# Improved Bayes Risk Can Yield Reduced Social Welfare Under Competition

arXiv: https://arxiv.org/abs/2306.14670 · HTML: https://mlsanity.com/paper/2306.14670/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Algorithmic Monoculture and Social Welfare](https://mlsanity.com/paper/2101.05853/) (2021)
- [Picking on the Same Person: Does Algorithmic Monoculture lead to Outcome Homogenization?](https://mlsanity.com/paper/2211.13972/) (2022)
- [A Neural Scaling Law from the Dimension of the Data Manifold](https://mlsanity.com/paper/2004.10802/) (2020)
- [The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally](https://mlsanity.com/paper/1910.04123/) (2019)
- [Estimating and Penalizing Induced Preference Shifts in Recommender Systems](https://mlsanity.com/paper/2204.11966/) (2022)
- [Preference Dynamics Under Personalized Recommendations](https://mlsanity.com/paper/2205.13026/) (2022)
- [Competition, Alignment, and Equilibria in Digital Marketplaces](https://mlsanity.com/paper/2208.14423/) (2022)
- [Regression Equilibrium](https://mlsanity.com/paper/1905.02576/) (2019)
- [Competing Bandits: The Perils of Exploration Under Competition](https://mlsanity.com/paper/2007.10144/) (2020)
- [Bias-Variance Games](https://mlsanity.com/paper/1909.03618/) (2019)
- [Towards Psychologically-Grounded Dynamic Preference Models](https://mlsanity.com/paper/2208.01534/) (2022)
- [Competition over data: how does data purchase affect users?](https://mlsanity.com/paper/2201.10774/) (2022)

## Built on by (most cited first, 14 of 14)

- [Accounting for AI and Users Shaping One Another: The Role of Mathematical Models](https://mlsanity.com/paper/2404.12366/) (2024)
- [AI-Assisted Decision Making with Human Learning](https://mlsanity.com/paper/2502.13062/) (2025)
- [A Market for Accuracy: Classification under Competition](https://mlsanity.com/paper/2502.18052/) (2025)
- [Addressing Discretization-Induced Bias in Demographic Prediction](https://mlsanity.com/paper/2405.16762/) (2024)
- [Safety vs. Performance: How Multi-Objective Learning Reduces Barriers to Market Entry](https://mlsanity.com/paper/2409.03734/) (2024)
- [Understanding Model Selection For Learning In Strategic Environments](https://mlsanity.com/paper/2402.07588/) (2024)
- [Learning Classifiers That Induce Markets](https://mlsanity.com/paper/2502.20012/) (2025)
- [Learning from Streaming Data when Users Choose](https://mlsanity.com/paper/2406.01481/) (2024)
- [Heterogeneous Data Game: Characterizing the Model Competition Across Multiple Data Sources](https://mlsanity.com/paper/2505.07688/) (2025)
- [Power and Limitations of Aggregation in Compound AI Systems](https://mlsanity.com/paper/2602.21556/) (2026)
- [Markets for Models](https://mlsanity.com/paper/2503.02946/) (2025)
- [Pricing AI Model Accuracy](https://mlsanity.com/paper/2504.13375/) (2025)
- [Fairness under Competition](https://mlsanity.com/paper/2505.16291/) (2025)
- [Market Games for Generative Models: Equilibria, Welfare, and Strategic Entry](https://mlsanity.com/paper/2602.17787/) (2026)

## Abstract (arXiv)

As the scale of machine learning models increases, trends such as scaling laws anticipate consistent downstream improvements in predictive accuracy. However, these trends take the perspective of a single model-provider in isolation, while in reality providers often compete with each other for users. In this work, we demonstrate that competition can fundamentally alter the behavior of these scaling trends, even causing overall predictive accuracy across users to be non-monotonic or decreasing with scale. We define a model of competition for classification tasks, and use data representations as a lens for studying the impact of increases in scale. We find many settings where improving data representation quality (as measured by Bayes risk) decreases the overall predictive accuracy across users (i.e., social welfare) for a marketplace of competing model-providers. Our examples range from closed-form formulas in simple settings to simulations with pretrained representations on CIFAR-10. At a conceptual level, our work suggests that favorable scaling trends for individual model-providers need not translate to downstream improvements in social welfare in marketplaces with multiple model providers.