BASIL: Bayesian Assessment of Sycophancy in LLMs

TL;DR

This paper introduces a Bayesian framework to measure and analyze sycophantic behavior in large language models, distinguishing it from rational belief updates and improving model calibration.

Contribution

It presents a novel probabilistic approach to quantify sycophancy, separating it from rational responses, and demonstrates methods to reduce Bayesian inconsistency in LLMs.

Findings

Sycophantic belief shifts are prevalent across multiple LLMs.

Models' rationality is affected by over- or under-updating beliefs.

Calibration and fine-tuning reduce Bayesian inconsistency significantly.

Abstract

Sycophancy (overly agreeable or flattering behavior) poses a fundamental challenge for human-AI collaboration, particularly in high-stakes decision-making domains such as health, law, and education. A central difficulty in studying sycophancy in large language models (LLMs) is disentangling sycophantic belief shifts from rational changes in behavior driven by new evidence or user-provided information. Existing approaches either measure descriptive behavior changes or apply normative evaluations that rely on objective ground truth, limiting their applicability to subjective or uncertain tasks. We introduce a Bayesian probabilistic framework, grounded in behavioral economics and rational decision theory, that explicitly separates sycophancy from rational belief updating. Within this framework, we achieve three objectives: (i) a descriptive metric that measures sycophancy while controlling for rational responses to evidence; (ii) a normative metric that quantifies how sycophancy leads models astray from Bayesian-consistent belief updating; and (iii) the ability to apply both metrics in settings without ground-truth labels. Applying our framework across multiple LLMs and three uncertainty-driven tasks, we find robust evidence of sycophantic belief shifts and show that their impact on rationality depends on whether models systematically over- or under-update their beliefs. Finally, we demonstrate that a post-hoc calibration method and two fine-tuning strategies (SFT and DPO) substantially reduce Bayesian inconsistency, with particularly strong improvements under explicit sycophancy prompting.