Recursive mentalizing and public salience in the perception of common knowledge

Common knowledge-what everyone knows that everyone knows, ad infinitum-is theoretically required for coordination. But a finite mind cannot represent infinitely embedded propositions, and even a few are cognitively taxing. We propose that people perceive common knowledge by combining a capacity-limited ability for recursive mentalizing with an intuitive sense of public salience: When an event is jointly and openly witnessed, they infer that recursively embedded beliefs are licensed. We probed participants' attributions of embedded beliefs to characters in fictitious vignettes. Study 1 presented narratives in which the information available to characters was either asymmetrical, reciprocal, or public. Participants indicated their confidence in the characters' beliefs with 0, 2, 4, 6, and 18 embeddings (the latter judged indirectly). Ratings showed i) a decline with number of embeddings, reflecting cognitive load, ii) modest overattribution of embedded beliefs in the nonpublic conditions, iii) far higher attribution of embedded beliefs in the public conditions, and iv) high indirect judgments that arbitrarily deep beliefs were justified. Study 2 replicated these findings with animated videos in which the characters' information was private, reciprocal, doubly reciprocal, or public. Together, the studies indicate that people attribute common knowledge to observers of a publicly salient event, while being susceptible to capacity-driven recursion collapse and heuristic extrapolation (false embedded beliefs). This can explain how humans achieve coordination from sparse cues, yet sometimes miscoordinate when publicness is absent or embedding grows complex.