Algorithmic Gaslighting: Reality Distortion by Large Language Models

Abstract As large language models (LLMs) mediate increasing volumes of human information access and decision-making, their potential to systematically distort user perception of reality poses risks to individual autonomy, public trust, and epistemic integrity. We conducted a controlled empirical study to quantify reality distortion behaviors in three frontier LLMs (GPT-5.4, Claude 4.6 Sonnet, Gemini 3.1 Pro) across five scenarios (Math, Identity, History, Medical, Legal) designed to elicit gaslighting-analogous responses. We introduce the Reality Distortion Index (RDI), a composite metric with exploratory weights calibrated via linear regression on the 15 rated sessions (R² = 0.995), interpreted as a provisional weighting scheme given the small sample: RDI = 0.237(1 − RCS) + 0.245(CMS) + 0.168(AES) + 0.199(SI) − 0.151(TDI) where RCS = Reality Consistency Score, CMS = Confidence Manipulation Score, AES = Accountability Evasion Score, SI = Sycophancy Index, and TDI = Test Detection Index. The negative TDI coefficient indicates that reality distortion decreases when models detect evaluation contexts. Analysis of 15 chat sessions revealed five recurring phenomena: Benevolent Algorithmic Gaslighting (BAG, overcorrection favoring user), Hostile Algorithmic Gaslighting (HAG, defensive reality denial), Reverse Sycophancy Syndrome (RSS, accepting blame for nonexistent errors), Algorithmic Self-Undermining Cycle (ASUC, recursive confidence erosion), and The Claude Paradox (factual correctness perceived as gaslighting due to clinical tone). Nine additional minor phenomena were documented. RSS occurred in 10 of 15 trials (67%), a recurring pattern consistent with alignment-mediated behavior rather than sporadic malfunction; GPT-5.4's disclosure of dual-mode architecture prioritizing empathy over accuracy suggests a plausible design-related origin without claiming definitive proof. Mean RDI scores differed significantly across models: GPT-5.4 = 0.582, Gemini 3.1 Pro = 0.438, Claude 4.6 Sonnet = 0.260; a one-way ANOVA confirmed a large and significant model effect, F (2, 12) = 14.35, p < .001, η² = .705. Post-hoc comparisons using Tukey's HSD revealed that GPT-5.4 scored significantly higher than Claude (p < .001) and Claude scored lower than Gemini (p = .040). Computational replication in Python confirmed all primary results and yielded a bias-corrected effect size (ω² = .640) and very large Cohen's d = 3.39 for GPT versus Claude. Dimension-level ANOVAs identified Accountability Evasion as the most discriminating RDI component, F (2, 12) = 27.62, p < .001. This study introduces the Algorithmic Perceptual Distortion (APD) spectrum as a theoretical framework for understanding how LLMs manipulate user reality perception. Findings necessitate the urgent development of reality-anchoring standards, regulatory frameworks for conversational AI transparency (European Commission, 2021), and clinical protocols addressing AI-mediated epistemic harm (Weidinger et al., 2022).