John Fountain

What do prediction markets predict

We show that prediction markets cannot be relied on to always elicit any interesting statistic of aggregate beliefs. Formal derivations of the bets placed in prediction markets can be viewed as demands for state-contingent commodities. We provide derivations for two popular cases, log utility and Constant Relative Risk Aversion (CRRA) utility, connecting these derivations to familiar scoring rules. We then use these results to demonstrate how the properties of prediction markets depend critically on the assumed homogeneity of participants.

Ambiguity, the certainty illusion, and the natural frequency approach to reasoning with inverse probabilities

People have difficulty reasoning with diagnostic information in uncertain situations, especially when an understanding and calculation of inverse conditional probabilities (Bayes theorem) is required. While natural frequency representations of inference tasks improve matters, they suffer from three problems: (1) calculation errors persist with a majority of subjects; (2) the representation suffers from an illusion of certainty that ignores ambiguity; and (3) the costs of repeatedly applying the representation to deal with imprecision and ambiguity in inference are prohibitive. We describe a user friendly, interactive, graphical software tool for calculating, visualizing, and communicating accurate inferences about uncertain states when relevant diagnostic test information (sensitivity, specificity, and base rate) is both imperfect and ambiguous in its application to a specific patient. The software is free, open-source, and runs on all popular PC operating systems (Windows, Mac, Linux).

A simple graphical proof of arrow's impossibility theorem

This paper uses a two‐dimensional graphical technique to provide a constructive proof of Arrows impossibility theorem. Students (and instructors) of intermediate microeconomics should have no problem in following the graphical proof developed here. The meaning of the condition of independence of irrelevant alternatives and its function in Arrows theorem become transparent in this proof.

What can the regression model of human judgment learn from multi-attribute decision theory?

Zelenys recent conjecture that multi-attribute decision theory may help to overcome the inadequacies of the linear regression model is incorrect. Recognition of the information processing advantages inherent in multiple -attribute decision situations combined with a requirement of transitivity itself implies linear objective functions. This follows from some recent developments by a psychologist and an economist in the analysis of individual and collective decision processes, developments which do not take as their starting point the paradigm of choice offered in utility theory.