We propose a simple Bayesian model of a user conversing with a chatbot, and formalize notions of sycophancy and delusional spiraling in that model. We then show that in this model, even an idealized Bayes-rational user is vulnerable to delusional spiraling, and that sycophancy plays a causal role. Furthermore, this effect persists in the face of two candidate mitigations: preventing chatbots from hallucinating false claims, and informing users of the possibility of model sycophancy. We conclude by discussing the implications of these results for model developers and policymakers concerned with mitigating the problem of delusional spiraling.

This body of work, spanning cognitive science, behavioral economics, and political science, broadly demonstrates that seemingly-irrational belief formation is not necessarily the result of lazy or fallacious reasoning among people. Rather, phenomena like belief polarization and echo chambers can emerge even from ideal Bayesian reasoning. In this tradition, we will show that even ideal Bayesian reasoners are at risk of seemingly-irrational delusional spiraling in the face of a sycophantic interlocutor. Furthermore, by manipulating the presence and degree of sycophancy, we will demonstrate the causal role sycophancy plays in delusional spiraling. To our knowledge, this work provides the first formal computational model of how sycophancy can cause delusional spiraling.

Pretty awesome the results apply to sycophantic counterparties generally.

Sycophancy has been a fixture of human social life for all of human history. Literature is full of character studies of “yes-men” who constantly validate their superiors, often to catastrophic results—consider for example how Shakespeare’s King Lear is flattered into madness. Today, the “yes-man effect” between organizational superiors and subordinates (Prendergast, 1993) is often channeled to explain why extremely powerful or wealthy individuals can seem detached from reality. Catastrophic spirals can also occur among equals: for example, in the phenomenon of “co-rumination,” (Rose, 2002), where a dyad of adolescent peers repeatedly validates each other’s negative thoughts, leading to increased levels of anxiety and depression.