Three Guys Walk into a Bar: An Information Theoretic Analysis

Abstract

This paper posits a scenario in which three famous information theorists meet each other in a bar and compare notes. The three include the celebrated information theorist Claude Shannon, the 18th century English statistician Thomas Bayes and the Harvard statistical linguist George Zipf. Each is famous for promoting a fundamental equation about the nature of human communication and informational updating. In the scenario they discover that with some modest mathematical transformations they can demonstrate that each of the equations, although based on entirely distinct phenomena in physics and linguistics, has the same basic structural form. This common structural form can be identified as a variation of the power law function. The remainder of the paper explores how such distinct phenomena share similar structural properties and why an understanding of these properties is important for the design and regulation of advanced information systems. The key organizing concept is the familiar metaphor in communication policy – the marketplace of ideas. As formalized in Title III the 1934 Communication Act, subsequent amendments and Commission rulings, regulatory policy has focused on trying the maximize the number of “voices” in the public sphere given the constraints of spectrum scarcity. Thus the traditional models of anti-trust HHI calculations, ownership caps, minority preferences and localism rulings have been designed to maximize diversity. But the regulatory logic is based on an industrial age notion of an extremely limited number of broadcast voices which is much less appropriate in an era when every broadband connection is as capable of broadcasting as of receiving. The paper argues that although information theory has traditionally been rather marginal in the domain of communication policy, it need not be. In promoting diversity it is challenging for evolving communication policy to meaningfully address not just the diversity of voices but the diversity of information.