Improved Bayes Risk Can Yield Reduced Social Welfare Under Competition

TL;DR

This paper shows that in competitive markets, increasing model scale and data quality can paradoxically reduce overall social welfare and predictive accuracy across users, challenging traditional scaling law assumptions.

Contribution

It introduces a model of competition for classification tasks demonstrating how scaling trends may harm social welfare in multi-provider settings.

Findings

Improving data representation quality can decrease social welfare in competitive markets.

Competitive dynamics can cause non-monotonic or decreasing accuracy with scale.

Simulations on CIFAR-10 illustrate the impact of competition on predictive accuracy.

Abstract

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.