How Big Is (Sample) Space? Judgment and Decision Making With Unknown States and Outcomes

Abstract

Many real-world decisions must be made when we do not know all of the possible relevant states beforehand, that is, the “sample space” (Ω). Standard probability theory takes Ω for granted. Moreover, there is scant psychological research on how people construct Ω. We report four exploratory experimental studies investigating the impact of sample information on judgments about the nature of Ω, borrowing ideas from the literatures on probability judgment, sampling models, and biological diversity estimation.Study 1 demonstrates that laypeople may use reasonable heuristics for assessing the size of Ω when given capture–recapture sample information. Studies 2–4 show that the biologists’ intuition that a larger number of unique states in a sample (numerical diversity) implies a larger Ω also applies to many laypeople, but this can be overridden by prior beliefs about Ω. Study 3 demonstrates that greater qualitative diversity in a sample also magnifies assessments of the size of Ω. Finally, Study 4, in line with the literature on natural sample spaces and knowledge-partitioning, shows that estimates of the size of Ω can be altered by directing people’s memory to retrieving different subsets of Ω. Implications and future directions for research in this area are discussed in the conclusion.