Do LLMs Exhibit Human-Like Bayesian Judgment and Moral Inconsistency? A Replication Study of Cao et al. (2019)

This study replicates Cao et al. (2019) People Make the Same Bayesian Judgment They Criticize in Others using Large Language Models (LLMs) rather than human participants. Cao et al. (2019) found that humans exhibit an inconsistency in their responses - they make statistically accurate Bayesian judgments about profession likelihood based on gender, while simultaneously condemning others who make identical judgments. We examine whether contemporary LLMs (Claude Sonnet 3.7 and GPT-4o) display similar patterns of inconsistency. By comparing LLMs with different training methods and company missions, we attempt to identify whether algorithmic systems trained on human data inherit our inconsistencies or behave as more consistently Bayesian agents. This research helps our understanding of alignment in LLM systems, particularly regarding how different approaches to LLM development affect statistical reasoning versus encoded social norms.