This paper describes a study in which subjects were asked about various aspects of coin flipping. Many gave contradictory answers to closely-related questions. We offer two explanations for such responses: (a) switching among incompatible perspectives of uncertainty, including the outcome approach, judgment heuristics, and normative theory; and (b) reasoning via basic beliefs about coin flipping. As an example of the latter, people believe both that a coin is unpredictable and also that certain outcomes of coin flipping are more likely that others. Logically, these beliefs are not contradictory; they are, however, incomplete. Thus, contradictory statements (and statements at variance with probability theory) appear when these beliefs are applied beyond their appropriate domain.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education