On the Consistency of Approximate Multi-agent Probability Theory

Bayesian models have proven to accurately predict many aspects of human cognition, but they generally lack the resources to describe higher-order reasoning about other people’s knowledge. Recently, a number of suggestions have thus been made as to how these social aspects of cognition might be codified in computational reasoning systems. This paper examines one particularly ambitious attempt by Andreas Stuhlmüller and Noah Goodman, which was implemented in the stochastic programming language Church. This paper translates their proposal into a more conventional probabilistic language, comparing it to an alternative system which models subjective probabilities as random variables. Having spelled out their ideas in these more familiar and intuitive terms, I argue that the approximate reasoning methods used in their system have certain statistical consistency problems.