The Statistical Properties of Competitive Districts: What the
Central Limit Theorem Can Teach Us about Election Reform
Authors: Buchler Justin 
Published: April 2007

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.