Proceedings of the Annual Meeting of the Cognitive Science Society

Across two experiments, we use ordinal ranking to examinethe processing and representations involved in the estimationof large-scale, real-world proportions. Specifically, in twoexperiments people estimated two kinds of important real-world proportions: the demographic makeup of theircommunities, and spending by the U.S. Federal government.Our goal was to assess the metric scaling properties thatcharacterize perceptions of these quantities. In particular,previous work in numerical proportions has positedlogarithmic or linear representations (Opfer & Siegler, 2007),or linear representations with task-dependent rescaling (Barth& Paladino, 2011; Cohen & Blanc-Goldhammer, 2011). Thecurrent context differs markedly from this prior work in thatthe values we are examining are not explicitly presented toparticipants, nor directly experienced, but must be estimatedon the basis of masses of complex experiences. Ordinalranking of the quantities, combined with a Thurstonianmodeling approach, allows a unique means for estimating theinternal scale properties of numerical structures. We find thatpeople largely rely on mixed representations that emphasizelog-odds transformations of these vaguely known, butsocially important values. While the budget data explored inExperiment 1 were unable to distinguish log and log-oddstransformed internal models, the demographic proportionsexplored in Experiment 2 favored log-odds models.