Incompletely Known Sample Spaces: Models and Human Intuitions

This paper surveys models and human intuitions about incompletely known "sample spaces"(Ω). Given that there are very few guidelines for how best to form such beliefs when Ω is incompletely known, and there is very little research on the psychology behind beliefs about Ω, this survey is preliminary and brings in ideas and models from probability and statistics, biology, and psychology. Pilot experimental studies of how people estimate the cardinality of Ω when given sample information from it are presented, demonstrating that to a surprising extent their estimates correspond with those produced by normative statistical models. The paper concludes by outlining future directions for a research program on this topic.