Abstract

We propose a mathematical theory of public opinion based on Zaller (1992). We show how our theory can provide a rigorous account for various empirical implications identified by Zaller (1992). We then show that it can also account for empirical regularities on information and response volatility identified by Alvarez and Brehm (2002), media influence and polarization (Zaller, 1992), as well as media slant, priming, framing, and agenda setting. We then derive the "miracle of aggregation" argument due to Page and Shapiro (1992) and apply it to the study of polarization, media influence, and opinion change (Stimson, 2015 [2004]). Our theory provides a general framework for studying public opinion in a rigorous fashion.