Document Type


Publication Date



How much should we pay to remove the interdependence of biased information sources? This question is relevant in both statistics and political economy. When there are many information sources or variables, their dependence may be unknown, which creates multivariate ambiguity. One approach to answer our leading question involves use of decoupling inequalities from probability theory. We present a new inequality, designed to cope with this question, which holds for any type of dependence across information sources. We apply our method to a simple formalization of a political echo chamber. For a given set of marginal information, this bound is the sup over all possible joint distributions connecting the marginals. Our method highlights a price to pay for facing summed dependent (multivariate) data, similar to the probability premium required for univariate data. We show that a conservative decisionmaker will pay approximately 50% more than if the data were independent, in order to freely neglect the correlations.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.