Large language models and other highly capable AI systems ease the burdens of deciding what to say or do, but this very ease can undermine the effectiveness of our actions in social contexts. We explain this apparent tension by introducing the integrative theoretical concept of "mental proof," which occurs when observable actions are used to certify unobservable mental facts. From hiring to dating, mental proofs enable people to credibly communicate values, intentions, states of knowledge, and other private features of their minds to one another in low-trust environments where honesty cannot be easily enforced. Drawing on results from economics, theoretical biology, and computer science, we describe the core theoretical mechanisms that enable people to effect mental proofs. An analysis of these mechanisms clarifies when and how artificial intelligence can make low-trust cooperation harder despite making thinking easier.

Dominance hierarchies are group-level properties that emerge from the aggression of individuals. Although individuals can gain critical benefits from their position in a hierarchy, we do not understand how real-world hierarchies form. Nor do we understand what signals and decision-rules individuals use to construct and maintain hierarchies in the absence of simple cues such as size or spatial location. A study of conflict in two groups of captive monk parakeets (Myiopsitta monachus) found that a transition to large-scale order in aggression occurred in newly-formed groups after one week, with individuals thereafter preferring to direct aggression more frequently against those nearby in rank. We consider two cognitive mechanisms underlying the emergence of this order: inference based on overall levels of aggression, or on subsets of the aggression network. Both mechanisms were predictive of individual decisions to aggress, but observed patterns were better explained by rank inference through subsets of the aggression network. Based on these results, we present a new theory, of a feedback loop between knowledge of rank and consequent behavior. This loop explains the transition to strategic aggression and the formation and persistence of dominance hierarchies in groups capable of both social memory and inference.

We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based on maximizing mutual information between data and cluster labels. We demonstrate that this intuition suffers from a fundamental conceptual flaw that causes clustering performance to deteriorate as the amount of data increases. Instead, we return to the axiomatic foundations of information theory to define a meaningful clustering measure based on the notion of consistency under coarse-graining for finite data.

Conflict destabilizes social interactions and impedes cooperation at multiple scales of biological organization. Of fundamental interest are the causes of turbulent periods of conflict. We analyze conflict dynamics in an monkey society model system. We develop a technique, Inductive Game Theory, to extract directly from time-series data the decision-making strategies used by individuals and groups. This technique uses Monte Carlo simulation to test alternative causal models of conflict dynamics. We find individuals base their decision to fight on memory of social factors, not on short timescale ecological resource competition. Furthermore, the social assessments on which these decisions are based are triadic (self in relation to another pair of individuals), not pairwise. We show that this triadic decision making causes long conflict cascades and that there is a high population cost of the large fights associated with these cascades. These results suggest that individual agency has been over-emphasized in the social evolution of complex aggregates, and that pair-wise formalisms are inadequate. An appreciation of the empirical foundations of the collective dynamics of conflict is a crucial step towards its effective management.