On the Commodification of Information: An Exploratory Pre-Bayesian Formulation
Patrick Beissner and M. Ali Khan, ANU
Abstract: Motivated, by Arrow's information (disclosure) paradox (AIP/ADP), we formalize the commodification of information based on extension through introspective extrapolation of the known to all that is unknown, as opposed to one based on a Bayesian updating of prior known information about all that constitutes the unknown. The essential idea involves a lottery of information-batches that consolidates a buyer's presumptions of what is already known: this shrinking operation conceived as a correspondence from the space of sub-sigma-algebras to the collection of all compact convex subsets of probability measures extended to the entire sigma-algebra, and then averaged out as an application of the Debreu integral. A buyer's utility function for information, when formalized as Hurwicz expected utility, is monotone, continuous and linear in information, in strong counterpoint to the celebrated Radner-Stiglitz non-concavity theorem, properties that no longer hold when Gul-Pesendorfer axiomatics are substituted by those of the smooth ambiguity or variational preference models. The paper concludes by relating the formulation and the results to a rich antecedent literature.