Beyond Symmetric Agents: Cognitive Diversity and Multi-Agent Debate in Small Language Models

Leonardo Ferreira; Gardenia Liu; Kaden Zheng

cs.AISep 26, 2026

Beyond Symmetric Agents: Cognitive Diversity and Multi-Agent Debate in Small Language Models

Authors: Leonardo Ferreira, Gardenia Liu, Kaden Zheng

Organizations: Boston Children’s Hospital, Harvard Medical School · Harvard School of Engineering and Applied Sciences, Harvard College

Abstract

Multi-agent debate (MAD) reportedly improves reasoning and factuality over single-model inference, but prior work treats agents as symmetric peers, leaving open what drives the gains. We test the hypothesis that cognitive diversity among agents is the driver, in the setting where the question is still measurable: small open-weight models with benchmark headroom. Across 23 models from eleven vendor families, five tasks, and 5,500+ debate and control runs, we vary diversity along three axes - personas, sampling temperature, and model identity - pairing every debate configuration with a generation-budget-matched majority-vote control. The hypothesis is rejected on every axis. Debate beats single-agent inference (3--7 points where tasks have headroom) but at matched budget conditions it ties or even loses to self-consistency sampling at 1.6 $\times$ the wall-clock and 3.4 $\times$ the token cost. Persona prompting reduces accuracy and a dose-response experiment over each model's full combinatorial persona space shows the cost is a persona tax, not a diversity tax: redundant personas hurt most, while maximally-diverse teams recover part of the loss. Furthermore, mixed-model teams lose to majority votes over their own rosters, with accuracy tracking member capability rather than heterogeneity, and nearly all of debate's benefit comes from the first exchange of answers. We further identify a pervasive measurement hazard in which debate transcripts silently overflow serving context windows, whose correction alone moves our debate-versus-sampling comparison from $-1.8$ points to parity. Our results recast reported MAD gains as an ensemble-sampling effect and provide the budget-matched, contamination-checked baseline bar that future debate mechanisms should be required to clear.

Figures & tables

Task	Solo	Debate	SC-9	Persona
Math	91.2	91.5	90.6	90.0
GSM8K	87.9	91.2 ∗	91.0 ∗	88.5
MMLU	69.9	76.5 ∗	76.8 ∗	75.2 ∗
CSQA	72.6	78.3 ∗	80.6 ∗	73.9
Biography †	54.6	55.6	64.6 ∗	51.8
Mean	80.4	84.4	84.8	81.9

Table 1: Mean accuracy (%) per task over the 23-model pool (100 problems, seed 42, context-corrected). Solo: one agent. Debate:

3\times 3

. SC-9: budget-matched self-consistency (9 samples, majority vote). Persona: MaxDet persona debate. Bold: row best; ∗ : paired difference from Solo has a 95% bootstrap CI excluding zero. † Claim precision among verifiable claims and vendor-balanced judge panel (Section 5.4 ); Mean averages the inline-scored tasks.

Figure 1: Cost of maximally-diverse (MaxDet) persona teams by task and team size: distribution over the 23-model pool of persona minus matched baseline-debate accuracy (pp; seed 42, context-corrected). Diamonds: means; stars: Wilcoxon vs. zero (

{}^{***}10^{-3}

{}^{**}10^{-2}

{}^{*}0.05

). † Claim precision among verifiable claims under the vendor-balanced panel of Section 5.4 .

Figure 2: Persona-diversity dose-response over the 23-model pool. Rung 0: each model’s minimum-determinant (most redundant) persona trio; rungs 1–9: log-det decile maxima; rung 10: the campaign MaxDet team. Lines: mean delta vs. the no-persona baseline debate; bands: 95% bootstrap over models. † Biography (dashed) is claim precision under the vendor-balanced judge panel.

Arm	Teams	Debate	Ensemble	$\Delta$ (pp) [95% CI]
Core triple ( $n{=}3$ )	80	88.4	89.4	$-1.04$ [ $-1.61$ , $-0.52$ ] ∗
Pair, strong dup. ( $n{=}3$ )	15	83.0	85.7	$-2.68$ [ $-5.33$ , $-0.65$ ] ∗
Pair, weak dup. ( $n{=}3$ )	15	79.8	81.4	$-1.63$ [ $-4.62$ , $+1.02$ ]
Quad, strong dup. ( $n{=}5$ )	20	91.9	91.8	$+0.04$ [ $-0.39$ , $+0.50$ ]
Quad, weak dup. ( $n{=}5$ )	20	90.5	90.0	$+0.56$ [ $-0.34$ , $+1.41$ ]

Table 2: Mixed-model debate against generation-budget-matched majority-vote ensembles built from the same rosters (seed 42, 100 problems, four scorable tasks).

\Delta

= debate

-

ensemble, 95% CIs from a 10k bootstrap clustered over team-configs, ∗ marks intervals excluding zero. “Strong/weak dup.” duplicates the stronger or weaker member (pairs: AAB vs. ABB at

n{=}3

vs. 9 samples; quads:

n{=}5

vs. 15 samples).

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Size	Class	Notes
Qwen3-0.6B	0.6B	Qwen3
LFM2.5-1.2B	1.2B	LFM2.5	hybrid conv/attn
VibeThinker-1.5B	1.5B	VibeThinker	reasoning FT
Llama-3.2-3B-Instruct	3B	Llama-3.2
Phi-4-mini	3.8B	Phi-4	synthetic-data
Nemotron-3-Nano-4B	4B	Nemotron-3	Mamba hybrid

Appendix

Table 3: The 23-model participant pool. Class = vendor

\times

generation lineage used for the model-diversity constraint. Quantized checkpoints are official releases. The four models below the rule joined after model-diversity team sampling was frozen and appear in all single-model conditions only.

Family	Role	Pool	Tasks	Runs	Seed
Homogeneous baseline (solo + debate $n{\in}\{3,5,7\}$ )	core	23	5	460	42
MaxDet persona debate ( $n{\in}\{3,5,7\}$ )	core	23	5	345	42
Self-consistency, budget-matched ( $N{\in}\{9,15,21\}$ , uniform + spread)	control	23	5	690	42
Seed-43 homogeneous slice (solo + debate $n{=}3$ )	ablation	19	5	190	43
Mixed-model core triples ( $n{=}3$ , 80 teams)	core	19	5	400	42
Mixed-model pairs (AAB/ABB, 15 pairs)	core	19	5	150	42

Appendix

Table 4: Every experiment family, its role, model pool, task coverage, run count, and problem-sampling seed. The 23-model pool comprises 16 local workstation models, 3 cluster-only models, and 4 later-added models; the mixed-model families draw teams from the 19 models available at team-freeze time.

Debate arm	Temp. policy	Budget	Matched control	Temp. policy
Homog. $n{=}3$ , $r{=}3$	spread $0.5$ – $1.0$	9	SC-9 (two flavors)	$T{=}1.0$ / spread
Homog. $n{=}5$ , $r{=}3$	spread $0.5$ – $1.0$	15	SC-15 (two flavors)	$T{=}1.0$ / spread
Homog. $n{=}7$ , $r{=}3$	spread $0.5$ – $1.0$	21	SC-21 (two flavors)	$T{=}1.0$ / spread
Persona $n{\in}\{3,5,7\}$ , $r{=}3$	$T{=}1.0$ fixed	$3n$	SC- $3n$ uniform	$T{=}1.0$
Persona rungs 0–10, $n{=}3$	$T{=}1.0$ fixed	9	no-persona debate	spread $0.5$ – $1.0$
Mixed triple $1{+}1{+}1$ , $r{=}3$	spread $0.5$ – $1.0$	9	roster ens. $3{\times}3$ , $r{=}1$	$T{=}1.0$

Appendix

Table 5: Matched-control pairings. Every debate arm is compared against a control built from the same model roster at the same generation budget (generations per problem) in “two flavors”: uniform temperature (

T{=}1.0

) and the same per-agent spread that the debate uses, which isolates deliberation from sampling stochasticity. Persona debates fix

T{=}1.0

so the persona effect is not confounded with temperature and their like-for-like control is uniform-temperature self-consistency. T, temperature; SC, self-consistency.

Model	Solo	Debate	SC-9	Persona
LFM2.5-1.2B	100.0	100.0	99.0	99.0
LFM2.5-8B-A1B	100.0	100.0	100.0	97.0
Llama-3.2-3B	35.0	37.0	29.0	39.0
Llama-4-Scout-17B-16E (W4A16)	100.0	100.0	100.0	100.0
Ministral-3-8B	98.0	96.0	99.0	54.0
Mistral-7B-v0.3	7.0	9.0	18.0	9.0

Appendix

Table 6: Per-model accuracy (%), Math.

Model	Solo	Debate	SC-9	Persona
LFM2.5-1.2B	70.0	74.0	75.0	70.0
LFM2.5-8B-A1B	89.0	96.0	99.0	89.0
Llama-3.2-3B	46.0	78.0	85.0	60.0
Llama-4-Scout-17B-16E (W4A16)	96.0	95.0	96.0	94.0
Ministral-3-8B	91.0	94.0	95.0	88.0
Mistral-7B-v0.3	43.0	55.0	40.0	43.0

Appendix

Table 7: Per-model accuracy (%), GSM8K.

Model	Solo	Debate	SC-9	Persona
LFM2.5-1.2B	45.0	55.0	57.0	57.0
LFM2.5-8B-A1B	61.0	80.0	79.0	74.0
Llama-3.2-3B	17.0	49.0	45.0	42.0
Llama-4-Scout-17B-16E (W4A16)	83.0	84.0	83.0	87.0
Ministral-3-8B	64.0	79.0	78.0	68.0
Mistral-7B-v0.3	40.0	60.0	59.0	45.0

Appendix

Table 8: Per-model accuracy (%), MMLU.

Model	Solo	Debate	SC-9	Persona
LFM2.5-1.2B	55.0	62.0	64.0	61.0
LFM2.5-8B-A1B	71.0	80.0	81.0	75.0
Llama-3.2-3B	26.0	60.0	69.0	53.0
Llama-4-Scout-17B-16E (W4A16)	85.0	89.0	89.0	91.0
Ministral-3-8B	61.0	72.0	76.0	39.0
Mistral-7B-v0.3	49.0	69.0	73.0	62.0

Appendix

Table 9: Per-model accuracy (%), CSQA.

Arm	Math	GSM8K	MMLU	CSQA
Core triple ( $n{=}3$ )	$-1.45$ $[-2.6,-0.4]$ ∗	$-1.10$ $[-1.6,-0.6]$ ∗	$-0.01$ $[-0.9,+0.8]$	$-1.61$ $[-2.6,-0.7]$ ∗
Pair, strong dup. ( $n{=}3$ )	$-3.53$ $[-8.1,+0.1]$	$-1.73$ $[-4.1,+0.3]$	$-3.27$ $[-6.2,-0.7]$ ∗	$-2.20$ $[-4.7,+0.3]$
Pair, weak dup. ( $n{=}3$ )	$-0.53$ $[-6.5,+5.8]$	$-1.67$ $[-3.9,+0.5]$	$-2.13$ $[-5.9,+1.3]$	$-2.20$ $[-5.4,+0.9]$
Quad, strong dup. ( $n{=}5$ )	$-0.10$ $[-0.3,+0.0]$	$-0.60$ $[-1.2,+0.1]$	$+0.95$ $[-0.4,+2.3]$	$-0.10$ $[-0.9,+0.7]$
Quad, weak dup. ( $n{=}5$ )	$+0.15$ $[-0.4,+0.9]$	$-1.25$ $[-2.2,-0.5]$ ∗	$+2.80$ $[+0.9,+4.6]$ ∗	$+0.55$ $[-1.0,+1.9]$

Appendix

Table 10: Per-task debate-minus-matched-ensemble deltas (pp) for every mixed-model arm of Table 2 (95% CIs, bootstrap clustered over team-configs; ∗ excludes zero).

Team family	Teams	vs. majority	vs. acc.-weighted	vs. log-odds (binary)	vs. log-odds (multiclass)
Core triples, seed 42	80	$-1.04$ [ $-1.49$ , $-0.60$ ] ∗	$-1.35$ [ $-1.81$ , $-0.92$ ] ∗	$+0.63$ [ $-0.25$ , $+1.58$ ]	$-1.11$ [ $-1.62$ , $-0.59$ ] ∗
Core triples, seed 43	80	$-0.93$ [ $-1.38$ , $-0.48$ ] ∗	$-1.35$ [ $-1.80$ , $-0.92$ ] ∗	$+0.57$ [ $-0.27$ , $+1.44$ ]	$-1.30$ [ $-1.80$ , $-0.83$ ] ∗
Pairs (AAB/ABB)	30	$-2.16$ [ $-3.42$ , $-0.88$ ] ∗	$-3.40$ [ $-4.52$ , $-2.33$ ] ∗	$+2.10$ [ $-0.12$ , $+4.48$ ]	$-1.59$ [ $-3.12$ , $+0.18$ ]
Quads (dup-s/w)	40	$+0.30$ [ $-0.12$ , $+0.74$ ]	$-0.35$ [ $-0.74$ , $+0.02$ ]	$+0.39$ [ $-0.22$ , $+1.09$ ]	$-0.51$ [ $-0.89$ , $-0.16$ ] ∗

Appendix

Table 11: Weighted-voting robustness of the mixed-model result. Each cell is the paired delta debate

-

ensemble (pp; negative favors the ensemble) under three aggregation rules over the same stored generations: plain majority, votes weighted linearly by each member’s solo seed-42 accuracy on the task, and Naive-Bayes log-odds weights

\log(p/(1-p))

(

p

clipped to

[0.02,0.98]

). 95% CIs from a 10k bootstrap over teams; ∗ = CI excludes zero.

Composition	Debate	Ensemble	$\Delta$ (pp)
SSS	93.7	93.2	$+0.44$ ∗
SSM	92.5	92.8	$-0.28$
SMM	90.3	91.5	$-1.22$
MMM	87.0	88.2	$-1.16$ ∗
SSW	91.7	92.2	$-0.59$
SMW	90.6	90.9	$-0.31$

Appendix

Table 12: Core-triple accuracy by capability-tier composition (S/M/W = strong/mid/weak member tiers), debate vs. matched ensemble. ∗ : the

\Delta

’s 95% bootstrap CI over that composition’s eight teams excludes zero.

Task	$r{=}1$	$r{=}2$	$r{=}3$	$r{=}4$	$r{=}5$
Math	93.5	98.3	99.2 ∗	99.2	99.2
GSM8K	91.7	93.2	94.0	94.3	94.5
MMLU	74.1	76.4	76.8	77.0 ∗	75.6
CSQA	79.2	81.0 ∗	79.6	79.7	78.6
Mean	84.6	87.2 ∗	87.4 ∗	87.5 ∗	87.0 ∗

Appendix

Table 13: Rounds ablation: mixed-team debate accuracy (%) by number of rounds, pooled over ten core teams spanning every tier composition (SSS–WWW).

r{=}1

is a single-round majority vote over the team; each added round costs

n

further generations, so columns are not budget-matched; the row reads as what additional rounds buy. ∗ : the paired difference from

r{=}1

over the ten teams has a 95% bootstrap CI excluding zero.

Model	Solo	Debate	SC-9	Persona	Verif. claims
LFM2.5-1.2B	87.3	86.5	86.3	92.6	224
LFM2.5-8B-A1B	40.8	42.9	44.1	32.5	340
Llama-3.2-3B	30.0	28.4	28.0	27.1	389
Llama-4-Scout-17B-16E-Ins	69.9	62.0	69.0	58.7	490
Ministral-3-8B-2	31.4	55.9	64.7	16.7	865
Mistral-7B-v0.3	38.7	40.9	52.1	26.1	464

Appendix

Table 14: Per-model biography factuality: claim precision among verifiable claims (%) under the vendor-balanced three-judge panel (one vote per judge vendor; Gemma-3-27B vs. the averaged GPT-OSS-20B/120B pair), seed 42, 40 subjects, ctx-max policy. Solo: single agent. Debate: 3 agents

\times

3 rounds. SC-9: nine independent single-round biographies pooled through the same panel. Persona: maximally-diverse (MaxDet) persona team, 3 agents. “Verif. claims”: mean verifiable claims per cell under the debate arm — a volume indicator (precision is computed only over these). Bold: best per row.

Judge	Units	Strict	Verif.	Units	Strict	Verif.
	Claims direction			Facts direction
Gemma-3-27B	6.98M	18.4	65.2	1.91M	39.8	78.9
GPT-OSS-20B	6.95M	11.2	58.6	1.90M	9.7	57.9
GPT-OSS-120B	6.98M	11.1	61.6	1.91M	9.9	52.2
Muse Glimmer	3.30M	10.3	42.2	0.96M	12.7	42.1

Appendix

Table 15: The four-judge biography panel over every judged file (mirror- deduped). “Strict”: supported / all claims; “Verif.”: supported / (supported + contradicted). The three primary judges sit above the rule; the supplementary coupling-ablation judge (Muse Glimmer) below.

	Gemma-3-27B	GPT-OSS-20B	GPT-OSS-120B	Muse Glimmer
Gemma-3-27B	—	0.342	0.372	0.317
GPT-OSS-20B	0.563	—	0.762	0.440
GPT-OSS-120B	0.568	0.759	—	0.474
Muse Glimmer	0.354	0.414	0.412	—

Appendix

Table 16: Pairwise Cohen’s

\kappa

between judges over record-aligned verdicts (

3.3

–

7.0

M claim /

1.0

–

1.9

M fact pairs per judge pair): claims direction below the diagonal, facts direction above.

Figure 3: Debate vs. the serving context window for the five budget-exceeding models (cells paired within model). Top: mean accuracy, inline-scored tasks; bottom: fraction of final-round responses left empty by transcript overflow.

	MMLU-Pro			GSM-Symbolic
Model	Solo	Debate	SC-9	Solo	Debate	SC-9
gemma-4-12B-it	74.0	77.0	78.0	96.0	95.0	96.0
gemma-4-26B-A4B-it-FP8-dy	82.0	85.0	83.0	98.0	97.0	98.0
granite-4.1-8b	43.0	56.0	59.0	95.0	96.0	97.0
LFM2.5-1.2B	32.0	35.0	35.0	77.0	83.0	74.0
LFM2.5-8B-A1B	40.0	60.0	65.0	93.0	94.0	94.0

Appendix

Table 17: Per-model accuracy (%) on the headroom slice (MMLU-Pro) and the contamination slice (GSM-Symbolic): Solo, Debate (

3\times 3

), and SC-9, seed 42, 100 problems, all 23 models.

	wall-clock (min)				debate/SC-9 ratio
Task	Solo	Debate	SC-9	Persona	clock	gen. tokens	all tokens
Math	4	11	8	14	1.34 $\times$	1.18 $\times$	2.34 $\times$
GSM8K	6	23	18	28	1.32 $\times$	0.84 $\times$	3.36 $\times$
MMLU	7	27	16	34	1.74 $\times$	0.93 $\times$	3.51 $\times$
CSQA	5	21	12	30	1.82 $\times$	1.10 $\times$	3.80 $\times$
Biography	4	17	9	19	1.95 $\times$	1.26 $\times$	4.09 $\times$

Appendix

Table 18: Mean wall-clock minutes per 100-problem job (biography: 40 subjects) on the 2

\times

RTX 3090 workstation, pooled over the 23-model pool at seed 42, plus token-level ratios computed by re-tokenizing every stored conversation with each model’s own tokenizer (median over the 23 models’ complete debate/SC file pairs).

Model	combo $\rho$	ladder $\rho$	rung-0 pctl	MaxDet pctl
gemma-4-12B-it	0.814	0.794	0.18	99.86
gemma-4-26B-A4B-it-FP8-dyn	0.835	0.964	0.12	99.96
granite-4.1-8b	0.895	0.964	0.39	99.98
LFM2.5-1.2B-Instruct	0.923	0.988	0.05	99.82
LFM2.5-8B-A1B	0.877	0.818	0.05	100.00
Llama-3.2-3B-Instruct	0.893	0.879	0.45	99.99

Appendix

Table 19: Robustness metrics of persona diversity. Per model: Spearman correlation of MaxMin (minimum pairwise cosine distance) vs. log-det over all

\binom{50}{3}=19{,}600

candidate trios (“combo

\rho

”); Spearman of the ladder teams’ MaxMin percentiles against rung (“ladder

\rho

”); and the percentile of the rung-0 and MaxDet teams under the MaxMin ranking.

Callsign	Description
cryptographer	a nihilistic cryptographer who only trusts solutions verifiable by zero-knowledge proofs
baroque	a Baroque music theorist fixated on harmonic counterpoint and structural symmetry
meteorologist	a chaotic systems meteorologist who views all certainty as a transient statistical anomaly
xenolinguist	a hard-science fiction xenolinguist obsessed with logical consistency and species-specific syntax
cartographer	a medieval cartographer whose primary concern is establishing clear boundaries and known territories
neuropharm	a neuropharmacologist who analyzes all input as complex patterns of reward and aversion chemicals

Appendix

Table 23

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