Bias-noise arbitrage and demand-driven differentiation of news media

We consider product differentiation on competitive news markets, as determined by the characteristics of demand confronting basic informational non-convexities in the activities of news reporting. Non-manipulative profit-maximizing news media imperfectly report the information they draw from some normally distributed flow of source data. A natural measure of information loss due to the media is the Kullback-Leibler divergence between the normal distributions of news and raw data. We show that reporting distortions depend on: (i) bias, defined as the difference between the means of the probability distributions of news and raw data; and (ii) noise, defined as the difference between the standard deviations of these distributions. We show that expected utility maximizing consumers with concave Bernoulli utility functions are noise-averse. Distortion-averse consumers are both biasand noise-averse. We show that the news products supplied at equilibrium are identical in terms of accuracy, as measured by their Kullback-Leibler divergence to raw data. These products make a one-dimensional locus in the mean-standard deviation space. This locus consists of horizontally differentiated products, ranging from conventional news products, characterized by large biases and by noise levels reduced to some incompressible minimum, to "noisy" news products, which set bias to zero at the expense of some maximum noise level. The frontier confronts distortion-averse consumers with a basic non-convexity. Non-convexity results in maximal product differentiation, the "conventional" and "noisy" extremes being the only news products actually demanded at equilibrium in some natural configurations of the latter. We moreover show that most types of noise-averse consumers choose their news providers in the close vicinity of the conventional end of the market. The model thus provides a rationale and partial explanation for the common distinction between mainstream and alternative news media.