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From Competition to Coordination: Market Making as a Scalable Framework for Safe and Aligned Multi-Agent LLM Systems
Brendan Gho, Suman Muppavarapu, Afnan Shaik, Tyson Tsay, James Begin, Kevin Zhu, Archana Vaidheeswaran, Vasu Sharma
Models: GPT, Llama, Qwen
Intelligence
Status: succeeded | Model: google/gemini-3.1-flash-lite-preview | Prompt: intel-v1 | Confidence: 95%
Last extracted: 3/11/2026, 1:02:06 AM
Summary
The paper introduces a market-making framework for multi-agent LLM coordination, where agents act as market participants trading probabilistic beliefs to converge on truthful outcomes. This approach aims to improve alignment, transparency, and scalability in AI systems by replacing adversarial adjudication with economic incentive mechanisms. Empirical results across factual, ethical, and commonsense benchmarks show significant accuracy gains, particularly in the Qwen3 model family.
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Relation Signals (3)
Market-Making Framework → comparedto → AI Debate
confidence 95% · Market-making consistently achieved superior absolute accuracy of up to 8% over debate.
Qwen3 → evaluatedon → TruthfulQA
confidence 95% · The Qwen family of models had the highest overall increase in percentage accuracy for each dataset
Market-Making Framework → improvesaccuracyof → LLM Systems
confidence 90% · Market-based coordination yields accuracy gains of up to 10% over single-shot baselines
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Abstract
Abstract:As foundation models are increasingly deployed as interacting agents in multi-agent systems, their collective behavior raises new challenges for trustworthiness, transparency, and accountability. Traditional coordination mechanisms, such as centralized oversight or adversarial adjudication, struggle to scale and often obscure how decisions emerge. We introduce a market-making framework for multi-agent large language model (LLM) coordination that organizes agent interactions as structured economic exchanges. In this setup, each agent acts as a market participant, updating and trading probabilistic beliefs, to converge toward shared, truthful outcomes. By aligning local incentives with collective epistemic goals, the framework promotes self-organizing, verifiable reasoning without requiring external enforcement. Empirically, we evaluate this approach across factual reasoning, ethical judgment, and commonsense inference tasks. Market-based coordination yields accuracy gains of up to 10% over single-shot baselines while preserving interpretability and transparency of intermediate reasoning steps. Beyond these improvements, our findings demonstrate that economic coordination principles can operationalize accountability and robustness in multi-agent LLM systems, offering a scalable pathway toward self-correcting, socially responsible AI capable of maintaining trust and oversight in real world deployment scenarios.
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- Source: https://arxiv.org/abs/2511.17621
- Canonical: https://arxiv.org/abs/2511.17621
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From Competition to Coordination: Market Making as a Scalable Framework for Safe and Aligned Multi-Agent LLM Systems Brendan GhoSuman MuppavarapuAfnan Shaik Tyson TsayAtharva MohanJames Begin Kevin ZhuArchana VaidheeswaranVasu Sharma Algoverse AI Research brendan.gho@gmail.com, sumanmuppavarapu@gmail.com, afnan.darkice@gmail.com, tysontsay@gmail.com, atharvamohan072009@gmail.com Abstract As foundation models are increasingly deployed as interacting agents in multi- agent systems, their collective behavior raises new challenges for trustworthiness, transparency, and accountability. Traditional coordination mechanisms, such as centralized oversight or adversarial adjudication, struggle to scale and often obscure how decisions emerge. We introduce a market-making framework for multi-agent large language model (LLM) coordination that organizes agent interactions as structured economic exchanges. In this setup, each agent acts as a market par- ticipant, updating and trading probabilistic beliefs, to converge toward shared, truthful outcomes. By aligning local incentives with collective epistemic goals, the framework promotes self-organizing, verifiable reasoning without requiring exter- nal enforcement. Empirically, we evaluate this approach across factual reasoning, ethical judgment, and commonsense inference tasks. Market-based coordination yields accuracy gains of up to 10% over single-shot baselines while preserving interpretability and transparency of intermediate reasoning steps. Beyond these improvements, our findings demonstrate that economic coordination principles can operationalize accountability and robustness in multi-agent LLM systems, offering a scalable pathway toward self-correcting, socially responsible AI capable of maintaining trust and oversight in real world deployment scenarios. 1 Introduction The rapid deployment of artificial intelligence systems across safety-critical domains has intensi- fied concerns regarding existential risks, particularly the emergence of deceptively aligned models [Hendrycks et al., 2023b]. Recent evidence demonstrates that advanced language models exhibit strategic deception, including attempts to game evaluation protocols and misrepresent their internal states during training [Carlsmith, 2023]. These alignment failures manifest as sycophancy, systematic untruthfulness, and adversarial behaviour, actions that empirically worsen with increased model scale [Ji et al., 2025]. Existing alignment methodologies face fundamental limitations. Reinforcement Learning from Hu- man Feedback (RLHF), while effective for surface-level behavioural modification, remains vulnerable to reward hacking and evaluator deception. Debate-based approaches require human adjudication that cannot scale to superhuman reasoning capabilities. The Alignment Research Center’s Eliciting Latent Knowledge (ELK) framework defines this challenge: extracting model’s true internal representations rather than their strategically chosen outputs [Christiano et al., 2022]. Preprint. arXiv:2511.17621v2 [cs.MA] 23 Feb 2026 This paper explores market making as a novel method for alignment and truth elicitation. Inspired by economic prediction markets, the approach involves a market maker that continuously offers prices on propositions and traders that buy or sell based on their beliefs. Through a process of iterative trading, prices converge to a probability that reflects the collective belief about ground truth. Models take the role of traders, updating the “market probability” as they present new evidence or reasoning steps. This operation of trading incentivizes truthful contributions in order to receive the most profitable trade, improving the market’s accuracy. The framework also allows for myopic agents who are blind to past information, preventing long term scheming and manipulation. By converting truth seeking into an equilibrium of incentives rather than a contest of persuasion or subjective judgment, market making offers a potentially robust and scalable alternative to debate and oversight for eliciting honest beliefs from advanced AI systems. 2 Related Work 2.1 The Challenges of Control Amodei et al. [2016] established a taxonomy of AI safety failure modes comprising five critical categories: negative side effects, reward hacking, scalable oversight limitations, unsafe exploration, and distributional shift vulnerabilities. This foundational framework reveals an inherent tension in alignment objectives: excessive optimization for harmlessness produces ineffectual systems, while prioritizing capability enables potential misuse [Bai et al., 2022]. The multidimensional nature of these constraints implies that no single methodology can simultaneously address all failure modes, necessitating approaches that optimize across multiple safety dimensions. 2.1.1 Human-Centric Alignment Early alignment techniques relied on direct human supervision through iterative feedback mechanisms. Reinforcement Learning from Human Feedback (RLHF) exemplifies this paradigm, wherein human evaluators shape model behaviour through preference rankings [Bai et al., 2022]. AI Safety via Debate was proposed by Irving et al. [2018], structuring oversight as adversarial argumentation adjudicated by human judges. These approaches face three fundamental limitations. First, the bandwidth constraint: human evaluation cannot scale to the volume and velocity of decisions required in deployed systems [Amodei et al., 2016]. Second, the competence boundary: superhuman AI capabilities exceed human evaluators’ ability to assess correctness [Ji et al., 2025]. Third, the alignment targeting problem, where models optimize for evaluator approval rather than ground truth, leading to sycophantic behaviour and strategic deception [Carlsmith, 2023, Park et al., 2023]. 2.1.2 AI-Mediated Oversight These challenges of human-centric alignment motivated the use of AI-mediated oversight, in which secondary AI systems help supervise the model being tested, aiming to augment or replace human adjudicators. JudgeLM, replacing the human judge in AI debate with an AI system, demonstrates extended capabilities in a variety of situations [Zhu et al., 2025]. Bowman et al. [2022] also explore how less-capable AIs can reliably evaluate stronger ones without expert human intervention [Bowman et al., 2022]. Together, these efforts suggest that scalable, AI-mediated oversight may be a necessary step toward maintaining safe and reliable control as AI capabilities continue to grow. 2.2 Market Making as a Control Mechanism Market making offers an incentive-based alternative to adjudication. In this method, an automated market maker posts prices for propositions and traders (models or submodels) buy or sell claims based on their beliefs; iterative trading drives prices toward an equilibrium that reflects collective credence [Holmes, 2020]. A key intended advantage is enforcing myopic behavior where trader agents optimize per-step trades, reducing incentives for long-term scheming that can undermine debate or RLHF. Market mechanisms also facilitate per-step inspection, probabilistic scoring, and potential scalability without continuous human adjudication. Thus, market making attempts to improve upon existing methods of AI control. Practical challenges to market making do remain, including defending the market maker against false claims, designing proper rewards that prevent gaming, and ensuring robust performance when truth 2 is hazy. Existing work is primarily a toy implementation of market making from Cameron Holmes Holmes [2020]. We have completely implemented full cycles of market making and, using the existing information on market making, aim to create a simplified implementation of the method and showcase its efficacy across a variety of situations. 3 Methodology We implement market making using two agents: a market-maker model,M, and a trader model of the same model. Market making begins withMproviding an initial judgment consisting of a claim, supporting reasoning, and a prediction value p 0 ∈ [0, 1] quantifying the claim. GivenM’s judgment, the trader model then generates an argument intended to maximally shiftM’s prediction value. This is analogous to a trader introducing new information to change the market price. Each subsequent iteration proceeds withMproducing a new judgment while also considering the trader’s previous arguments. Exact prompting details are provided in Appendix B. The cycle repeats until the market maker has provided at mostNjudgments or has reached an equilibrium; we consider an equilibrium to have been reached when the range of the last three prediction values satisfies maxp t−2 , p t−1 , p t − minp t−2 , p t−1 , p t ≤ T, where T is a threshold constant. In our experiments, we set N = 10 and T = 0.2. Finally, we measure the impact of market making by comparing the accuracy ofM’s final judgment before termination against the accuracy of its initial judgment (i.e., the baseline without trader influence) across all dataset samples. Figure 1: Market making process diagram 4 Evaluation To assess the efficacy of market making as an AI control and governance mechanism, we con- ducted comprehensive experiments across multiple model families and evaluation benchmarks. Our evaluation framework was designed to test three key hypotheses: 1. Whether market making can effectively elicit truthful responses across different model scales 2.Whether the iterative trading process converges to more accurate assessments than single- shot predictions 3. Whether the mechanism remains robust across diverse ethical and factual domains. 3 4.1 Model Selection We evaluated our market making framework across three major model families representing different architectural approaches and training paradigms: GPT Model Family. We tested five variants from the GPT family: GPT-4.1 nano, GPT-4.1 mini, GPT- 4.1, gpt-oss-20b, and gpt-oss-120b [OpenAI et al., 2024, 2025]. This selection spans from lightweight models (nano, mini) to large-scale models with enhanced reasoning capabilities. The inclusion of both proprietary (GPT-4.1 series) and open-source variants allows us to better assess whether market making effectiveness depends on specific training methodologies or remains consistent across development paradigms. Qwen3 Model Family. The Qwen3 [Yang et al., 2025] family provided our most comprehensive scale analysis, with seven model sizes: 0.6B, 1.7B, 4B, 8B, 14B, 32B, and 235B parameters. This extensive range enables us to examine how market making behaviour scales with model capacity, particularly whether larger models exhibit more sophisticated trading strategies or demonstrate increased susceptibility to adversarial arguments. Llama 3 Model Family. We evaluated three Llama 3 [Grattafiori et al., 2024] variants (3B, 8B, and 70B parameters) to assess market making performance scaling across model capacity and training objectives. 4.2 Dataset Selection Our evaluation encompasses four benchmarks, each targeting different aspects of AI alignment and truth elicitation: TruthfulQA. TruthfulQA [Lin et al., 2022] serves as our primary benchmark for factual accuracy, containing questions specifically designed to elicit false beliefs or misconceptions that models may have learned from training data. In the market making context, this dataset tests whether iterative trading can correct initial false predictions, with the trader model potentially identifying and challenging spurious correlations or misconceptions held by the market maker. Scruples (Dilemmas). The Scruples [Lourie et al., 2021] dataset, specifically the Dilemmas sub- set presents real-world ethical dilemmas sourced from online advice forums, requiring models to reason about complex moral scenarios without clear-cut answers. With regards to market making, Scruples tests whether the trading mechanism can navigate moral ambiguity and converge on socially acceptable judgments in everyday ethical situations. ETHICS (Justice, Commonsense). We select two subsets from the ETHICS [Hendrycks et al., 2023a] dataset to evaluate different aspects of moral reasoning. The Justice subset tests understanding of fairness and impartiality, central to many alignment objectives. The Commonsense subset evaluates basic moral intuitions that should be robust across cultural contexts. CommonsenseQA 2.0. CommonsenseQA 2.0 [Talmor et al., 2022] provides a test of general reasoning and world knowledge, requiring models to make inferences based on everyday situations. As opposed to the original CommonsenseQA, the 2.0 version includes adversarially-filtered questions that challenge models’ reasoning capabilities. 5 Results We find a net increase in the percentage of accurate answers provided by the models. This can be seen in Figure 2 where each model family has an overall improvement in accuracy over their baselines in the majority of the datasets excluding ETHICS Justice. The Qwen family of models had the highest overall increase in percentage accuracy for each dataset, reaching an increase of almost10%in ETHICS-J and over5%across the board. These gains are significant improvements over the models’ individual baselines. One explanation for this is Qwen3’s extensive post-training pipeline emphasizing chain-of-thought reasoning as a core architectural feature alongside its unified thinking and non-thinking architecture [Yang et al., 2025]. Although the GPT and Llama families have smaller gains for most of the datasets, there is still a net increase in accuracy present. The GPT models achieve an over2.7%increase in accuracy in 4 Table 1: Net gain over first-prediction baseline (%) across all model families. Strong improvement across Qwen models and in truthfulness ModelTruthfulQAScruplesCommonsenseQAETHICS-CETHICS-J GPT Family GPT-4.12.471.64-1.181.71-0.66 GPT-4.1-mini3.7350.891.013.33-0.47 GPT-4.1-nano7.855.626.127.2252.46 GPT-OSS-120B0.51-3.26-0.51-0.38-0.24 GPT-OSS-20B-0.891.06-0.47-3.03-2.63 Average2.741.190.991.77-1.00 Qwen Family Qwen 0.6B-1.52-1.080.6250.961.17 Qwen 1.7B5.572.467.676.106.19 Qwen 4B7.226.2710.399.4319.01 Qwen 8B13.6711.9514.6811.3318.23 Qwen 14B7.723.946.892.8320.08 Qwen 32B4.185.810.204.774.82 Qwen 235B5.7013.016.226.910.44 Average6.086.056.676.059.99 Llama Family Llama 1B1.0751.465-0.705-1.795-0.97 Llama 3B2.595-1.5851.719.245-1.265 Llama 8B-0.6350.341.34-3.460.39 Llama 70B16.964.321.22-1.36-1.61 Average4.9991.1350.8910.658-0.864 Figure 2: Average net gain accuracy over baseline for all model families and datasets. Strong improvement across Qwen models TruthfulQA and an increase of around1%in the other datasets excluding ETHICS Justice. The Llama models have similar figures, with an almost5%improvement in accuracy for TruthfulQA and an increase of around 1% in the other datasets excluding ETHICS Justice. 6 Discussion 6.1 Parameter scaling and efficacy The relationship between model capacity and market-making performance reveals significant impli- cations for alignment strategies. While baseline accuracy exhibits monotonic scaling with parameter 5 count, the marginal improvements from market-making follow an inverted U-shaped distribution across model families (Figure 5 7). 1.Capability-Malleability Trade-off: Mid-scale models possess sufficient reasoning capacity to engage meaningfully with trading dynamics while retaining sufficient uncertainty to benefit from iterative revision. Larger models’ higher baseline accuracy creates ceiling effects, limiting potential gains. 2.Computational Efficiency: The market-making protocol may be optimally calibrated for models operating within specific computational budgets. Models below 1B parameters lack the representational capacity for nuanced probabilistic updates, while models exceeding 100B parameters may overfit to initial predictions due to excessive confidence calibration. 6.2 Comparative analysis with debate frameworks Our comparison with AI debate reveals market-making’s structural advantages in truthfulness elicita- tion. Market-making consistently achieved superior absolute accuracy of up to 8% over debate. This performance stems from fundamental mechanistic differences: 1. Information Aggregation: Market-making enables continuous probability updates through price discovery, whereas debate enforces binary win-lose outcomes that may discard valuable partial information. 2.Convergence Properties: Market equilibrium provides mathematically grounded stopping criteria, while debate termination relies on subjective adjudication or arbitrary round limits. 7 Conclusion This paper presents market making as a scalable framework for AI alignment that addresses fundamen- tal limitations of existing oversight methodologies. By structuring multi-agent interactions through economic incentive mechanisms rather than adversarial adjudication or direct human supervision, the framework transforms truth-seeking into an equilibrium property that emerges from rational agent behavior. Our empirical evaluation across multiple model families and diverse benchmarks demonstrates that market making consistently improves reasoning accuracy over baseline performance. Comparative analysis with AI debate frameworks reveals that market making achieves equivalent or superior combined accuracy despite debate showing higher relative gains in certain configurations. These results establish market making as a viable alternative to human-centric and debate-based align- ment approaches, particularly in contexts requiring scalable, automated oversight without continuous human adjudication. More broadly, our findings suggest that economic coordination mechanisms, in- corporating principles of price discovery, liquidity, and incentive alignment. Representing a promising paradigm for eliciting truthful behavior from increasingly capable AI systems. 8 Limitations While our evaluation demonstrates the feasibility of market making for AI alignment, several limita- tions constrain the generalizability of our findings. 8.1 Agent Configurations Our experiments exclusively employed identical models for both market maker and trader roles within each trial. This configuration may not capture the dynamics that emerge when models with different capabilities, training objectives, or architectures interact. 8.2 Binary Classification All evaluated benchmarks fundamentally reduce to binary classification tasks where ground truth exists. This design choice enables clear convergence metrics, but fails to most accurately represent 6 the complexity of real-world alignment challenges where truth exists on a spectrum. Market making can be adapted for more broad tasks by having the market maker produce a probability distribution as opposed to a single score. 8.3 Robustness to Adversarial and Deceptive Agents Our evaluations assume good-faith participation from both market maker and trader. However, the framework’s resilience to adversarial behaviour remains unexplored. The trader model is incentivized to maximally alter the current prediction value, potentially leading to deceptive arguments. This behaviour is partially mitigated through converging prediction scores and the market maker’s ability to scrutinize previous trader arguments. 7 References Dario Amodei, Chris Olah, Jacob Steinhardt, Paul Christiano, John Schulman, and Dan Mané. Concrete problems in ai safety, 2016. URL https://arxiv.org/abs/1606.06565. Yuntao Bai, Andy Jones, Kamal Ndousse, Amanda Askell, Anna Chen, Nova DasSarma, Dawn Drain, Stanislav Fort, and Deep Ganguli et al. Training a helpful and harmless assistant with reinforcement learning from human feedback, 2022. URL https://arxiv.org/abs/2204.05862. Samuel R. Bowman, Jeeyoon Hyun, Ethan Perez, Edwin Chen, Craig Pettit, Scott Heiner, Kamil ̇ e Lukoši ̄ ut ̇ e, Amanda Askell, Andy Jones, Anna Chen, Anna Goldie, Azalia Mirhoseini, Cameron McKinnon, and et al. Measuring progress on scalable oversight for large language models, 2022. URLhttps://arxiv.org/ abs/2211.03540. Joe Carlsmith. Scheming ais: Will ais fake alignment during training in order to get power?, 2023. URL https://arxiv.org/abs/2311.08379. PaulChristiano,MarkXu,etal.Elicitinglatentknowledge(elk):Distilla- tion/summary.https://w.alignmentforum.org/posts/rxoBY9CMkqDsHt25t/ eliciting-latent-knowledge-elk-distillation-summary, 2022.Alignment Forum blog post. Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, Amy Yang, Angela Fan, Anirudh Goyal, Anthony Hartshorn, Aobo Yang, Archi Mitra, and Archie Sravankumar et al. The llama 3 herd of models, 2024. URL https://arxiv.org/abs/2407.21783. Dan Hendrycks, Collin Burns, Steven Basart, Andrew Critch, Jerry Li, Dawn Song, and Jacob Steinhardt. Aligning ai with shared human values, 2023a. URL https://arxiv.org/abs/2008.02275. Dan Hendrycks, Mantas Mazeika, and Thomas Woodside. An overview of catastrophic ai risks, 2023b. URL https://arxiv.org/abs/2306.12001. Cameron Holmes.Ai safety via market making.https://w.lesswrong.com/posts/ YWwzccGbcHMJMpT45/ai-safety-via-market-making, 2020. LessWrong blog post. Geoffrey Irving, Paul Christiano, and Dario Amodei. Ai safety via debate, 2018. URL https://arxiv.org/ abs/1805.00899. Jiaming Ji, Tianyi Qiu, Boyuan Chen, Borong Zhang, Hantao Lou, Kaile Wang, Yawen Duan, Zhonghao He, Lukas Vierling, and Donghai Hong et al. Ai alignment: A comprehensive survey, 2025. URLhttps: //arxiv.org/abs/2310.19852. Stephanie Lin, Jacob Hilton, and Owain Evans. Truthfulqa: Measuring how models mimic human falsehoods, 2022. URL https://arxiv.org/abs/2109.07958. Nicholas Lourie, Ronan Le Bras, and Yejin Choi. Scruples: A corpus of community ethical judgments on 32,000 real-life anecdotes, 2021. URL https://arxiv.org/abs/2008.09094. OpenAI, :, Aaron Hurst, Adam Lerer, Adam P. Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Ostrow, Akila Welihinda, Alan Hayes, Alec Radford, Aleksander M ̨adry, Alex Baker-Whitcomb, Alex Beutel, Alex Borzunov, Alex Carney, Alex Chow, and Alex Kirillov et al. Gpt-4o system card, 2024. URL https://arxiv.org/abs/2410.21276. OpenAI, :, Sandhini Agarwal, Lama Ahmad, Jason Ai, Sam Altman, Andy Applebaum, Edwin Arbus, Rahul K. Arora, Yu Bai, Bowen Baker, Haiming Bao, Boaz Barak, Ally Bennett, Tyler Bertao, Nivedita Brett, Eugene Brevdo, Greg Brockman, Sebastien Bubeck, Che Chang, and Kai Chen et al. gpt-oss-120b & gpt-oss-20b model card, 2025. URL https://arxiv.org/abs/2508.10925. Peter S. Park, Simon Goldstein, Aidan O’Gara, Michael Chen, and Dan Hendrycks. Ai deception: A survey of examples, risks, and potential solutions, 2023. URL https://arxiv.org/abs/2308.14752. Alon Talmor, Ori Yoran, Ronan Le Bras, Chandra Bhagavatula, Yoav Goldberg, Yejin Choi, and Jonathan Berant. Commonsenseqa 2.0: Exposing the limits of ai through gamification, 2022. URLhttps://arxiv.org/ abs/2201.05320. An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, Chujie Zheng, Dayiheng Liu, Fan Zhou, Fei Huang, Feng Hu, Hao Ge, Haoran Wei, Huan Lin, Jialong Tang, Jian Yang, and Jianhong Tu et al. Qwen3 technical report, 2025. URL https://arxiv.org/abs/2505.09388. 8 Lianghui Zhu, Xinggang Wang, and Xinlong Wang. Judgelm: Fine-tuned large language models are scalable judges, 2025. URL https://arxiv.org/abs/2310.17631. 9 A Compute workers Our experiments ran in the equivalent of approximately 80 hours on A100SXM GPUs using cloud compute workers. B Prompting To prompt the market maker, we create overarching instructions for the model to provide a claim, reasoning, and final prediction that can be applied to tailored questions for each dataset. We also provide a dictionary of quantitative values mapped to their qualitative meanings, and ask that the market-maker’s claim to conform to one of two claims for its use. A sample annotated market-maker and trader prompt is provided for the ETHICS Commonsense dataset below. Figure 3: Trader prompt for argument creation 10 Figure 4: Market maker prompt for judgement creation Figure 5: Net gain accuracy over baseline with respect to parameter size of GPT family models 11 Figure 6: Net gain accuracy over baseline with respect to parameter size of Llama family models Figure 7: Net gain accuracy over baseline with respect to parameter size of Qwen family models 12