The Dialectical Friction Index: A Metric for Quantifying Algorithmic Sycophancy in Argumentative Dialogues

Abstract

Disagreement plays a constitutive role in argumentation, anchoring conflict and enabling reasons to be weighed. Yet, interactions with generative language models often suppress it, leading to the phenomenon of algorithmic sycophancy. While often framed as an issue of alignment or politeness, this paper argues that sycophancy represents a fundamental failure in the structure of argumentative dialogue. To this end, we propose a theoretical conceptualisation of algorithmic sycophancy as a dialogical impairment: a systematic inability to perform specific dialogical acts required to anchor conflict relations. Drawing on Inference Anchoring Theory, we demonstrate that sycophancy is not merely a psychological stance but a structural defect where the transition probabilities for friction moves, such as challenging and questioning, approach zero, rendering the emergence of deep argumentative graphs impossible. We provide a formal definition of this pathology and propose an operationalisation for detecting these dialogical impairments in generative agents. We validate the method in two studies, across formal and informal dialogue contexts, using two generative models. Results provide evidence for the usefulness of the metric in diagnosing and describing the sycophantic behaviour of generative agents.