On the Commodification of Information: An Exploratory Pre-Bayesian Formulation

Patrick Beissner and M. Ali Khan, ANU

**Motivated, by Arrow's information (disclosure) paradox (AIP/ADP), we formalize the commodification of information based on**

*Abstract:**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.