What I Disbelieve: Quantifying Belief With Negative Ranking Functions

Abstract

A challenge in exploring the psychology of human uncertainty is its measurement and quantification. Prior work has focused almost exclusively on probability, while the formal theories developed in philosophy are rarely tested. We tested Wolfgang Spohn's ranking theory, a normative account in which belief is graded by ordinal ranks of disbelief that combine by minimization rather than addition, as a descriptive model of human belief. Across six experiments, participants assigned ranks of disbelief to propositions involving personal experience, chance devices, sequential learning, and an Ellsberg urn. Ranks were reliable and, through the theory's two-sided rank function, distinguished belief, disbelief, and suspension of judgment. Participants respected the Law of Negation, never disbelieving both a proposition and its complement, in every task except a lottery. Disjunctions did not follow the theory's Law of Disjunction. Instead of taking the minimum rank of the disjuncts, participants averaged them. In a learning task, ranks aligned more closely than did subjective probabilities with objective probabilities. In an Ellsberg Urn scenario, the paradoxical behavior seen with betting was markedly reduced by ranks. We conclude that human belief has the bipolar, negation-respecting structure that ranking theory proposes, but combines disjuncts by averaging rather than by minimization. As a clear account of human belief dynamics with metrics that can be reliably measured, Ranking Theory provides a valuable framework for investigating and contrasting probabilistic and non-probabilistic accounts of human belief.