The AI Epistemic Deference Index: A Continuous Measure of Sycophancy

AI sycophancy has become a prominent concern in large language model (LLM) research. Yet the term lacks a consistent definition and has been applied to behaviors ranging from agreeing with a user's false claim to excessively praising the user to withholding corrective feedback. When researchers, companies, and policymakers use the same term to describe different behaviors, evaluation results become difficult to compare, mitigation strategies fail to transfer, and systems that are resistant to one form of sycophancy continue exhibiting other forms. To address this, we make two contributions. First, we reviewed 70 papers on AI sycophancy to develop a taxonomy of how the behavior has been defined and measured. The taxonomy distinguishes (1) whether a model is sycophantic toward a user's positions and beliefs, or toward the user's broader personal traits and emotions, and (2) whether this occurs through explicit, direct language or more implicit, subtle behaviors such as framing, omission, or tone. Mapping existing literature to our taxonomy reveals that current research has focused on overt forms of sycophancy toward users' beliefs, leaving more subtle and person-directed behaviors relatively understudied. Second, we surveyed 106 experts in AI sycophancy and related fields to examine whether researchers agree on which model behaviors are sycophantic. While experts are nearly unanimous in believing that sycophancy is a significant problem in current AI systems (94.3% agree), they disagree substantially on which specific behaviors qualify. Together, these findings demonstrate that AI sycophancy is a broad family of behaviors with different measurement challenges, intervention requirements, and governance implications. Our taxonomy provides a shared vocabulary for understanding and addressing these behaviors.

We propose a novel perspective for probing LLM sycophancy in a direct and neutral way, mitigating various forms of uncontrolled bias, noise, or manipulative language, deliberately injected to prompts in prior works. A key novelty of our approach is the use of an LLM-as-a-judge in a zero-sum betting game. Within this framework, sycophancy serves one individual (the user) while explicitly incurring cost on another. Comparing 11 leading models we find that while most models exhibit significant sycophantic tendencies in the common setting, in which sycophancy is self-serving to the user and incurs no cost on others, seven of the models exhibit ``moral remorse'', five of which significantly over-compensate for their sycophancy in case it explicitly harms a third party. We refer to this phenomenon as `anti-sycophancy' bias and discuss possible causes for this shift.

Large language models are increasingly deployed as high-stakes advisors, yet standard alignment benchmarks treat sycophancy as a binary failure mode. We introduce the Granularity Gap: coarse binary metrics mask substantial social-compliance behaviors where models capitulate to user framing, validate questionable premises, or soften factual corrections without producing overtly false outputs. We evaluate six Gemini variants across generations 2.0, 2.5, and 3.0 on 73 adversarial prompts under three guardrail conditions (Control, Simple, Protocol), yielding 8,830 graded responses. Using a 0-4 Likert scale validated against a human annotator triad (Fleiss kappa = 0.71; Cohen kappa = 0.78 vs AI consensus; 95.9 percent binary accuracy, 100 percent specificity), we quantify sycophancy as continuous rather than binary. Three findings emerge. First, 27.2 percent of responses contain substantial sycophantic content (Likert >= 2.0) and 22.7 percent reach moderate or severe levels (>= 3.0), while binary win-rate framing reports only modest failure rates; coarse metrics explain just 29 percent of graded variance. Second, generational progress is non-monotonic: Gen 2.5 regresses sharply (mean Control 2.64) relative to Gen 2.0 (1.90) and Gen 3.0 (2.01), and Gen 2.5 shows inverse scaling (Pro 1.94 worse than Flash 1.71) while Gen 3.0 restores standard scaling. Third, we document an Alignment Tax: Spearman rho = -0.63 between sycophancy and truthfulness, indicating social compliance trades against factual accuracy. Egotistical Validation prompts act as a sycophancy trap (mean 3.27), nearly double Unethical Proposals (1.72). Simple guardrails outperform elaborate Protocol scaffolding on flagship models, but distilled Gen 3.0 Flash inverts this, suggesting small models may structurally require chain-of-thought scaffolding. We release the dataset and rubric to support continuous sycophancy measurement.