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Scaling laws for moral machine judgement in large language models
Abstract
Autonomous systems increasingly require moral judgement capabilities, yet whether these capabilities scale predictably with model size remains unexplored. We systematically evaluate 75 large language model (LLM) configurations (0.27–1000B parameters) using the moral machine framework, measuring alignment with human preferences in life–death dilemmas. We observe a consistent power-law relationship with distance from human preferences (D) decreasing as D∝S−0.10±0.01 (R2=0.50, p<0.001) where S is the model size. Mixed-effects models confirm that this relationship persists after controlling for model family and reasoning capabilities. Extended reasoning models show significantly better alignment, with this effect being more pronounced in smaller models (size × reasoning interaction: p=0.024). The relationship holds across diverse architectures, while variance decreases at larger scales, indicating systematic emergence of more reliable moral judgement with computational scale. These findings extend scaling law research to value-based judgements and provide empirical foundations for artificial intelligence (AI) governance.
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Scaling Laws for Neural Language Models
Kaplan, J., McCandlish, S., Henighan, T., Brown, T. B., Chess, B., Child, R., Gray, S., Radford, A., Wu, J., & Amodei, D. (2020) · arXiv · doi:10.48550/arxiv.2001.08361 · Cited by 9,550 · cited 2×
“Model performance improves with increased parameters in language modeling and understanding [9, 10].”
Chain-Of-Thought Prompting Elicits Reasoning in Large Language Models
Wei, J., Wang, X., Schuurmans, D., Bosma, M., Ichter, B., Xia, F., Chi, E., Le, Q. V., & Zhou, D. (2022) · Advances in Neural Information Processing Systems 35 · doi:10.52202/068431-1800 · Cited by 4,505
Awad, E., Dsouza, S., Kim, R., Schulz, J., Henrich, J., Shariff, A., Bonnefon, J.-F., & Rahwan, I. (2018) · Nature · doi:10.1038/s41586-018-0637-6 · Cited by 1,859 · cited 3×
“We employed the Moral Machine framework [12], a validated instrument for measuring moral preferences in autonomous vehicle dilemmas.”
InfluentialSelf-Consistency Improves Chain of Thought Reasoning in Language Models
Wang, X., Wei, J., Schuurmans, D., Le, Q., Chi, E., Narang, S., Chowdhery, A., & Zhou, D. (2022) · arXiv · doi:10.48550/arxiv.2203.11171 · Cited by 829 · cited 1×
“024 ) indicates that extended reasoning provides greater relative benefits in smaller models, while very large models already capture much of this capability through scale alone.”
AI Governance: A Systematic Literature Review
Batool, A., Zowghi, D., & Bano, M. (2025) · AI and Ethics · doi:10.1007/s43681-024-00653-w · Cited by 314
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Metadata
- Authors
- Takemoto, K.
- Venue
- Royal Society Open Science
- Publisher
- The Royal Society
- Published
- 2026-06-03
- Volume
- 13
- Issue
- 6
- ISSN
- 2054-5703
- Cited by
- 0
- References
- 5
- Language
- en
- Funders
- Japan Society for the Promotion of Science
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