A Formal Link Between Information Entropy and the Effective Number of Parties

Information theory now informs fields as diverse as quantum physics, neuroscience, and economics. In this short note, I show that it informs political science too. In particular, I show that the effective number of parties—perhaps the most widely-used measure in all of comparative politics—is the antilogarithm of a common measure of information entropy: the Rényi entropy. This equivalence bridges the two fields, thereby allowing us to use advances in information theory to improve our understanding of electoral systems and their consequences.