The Prediction value

We introduce the prediction value (PV) as a measure of players' informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player $i$'s prediction value equals the difference between the conditional expectations of $v(S)$ when $i$ cooperates or not. We characterize the prediction value as a special member of the class of (extended) values which satisfy anonymity, linearity and a consistency property. Every $n$-player binomial semivalue coincides with the PV for a particular family of probability distributions over coalitions. The PV can thus be regarded as a power index in specific cases. Conversely, some semivalues -- including the Banzhaf but not the Shapley value -- can be interpreted in terms of informational importance.Comment: 26 pages, 2 table

The Axiomatic Structure of Empirical Content

In this paper, we provide a formal framework for studying the empirical content of a given theory. We define the falsifiable closure of a theory to be the least weakening of the theory that makes only falsifiable claims. The falsifiable closure is our notion of empirical content. We prove that the empirical content of a theory can be exactly captured by a certain kind of axiomatization, one that uses axioms which are universal negations of conjunctions of atomic formulas. The falsifiable closure operator has the structure of a topological closure, which has implications, for example, for the behavior of joint vis a vis single hypotheses. The ideas here are useful for understanding theories whose empirical content is well-understood (for example, we apply our framework to revealed preference theory, and Afriat's theorem), but they can also be applied to theories with no known axiomatization. We present an application to the theory of multiple selves, with a fixed finite set of selves and where selves are aggregated according to a neutral rule satisfying independence of irrelevant alternatives. We show that multiple selves theories are fully falsifiable, in the sense that they are equivalent to their empirical content

(WP 2016-03) Economics, Neuroeconomics, and the Problem of Identity

This paper reviews the debate in economics over neuroeconomics’ contribution to economics. It distinguishes majority and minority views, argues that this debate has been framed by mainstream economics’ conception of itself as an isolated science, and argues that this framing has put off the agenda in economics issues such as individual identity that are increasingly important in connection with the social and historical context of economic explanations in a changing complex world. The paper first discusses how the debate over neuroeconomics has been limited to the question of what information from other sciences might be employed in economics. It then goes on to the individual identity issue, and discusses how economics’ top-down, closed character generates a circular individual identity conception, while bottom-up, open character of psychology and neuroscience, and their continual concern with the changing relation between theory and evidence, has produced four competing individual identity conceptions in neuroeconomic research