The Statistical Properties of Competitive Districts: What the Central Limit Theorem Can Teach Us about Election Reform

Abstract

Any examination of newspaper editorials and reform group positions will indicate that the most commonly perceived problem with U.S. elections at the moment is that they are rarely competitive. This absence of competition has prompted recent proposals in several states, most prominently in California and Ohio, to reform the redistricting process to increase the frequency of competitive elections. These propositions failed, but that is unlikely the end of such attempts. The reason for these proposals is obvious. Political education in the U.S. indoctrinates us at a young age to believe that competition is good. In economics, market competition provides social benefits, and, by analogy, political competition must provide similar benefits. This argument is frequently made explicitly, such as by Schumpeter (1942), and it has its roots as far back as the often-assigned Federalist Papers #10 and #51. Of course, the economic definition of competition has little to do with the political definition of a competitive election. Broadly speaking, there are two economic definitions of competition: (1) competitive behavior, which generally means innovation, and (2) competitive market structures, which means many buyers, many sellers, and perfect information. In contrast, a competitive election generally means one in which the candidates' vote shares are roughly equal, or similarly, one in which each candidate has a roughly 50% chance of winning. The only obvious relationship between these definitions is that we might equate vote shares with market shares, but the benefits of a competitive market accrue regardless of whether sellers have equal market shares—they simply must charge the same price for the same goods, as determined by the intersection of the supply and demand curves. In fact, in a competitive market, each firm should have such a small market share that no firm is a price-giver, and the idea of an election for a single-member district in which there are so many candidates that no candidate has a significant vote share seems untenable. Alternatively, we might draw an analogy between pressure on sellers to charge the same price for the same good and pressure on candidates toward policy convergence, but the idea of all candidates offering the same bundle of policies makes many people uncomfortable as well. So, the analogy between the efficiency of a competitive market and the benefits of a competitive election falls apart. Of course, Schumpeter's (1942) argument was that political leaders should compete for votes by innovating with respect to policy based on the first definition of competition, but again, that means that the economic analogy has little to say about whether elections should be uncertain and decided by narrow margins. The fact that we happen to use the same word for different circumstances does not logically allow us to say the following: because competition is good in the marketplace, close elections are good. Free market economics cannot be used to defend the drawing of competitive districts without straining the analogy beyond its limits, regardless of how intuitively appealing the analogy is.