strategy | Setting | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Free | Control | 0.613 | 0.686 | 0.749 | 0.578 | 0.660 | 0.736 | 0.777 | 0.603 |
| NGT | Full | 0.476 | 0.693 | 0.739 | 0.611 | 0.477 | 0.714 | 0.762 | 0.604 |
| NGT | Framework | 0.665 | 0.736 | 0.757 | 0.606 | 0.707 | 0.769 | 0.808 | 0.671 |
| Delphi | Full | 0.567 | 0.674 | 0.691 | 0.579 | 0.584 | 0.687 | 0.700 | 0.605 |
| Delphi | Framework | 0.669 | 0.723 | 0.738 | 0.601 | 0.690 | 0.768 | 0.776 | 0.664 |
| Policy Delphi | Full | 0.551 | 0.608 | 0.712 | 0.621 | 0.574 | 0.619 | 0.709 | 0.607 |
| Strategy | Setting | |||||
|---|---|---|---|---|---|---|
| Free | Control | 1.000 | 0.210 | 0.135 | 0.107 | 0.069 |
| NGT | Full | 1.000 | 0.177 | 0.103 | 0.073 | 0.038 |
| NGT | Framework | 1.000 | 0.223 | 0.158 | 0.135 | 0.101 |
| Delphi | Full | 1.000 | 0.202 | 0.107 | 0.069 | 0.041 |
| Delphi | Framework | 1.000 | 0.202 | 0.138 | 0.116 | 0.089 |
| Policy Delphi | Full | 1.000 | 0.226 | 0.104 | 0.065 | 0.040 |
Multi-Agent LLM Systems
Multi-agent large language model systems coordinate multiple AI agents to solve tasks through communication, specialization, shared tools, and memory.
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