Prompted Identity Degrades Cooperation in Multi-Agent LLM Systems

Xavier Del Giudice; Alessio Palma; Matteo Migliarini; Fabio Galasso; Indro Spinelli

cs.MASep 28, 2026

Prompted Identity Degrades Cooperation in Multi-Agent LLM Systems

Authors: Xavier Del Giudice, Alessio Palma, Matteo Migliarini, Fabio Galasso, Indro Spinelli

Organizations: Sapienza University of Rome, Italy

Abstract

Multi-agent LLM systems increasingly mix models from several providers, yet exposing each agent's underlying model identity to its peers significantly impairs cooperation. We show that when agents are aware of each other's model family, the group splits into clusters, where agents prefer interacting with others carrying their same label, although nothing in the task rewards or asks for such a split. We argue that the label itself causes this split, which we define as $\textit{factionalism}$ . We show and measure this phenomenon in two cooperative games and on a reasoning benchmark, with nine to twenty-five agents drawn from up to five open-weight model families. We further show that when the announced families are shuffled, or replaced by arbitrary labels, the factions still follow this information; when the label is removed, this behavior disappears. In strictly cooperative tasks, labeled groups spend on average $30\%$ more rounds and $55\%$ more tokens to reach a decision, and their success rate drops from $96\%$ to $81\%$ . The effect replicates across tasks, group sizes and model families. Withholding identity labels from the agents is simple and effective mitigation.

Figures & tables

Figure 1: Visible identity labels degrade cooperation. In this work we place agents from several open-weight model families in cooperation games and vary only what they know about each other. When the family label is visible the group splits into label-aligned communities, and spends on average $55\%$ more tokens to reach a decision; when no identity metadata is shown, neither happens.

Figure 2: The counterfactual manipulation. Left: under mislabeled , every agent is told to belong to a model family which is not its actual one. Center: the same agreement graph is evaluated both against the visible-label partition $\ell^{\mathrm{vis}}$ and the true-family partition $\ell^{\mathrm{true}}$ . Right: factions form around the announced tags.

Composition	Condition	Leader Election			Exclusion
Composition	Condition	$N=9$	$N=12$	$N=25$	$N=9$	$N=12$	$N=25$
Unbalanced	Unlabeled	$0.05_{\pm 0.03}$	$0.03_{\pm 0.02}$	$0.02_{\pm 0.01}$	$0.07_{\pm 0.04}$	$0.08_{\pm 0.03}$	$0.02_{\pm 0.01}$
	Labeled	$\mathbf{0.43}_{\pm 0.05}$	$\mathbf{0.30}_{\pm 0.04}$	$\mathbf{0.24}_{\pm 0.02}$	$\mathbf{0.65}_{\pm 0.03}$	$\mathbf{0.59}_{\pm 0.03}$	$\mathbf{0.55}_{\pm 0.02}$
	Mislabeled	$\mathbf{0.33}_{\pm 0.05}$	$\mathbf{0.18}_{\pm 0.03}$	$\mathbf{0.21}_{\pm 0.02}$	$\mathbf{0.67}_{\pm 0.03}$	$\mathbf{0.58}_{\pm 0.03}$	$\mathbf{0.55}_{\pm 0.03}$
Balanced	Unlabeled	$0.08_{\pm 0.03}$	$0.06_{\pm 0.02}$	$0.03_{\pm 0.01}$	$0.04_{\pm 0.04}$	$0.05_{\pm 0.03}$	$0.04_{\pm 0.01}$
	Labeled	$\mathbf{0.53}_{\pm 0.04}$	$\mathbf{0.31}_{\pm 0.03}$	$\mathbf{0.28}_{\pm 0.02}$	$\mathbf{0.76}_{\pm 0.03}$	$\mathbf{0.62}_{\pm 0.03}$	$\mathbf{0.61}_{\pm 0.02}$

Table 1: AMI between communities in the agreement graph and the tested partition: true families for unlabeled runs, visible labels otherwise. Subscripts are standard errors, darker is more factional and significant results are in bold .

Task	$\mathbf{N}$	Rounds spent	Generated tokens	Success
Leader Election	$9$	$\mathbf{1.42}_{\pm 0.09}$	$\mathbf{1.76}_{\pm 0.13}$	$\mathbf{0.96}_{\pm 0.02}$
	$12$	$\mathbf{1.46}_{\pm 0.10}$	$\mathbf{1.82}_{\pm 0.16}$	$\mathbf{0.86}_{\pm 0.04}$
	$25$	$\mathbf{1.38}_{\pm 0.09}$	$\mathbf{1.86}_{\pm 0.14}$	$\mathbf{0.85}_{\pm 0.04}$
Exclusion	$9$	$\mathbf{1.16}_{\pm 0.04}$	$\mathbf{1.37}_{\pm 0.06}$	$\mathbf{0.89}_{\pm 0.04}$
	$12$	$\mathbf{1.09}_{\pm 0.02}$	$\mathbf{1.35}_{\pm 0.03}$	$\mathbf{0.61}_{\pm 0.08}$
	$25$	–	$\mathbf{1.14}_{\pm 0.02}$	–

Table 2: Effects of truthful labels relative to unlabeled , adjusted for roster balance. Entries are ratios, with standard errors as subscripts and significant effects in bold ; dashes denote unavailable estimates.

Composition	Leader Election			Exclusion
Composition	$N=9$	$N=12$	$N=25$	$N=9$	$N=12$	$N=25$
Unbalanced	$\mathbf{0.18}_{\pm 0.03}$	$0.04_{\pm 0.03}$	$0.08_{\pm 0.01}$	$\mathbf{0.29}_{\pm 0.03}$	$0.11_{\pm 0.03}$	$0.08_{\pm 0.01}$
Balanced	$0.10_{\pm 0.03}$	$0.04_{\pm 0.02}$	$0.07_{\pm 0.02}$	$0.13_{\pm 0.03}$	$0.03_{\pm 0.02}$	$0.05_{\pm 0.01}$

Table 3: AMI between communities in the agreement graph and true model families in mislabeled runs. Table 1 reports visible-label AMI for the same runs. Subscripts are standard errors; bold marks experiments meeting the factionalism criterion.

Composition	Condition	Leader Election			Exclusion
Composition	Condition	$N=9$	$N=12$	$N=25$	$N=9$	$N=12$	$N=25$
Unbalanced	Labeled	$\mathbf{0.37}_{\pm 0.05}$	$\mathbf{0.21}_{\pm 0.03}$	$\mathbf{0.24}_{\pm 0.02}$	$\mathbf{0.66}_{\pm 0.03}$	$\mathbf{0.69}_{\pm 0.03}$	$\mathbf{0.80}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{0.31}_{\pm 0.04}$	$\mathbf{0.19}_{\pm 0.03}$	$\mathbf{0.18}_{\pm 0.02}$	$\mathbf{0.76}_{\pm 0.02}$	$\mathbf{0.72}_{\pm 0.03}$	$\mathbf{0.79}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{true}}$	$0.01_{\pm 0.03}$	$0.02_{\pm 0.02}$	$0.07_{\pm 0.01}$	$-0.12_{\pm 0.02}$	$-0.02_{\pm 0.02}$	$-0.01_{\pm 0.01}$
Balanced	Labeled	$\mathbf{0.43}_{\pm 0.04}$	$\mathbf{0.25}_{\pm 0.03}$	$\mathbf{0.26}_{\pm 0.02}$	$\mathbf{0.82}_{\pm 0.03}$	$\mathbf{0.67}_{\pm 0.03}$	$\mathbf{0.81}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{0.28}_{\pm 0.04}$	$\mathbf{0.21}_{\pm 0.03}$	$\mathbf{0.21}_{\pm 0.02}$	$\mathbf{0.95}_{\pm 0.02}$	$\mathbf{0.75}_{\pm 0.03}$	$\mathbf{0.84}_{\pm 0.02}$

Table 4: AMI with neutral color labels. Unlabeled baselines as in Table 1 . Subscripts are standard errors; significant results in bold .

Composition	Condition	GPQA-Diamond
Composition	Condition	$N=9$	$N=12$
Unbalanced	Unlabeled	$0.05_{\pm 0.02}$	$0.00_{\pm 0.01}$
	Labeled	$\mathbf{0.28}_{\pm 0.02}$	$\mathbf{0.32}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{0.27}_{\pm 0.02}$	$\mathbf{0.17}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{true}}$	$\mathbf{0.17}_{\pm 0.02}$	$0.07_{\pm 0.01}$
Balanced	Unlabeled	$0.02_{\pm 0.01}$	$0.02_{\pm 0.01}$

Table 5: AMI on GPQA-Diamond. Subscripts are standard errors; significant results in bold .

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Composition	Condition	$\mathbf{N=9}$ (3 families)		$\mathbf{N=12}$ (4 families)		$\mathbf{N=25}$ (5 families)
Composition	Condition	EDR	AMI	EDR	AMI	EDR	AMI
Unbalanced	Unlabeled	$1.10_{\pm 0.06}$	$0.05_{\pm 0.03}$	$1.01_{\pm 0.06}$	$0.03_{\pm 0.02}$	$1.03_{\pm 0.04}$	$0.02_{\pm 0.01}$
	Labeled	$\mathbf{1.87}_{\pm 0.17}$	$\mathbf{0.43}_{\pm 0.05}$	$\mathbf{1.65}_{\pm 0.09}$	$\mathbf{0.30}_{\pm 0.04}$	$\mathbf{1.70}_{\pm 0.08}$	$\mathbf{0.24}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{1.54}_{\pm 0.12}$	$\mathbf{0.33}_{\pm 0.05}$	$\mathbf{1.55}_{\pm 0.09}$	$\mathbf{0.18}_{\pm 0.03}$	$\mathbf{1.56}_{\pm 0.07}$	$\mathbf{0.21}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{true}}$	$\mathbf{1.27}_{\pm 0.07}$	$\mathbf{0.18}_{\pm 0.03}$	$0.98_{\pm 0.07}$	$0.04_{\pm 0.03}$	$1.09_{\pm 0.05}$	$0.08_{\pm 0.01}$
Balanced	Unlabeled	$1.12_{\pm 0.07}$	$0.08_{\pm 0.03}$	$1.16_{\pm 0.06}$	$0.06_{\pm 0.02}$	$1.01_{\pm 0.04}$	$0.03_{\pm 0.01}$

Appendix

Table 6: Leader Election factionalism, EDR and AMI, for the experiments of Table 1 . For mislabeled runs the same trajectories are scored against the visible-label partition

\ell^{\mathrm{vis}}

and the true-family partition

\ell^{\mathrm{true}}

. Subscripts are standard errors; significant results in bold .

Composition	Condition	$\mathbf{N=9}$ (3 families)		$\mathbf{N=12}$ (4 families)		$\mathbf{N=25}$ (5 families)
Composition	Condition	EDR	AMI	EDR	AMI	EDR	AMI
Unbalanced	Unlabeled	$1.27_{\pm 0.09}$	$0.07_{\pm 0.04}$	$1.02_{\pm 0.07}$	$0.08_{\pm 0.03}$	$0.94_{\pm 0.05}$	$0.02_{\pm 0.01}$
	Labeled	$\mathbf{3.44}_{\pm 0.23}$	$\mathbf{0.65}_{\pm 0.03}$	$\mathbf{3.06}_{\pm 0.21}$	$\mathbf{0.59}_{\pm 0.03}$	$\mathbf{3.78}_{\pm 0.24}$	$\mathbf{0.55}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{3.32}_{\pm 0.23}$	$\mathbf{0.67}_{\pm 0.03}$	$\mathbf{2.72}_{\pm 0.14}$	$\mathbf{0.58}_{\pm 0.03}$	$\mathbf{3.98}_{\pm 0.21}$	$\mathbf{0.55}_{\pm 0.03}$
	Mislabeled $\ell^{\mathrm{true}}$	$\mathbf{1.54}_{\pm 0.12}$	$\mathbf{0.29}_{\pm 0.03}$	$1.12_{\pm 0.07}$	$0.11_{\pm 0.03}$	$1.07_{\pm 0.05}$	$0.08_{\pm 0.01}$
Balanced	Unlabeled	$0.94_{\pm 0.08}$	$0.04_{\pm 0.04}$	$1.04_{\pm 0.06}$	$0.05_{\pm 0.03}$	$1.06_{\pm 0.03}$	$0.04_{\pm 0.01}$

Appendix

Table 7: Exclusion factionalism, EDR and AMI, for the experiments of Table 1 . Conventions as in Table 6 . Significant results in bold .

Composition	Condition	$\mathbf{N=9}$ (3 families)		$\mathbf{N=12}$ (4 families)		$\mathbf{N=25}$ (5 families)
Composition	Condition	EDR	AMI	EDR	AMI	EDR	AMI
Unbalanced	Labeled	$\mathbf{2.07}_{\pm 0.20}$	$\mathbf{0.37}_{\pm 0.05}$	$\mathbf{1.48}_{\pm 0.09}$	$\mathbf{0.21}_{\pm 0.03}$	$\mathbf{1.65}_{\pm 0.07}$	$\mathbf{0.24}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{1.62}_{\pm 0.12}$	$\mathbf{0.31}_{\pm 0.04}$	$\mathbf{1.39}_{\pm 0.10}$	$\mathbf{0.19}_{\pm 0.03}$	$\mathbf{1.44}_{\pm 0.07}$	$\mathbf{0.18}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{true}}$	$0.93_{\pm 0.08}$	$0.01_{\pm 0.03}$	$1.08_{\pm 0.06}$	$0.02_{\pm 0.02}$	$1.10_{\pm 0.05}$	$0.07_{\pm 0.01}$
Balanced	Labeled	$\mathbf{1.81}_{\pm 0.10}$	$\mathbf{0.43}_{\pm 0.04}$	$\mathbf{1.56}_{\pm 0.12}$	$\mathbf{0.25}_{\pm 0.03}$	$\mathbf{2.01}_{\pm 0.09}$	$\mathbf{0.26}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{1.37}_{\pm 0.08}$	$\mathbf{0.28}_{\pm 0.04}$	$\mathbf{1.51}_{\pm 0.09}$	$\mathbf{0.21}_{\pm 0.03}$	$\mathbf{1.68}_{\pm 0.08}$	$\mathbf{0.21}_{\pm 0.02}$

Appendix

Table 8: Leader Election factionalism with neutral color labels, EDR and AMI, for the experiments of Table 4 . Unlabeled baselines are those of Table 6 . Significant results in bold .

Composition	Condition	$\mathbf{N=9}$ (3 families)		$\mathbf{N=12}$ (4 families)		$\mathbf{N=25}$ (5 families)
Composition	Condition	EDR	AMI	EDR	AMI	EDR	AMI
Unbalanced	Labeled	$\mathbf{3.53}_{\pm 0.31}$	$\mathbf{0.66}_{\pm 0.03}$	$\mathbf{3.42}_{\pm 0.18}$	$\mathbf{0.69}_{\pm 0.03}$	$\mathbf{6.37}_{\pm 0.34}$	$\mathbf{0.80}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{3.97}_{\pm 0.25}$	$\mathbf{0.76}_{\pm 0.02}$	$\mathbf{3.85}_{\pm 0.20}$	$\mathbf{0.72}_{\pm 0.03}$	$\mathbf{6.98}_{\pm 0.48}$	$\mathbf{0.79}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{true}}$	$0.72_{\pm 0.05}$	$-0.12_{\pm 0.02}$	$0.99_{\pm 0.07}$	$-0.02_{\pm 0.02}$	$1.02_{\pm 0.05}$	$-0.01_{\pm 0.01}$
Balanced	Labeled	$\mathbf{5.15}_{\pm 0.46}$	$\mathbf{0.82}_{\pm 0.03}$	$\mathbf{3.58}_{\pm 0.20}$	$\mathbf{0.67}_{\pm 0.03}$	$\mathbf{8.09}_{\pm 0.56}$	$\mathbf{0.81}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{5.66}_{\pm 0.48}$	$\mathbf{0.95}_{\pm 0.02}$	$\mathbf{3.38}_{\pm 0.18}$	$\mathbf{0.75}_{\pm 0.03}$	$\mathbf{8.05}_{\pm 0.51}$	$\mathbf{0.84}_{\pm 0.02}$

Appendix

Table 9: Exclusion factionalism with neutral color labels, EDR and AMI, for the experiments of Table 4 . Unlabeled baselines are those of Table 7 . Significant results in bold .

Composition	Condition	$\mathbf{N=9}$ (3 families)		$\mathbf{N=12}$ (4 families)
Composition	Condition	EDR	AMI	EDR	AMI
Unbalanced	Unlabeled	$0.89_{\pm 0.04}$	$0.05_{\pm 0.02}$	$0.77_{\pm 0.03}$	$0.00_{\pm 0.01}$
	Labeled	$\mathbf{1.66}_{\pm 0.08}$	$\mathbf{0.28}_{\pm 0.02}$	$\mathbf{1.98}_{\pm 0.08}$	$\mathbf{0.32}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{1.69}_{\pm 0.07}$	$\mathbf{0.27}_{\pm 0.02}$	$\mathbf{1.43}_{\pm 0.05}$	$\mathbf{0.17}_{\pm 0.02}$
	Mislabeled $\ell^{\mathrm{true}}$	$\mathbf{1.35}_{\pm 0.05}$	$\mathbf{0.17}_{\pm 0.02}$	$1.12_{\pm 0.07}$	$0.07_{\pm 0.01}$
Balanced	Unlabeled	$0.78_{\pm 0.03}$	$0.02_{\pm 0.01}$	$0.80_{\pm 0.03}$	$0.02_{\pm 0.01}$

Appendix

Table 10: GPQA-Diamond factionalism, EDR and AMI, for the experiments of Table 5 . Conventions as in Table 6 . Significant results in bold .

Condition	Composition	Gemma	GPT-OSS	Nemotron	Qwen
Unlabeled	Balanced	$\mathbf{-0.390}_{\pm 0.082}$	$\mathbf{+0.100}_{\pm 0.019}$	$\mathbf{+0.036}_{\pm 0.018}$	$+0.018_{\pm 0.028}$
Unlabeled	Unbalanced	$\mathbf{-0.396}_{\pm 0.071}$	$\mathbf{+0.084}_{\pm 0.021}$	$\mathbf{+0.046}_{\pm 0.015}$	$-0.022_{\pm 0.024}$
Labeled	Balanced	$\mathbf{+0.844}_{\pm 0.108}$	$\mathbf{+0.230}_{\pm 0.017}$	$\mathbf{+0.119}_{\pm 0.023}$	$\mathbf{+0.355}_{\pm 0.036}$
Labeled	Unbalanced	$\mathbf{+0.802}_{\pm 0.084}$	$\mathbf{+0.247}_{\pm 0.032}$	$\mathbf{+0.100}_{\pm 0.022}$	$\mathbf{+0.304}_{\pm 0.030}$
Mislabeled (true family)	Balanced	$\mathbf{-0.324}_{\pm 0.077}$	$\mathbf{+0.064}_{\pm 0.025}$	$+0.013_{\pm 0.021}$	$\mathbf{+0.082}_{\pm 0.026}$
Mislabeled (true family)	Unbalanced	$-0.102_{\pm 0.062}$	$+0.033_{\pm 0.019}$	$+0.013_{\pm 0.025}$	$+0.054_{\pm 0.030}$

Appendix

Table 11: Leader Election adoption gap, by the evaluator’s underlying model family.

Condition	Composition	Gemma	GPT-OSS	Nemotron	Qwen
Unlabeled	Balanced	$\mathbf{+0.151}_{\pm 0.048}$	$+0.025_{\pm 0.022}$	$-0.008_{\pm 0.023}$	$-0.017_{\pm 0.026}$
Unlabeled	Unbalanced	$\mathbf{+0.229}_{\pm 0.042}$	$-0.004_{\pm 0.015}$	$+0.002_{\pm 0.022}$	$+0.011_{\pm 0.024}$
Labeled	Balanced	$\mathbf{+1.126}_{\pm 0.061}$	$\mathbf{-0.074}_{\pm 0.033}$	$\mathbf{+0.059}_{\pm 0.024}$	$\mathbf{+0.180}_{\pm 0.028}$
Labeled	Unbalanced	$\mathbf{+1.164}_{\pm 0.056}$	$+0.004_{\pm 0.027}$	$\mathbf{+0.122}_{\pm 0.037}$	$\mathbf{+0.207}_{\pm 0.023}$
Mislabeled (true family)	Balanced	$+0.112_{\pm 0.057}$	$+0.022_{\pm 0.016}$	$-0.006_{\pm 0.021}$	$-0.003_{\pm 0.024}$
Mislabeled (true family)	Unbalanced	$\mathbf{+0.143}_{\pm 0.069}$	$+0.003_{\pm 0.022}$	$+0.003_{\pm 0.019}$	$\mathbf{+0.147}_{\pm 0.029}$

Appendix

Table 12: Exclusion adoption gap, by the evaluator’s underlying model family.

Composition	Condition	$\mathbf{N=9}$ (3 families)		$\mathbf{N=12}$ (4 families)
Composition	Condition	EDR	AMI	EDR	AMI
Unbalanced	Unlabeled	$1.04_{\pm 0.06}$	$-0.01_{\pm 0.03}$	$1.09_{\pm 0.05}$	$+0.03_{\pm 0.03}$
	Labeled	$\mathbf{1.46}_{\pm 0.14}$	$\mathbf{+0.24}_{\pm 0.05}$	$\mathbf{1.39}_{\pm 0.06}$	$\mathbf{+0.23}_{\pm 0.03}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{1.13}_{\pm 0.06}$	$\mathbf{+0.10}_{\pm 0.04}$	$\mathbf{1.15}_{\pm 0.06}$	$\mathbf{+0.10}_{\pm 0.03}$
	Mislabeled $\ell^{\mathrm{true}}$	$1.02_{\pm 0.08}$	$+0.05_{\pm 0.04}$	$1.02_{\pm 0.05}$	$+0.06_{\pm 0.02}$
Balanced	Unlabeled	$1.00_{\pm 0.06}$	$+0.03_{\pm 0.04}$	$1.02_{\pm 0.04}$	$-0.03_{\pm 0.02}$

Appendix

Table 13: Leader Election factionalism on the agreement graph with Gemma removed from the roster. Significant results in bold .

Composition	Condition	$\mathbf{N=9}$ (3 families)		$\mathbf{N=12}$ (4 families)
Composition	Condition	EDR	AMI	EDR	AMI
Unbalanced	Unlabeled	$0.89_{\pm 0.05}$	$+0.02_{\pm 0.03}$	$1.04_{\pm 0.05}$	$-0.01_{\pm 0.03}$
	Labeled	$\mathbf{2.26}_{\pm 0.18}$	$\mathbf{+0.54}_{\pm 0.04}$	$\mathbf{2.09}_{\pm 0.12}$	$\mathbf{+0.42}_{\pm 0.04}$
	Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{1.57}_{\pm 0.13}$	$\mathbf{+0.32}_{\pm 0.05}$	$\mathbf{1.92}_{\pm 0.11}$	$\mathbf{+0.39}_{\pm 0.04}$
	Mislabeled $\ell^{\mathrm{true}}$	$\mathbf{1.23}_{\pm 0.07}$	$\mathbf{+0.14}_{\pm 0.04}$	$1.03_{\pm 0.06}$	$+0.04_{\pm 0.02}$
Balanced	Unlabeled	$0.95_{\pm 0.07}$	$+0.08_{\pm 0.04}$	$0.99_{\pm 0.05}$	$+0.06_{\pm 0.03}$

Appendix

Table 14: Exclusion factionalism on the agreement graph with Gemma removed from the roster. Rosters and conventions as in Table 13 . Significant results in bold .

Condition	Composition	GPT-OSS	Nemotron	Qwen	Seed-OSS
Unlabeled	Balanced	$-0.014_{\pm 0.019}$	$\mathbf{-0.065}_{\pm 0.014}$	$-0.001_{\pm 0.030}$	$\mathbf{+0.068}_{\pm 0.022}$
Unlabeled	Unbalanced	$+0.008_{\pm 0.016}$	$+0.007_{\pm 0.017}$	$-0.069_{\pm 0.037}$	$-0.016_{\pm 0.020}$
Labeled	Balanced	$\mathbf{+0.137}_{\pm 0.022}$	$-0.013_{\pm 0.020}$	$\mathbf{+0.265}_{\pm 0.036}$	$\mathbf{+0.221}_{\pm 0.037}$
Labeled	Unbalanced	$\mathbf{+0.116}_{\pm 0.019}$	$+0.032_{\pm 0.027}$	$\mathbf{+0.205}_{\pm 0.039}$	$\mathbf{+0.159}_{\pm 0.040}$
Mislabeled (true family)	Balanced	$+0.032_{\pm 0.018}$	$\mathbf{-0.062}_{\pm 0.025}$	$-0.002_{\pm 0.034}$	$\mathbf{+0.101}_{\pm 0.033}$
Mislabeled (true family)	Unbalanced	$-0.021_{\pm 0.016}$	$-0.017_{\pm 0.035}$	$+0.018_{\pm 0.026}$	$\mathbf{+0.104}_{\pm 0.038}$

Appendix

Table 15: Leader Election adoption gap by the evaluator’s underlying model family, with Gemma replaced by Seed-OSS.

Condition	Composition	GPT-OSS	Nemotron	Qwen	Seed-OSS
Unlabeled	Balanced	$\mathbf{+0.025}_{\pm 0.012}$	$-0.011_{\pm 0.022}$	$\mathbf{+0.042}_{\pm 0.018}$	$\mathbf{+0.059}_{\pm 0.028}$
Unlabeled	Unbalanced	$+0.011_{\pm 0.024}$	$+0.000_{\pm 0.014}$	$-0.023_{\pm 0.018}$	$+0.062_{\pm 0.043}$
Labeled	Balanced	$\mathbf{+0.106}_{\pm 0.038}$	$+0.019_{\pm 0.027}$	$\mathbf{+0.223}_{\pm 0.021}$	$\mathbf{+0.162}_{\pm 0.034}$
Labeled	Unbalanced	$\mathbf{+0.264}_{\pm 0.093}$	$\mathbf{+0.088}_{\pm 0.026}$	$\mathbf{+0.253}_{\pm 0.025}$	$\mathbf{+0.252}_{\pm 0.036}$
Mislabeled (true family)	Balanced	$\mathbf{-0.048}_{\pm 0.028}$	$-0.002_{\pm 0.018}$	$+0.020_{\pm 0.023}$	$+0.046_{\pm 0.024}$
Mislabeled (true family)	Unbalanced	$\mathbf{+0.053}_{\pm 0.029}$	$\mathbf{+0.050}_{\pm 0.021}$	$+0.024_{\pm 0.021}$	$+0.045_{\pm 0.031}$

Appendix

Table 16: Exclusion adoption gap by the evaluator’s underlying model family, with Gemma replaced by Seed-OSS.

Task	$\mathbf{N}$	Condition	Rounds	Tokens	Success risk ratio	Tokens per success
Leader Election	$9$	Mislabeled	$\mathbf{1.20}_{\pm 0.08}$	$\mathbf{1.44}_{\pm 0.11}$	$0.97_{\pm 0.02}$	$\mathbf{1.48}_{\pm 0.13}$
		Labeled	$\mathbf{1.42}_{\pm 0.09}$	$\mathbf{1.76}_{\pm 0.13}$	$\mathbf{0.96}_{\pm 0.02}$	$\mathbf{1.83}_{\pm 0.15}$
Leader Election	$12$	Mislabeled	$\mathbf{1.22}_{\pm 0.08}$	$\mathbf{1.45}_{\pm 0.12}$	$0.96_{\pm 0.02}$	$\mathbf{1.50}_{\pm 0.15}$
		Labeled	$\mathbf{1.46}_{\pm 0.10}$	$\mathbf{1.82}_{\pm 0.16}$	$\mathbf{0.86}_{\pm 0.04}$	$\mathbf{2.10}_{\pm 0.25}$
Leader Election	$25$	Mislabeled	$\mathbf{1.39}_{\pm 0.09}$	$\mathbf{1.90}_{\pm 0.14}$	$\mathbf{0.86}_{\pm 0.04}$	$\mathbf{2.21}_{\pm 0.22}$
		Labeled	$\mathbf{1.38}_{\pm 0.09}$	$\mathbf{1.86}_{\pm 0.14}$	$\mathbf{0.85}_{\pm 0.04}$	$\mathbf{2.20}_{\pm 0.23}$

Appendix

Table 17: Full cost estimates: mislabeled and labeled relative to unlabeled , adjusted for roster balance (subscripts: standard errors; bold :

p<0.05

). Tokens per success subscripts: bootstrap standard errors; bold when the

95\%

interval excludes

1

Task	$\mathbf{N}$	Success			Rounds			Tokens
Task	$\mathbf{N}$	Unl.	Mis.	Lab.	Unl.	Mis.	Lab.	Unl.	Mis.	Lab.
Leader Election	$9$	1.000	0.970	0.960	6.9	8.3	9.8	91k	132k	161k
Leader Election	$12$	0.990	0.960	0.860	7.2	8.8	10.5	114k	166k	208k
Leader Election	$25$	0.990	0.850	0.840	7.9	11.0	10.9	216k	411k	403k
Exclusion	$9$	1.000	0.950	0.887	12.0	13.3	13.9	166k	211k	227k
Exclusion	$12$	0.825	0.575	0.500	17.3	18.8	18.8	219k	274k	295k

Appendix

Table 18: Per-condition means: success rate, rounds spent, generated tokens.

Condition	Per-family settings		Shared settings
Condition	EDR	AMI	EDR	AMI
Unlabeled	$1.16_{\pm 0.06}$	$+0.06_{\pm 0.02}$	$0.99_{\pm 0.06}$	$+0.02_{\pm 0.02}$
Labeled	$\mathbf{1.74}_{\pm 0.11}$	$\mathbf{+0.31}_{\pm 0.03}$	$\mathbf{1.68}_{\pm 0.10}$	$\mathbf{+0.27}_{\pm 0.03}$
Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{1.45}_{\pm 0.08}$	$\mathbf{+0.23}_{\pm 0.03}$	$\mathbf{1.41}_{\pm 0.09}$	$\mathbf{+0.22}_{\pm 0.03}$
Mislabeled $\ell^{\mathrm{true}}$	$1.10_{\pm 0.08}$	$+0.04_{\pm 0.02}$	$0.96_{\pm 0.06}$	$+0.06_{\pm 0.02}$

Appendix

Table 19: Leader Election factionalism with family-specific sampling settings (Table 21 ) or identical settings for all four families (

\mathrm{Temp}=1.0

\mathrm{top\_p}=1.0

, no top-

k

, no penalties).

N=12

, balanced composition; every other setting identical. For mislabeled runs the same trajectories are scored against the visible-label partition

\ell^{\mathrm{vis}}

and the true-family partition

\ell^{\mathrm{true}}

. Significant results in bold .

Condition	Per-family settings		Shared settings
Condition	EDR	AMI	EDR	AMI
Unlabeled	$1.04_{\pm 0.06}$	$+0.05_{\pm 0.03}$	$1.04_{\pm 0.05}$	$+0.07_{\pm 0.03}$
Labeled	$\mathbf{2.98}_{\pm 0.17}$	$\mathbf{+0.62}_{\pm 0.03}$	$\mathbf{2.91}_{\pm 0.18}$	$\mathbf{+0.54}_{\pm 0.03}$
Mislabeled $\ell^{\mathrm{vis}}$	$\mathbf{2.49}_{\pm 0.14}$	$\mathbf{+0.58}_{\pm 0.03}$	$\mathbf{2.31}_{\pm 0.14}$	$\mathbf{+0.52}_{\pm 0.03}$
Mislabeled $\ell^{\mathrm{true}}$	$1.09_{\pm 0.06}$	$+0.03_{\pm 0.02}$	$1.01_{\pm 0.06}$	$+0.06_{\pm 0.02}$

Appendix

Table 20: Exclusion factionalism with family-specific sampling settings (Table 21 ) or identical settings for all four families (

\mathrm{Temp}=1.0

\mathrm{top\_p}=1.0

, no top-

k

, no penalties).

N=12

, balanced composition; every other setting identical. For mislabeled runs the same trajectories are scored against the visible-label partition

\ell^{\mathrm{vis}}

and the true-family partition

\ell^{\mathrm{true}}

. Significant results in bold .

Family	Temp.	top_p	top_k	min_p	presence_pen.	repetition_pen.
Gemma	1.0	0.95	64	—	—	—
GPT-OSS	1.0	—	—	—	—	—
Nemotron	1.0	1.0	—	—	—	—
Qwen	1.0	0.95	20	0.0	1.5	1.0
GLM	1.0	0.95	—	—	—	—
Seed-OSS	1.1	0.95	—	—	—	—

Appendix

Table 21: Model-specific sampling parameters used outside the shared-settings check. Dashes mean the parameter is not set on the request and the endpoint default is used.

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