Candidate Competition with Entry and Valance Advantages:
An Exploration
Michael Cutrone
Ph.D. Candidate in Politics and Political Economy
Department of Politics
Princeton University
Princeton NJ 08544
mcutrone@princeton.edu
1.
Introduction
Throughout the past fifty years, the spatial model has become a major workhorse
in the analytical study of politics. Based on Hotelling’s (1929) model of spatial
competition, Anthony Downs (1957) developed a simple parsimonious model of mass
elections. Downs considers a highly stylized game of two-party electoral competition on
a unidimensional policy space where voters have symmetric, single-peaked preferences.
The analysis of this game leads to the now-infamous Median Voter Theorem. This states
that, when voters base their voting decisions purely on ideological proximity and
candidates are free to any policy position desired, there is a tendency in two-candidate
races for both candidates to converge to the center and for elections to be tied.
This result, while theoretically interesting, is rarely observed in empirical studies
and has led to an interesting question for students of American elections. So now we ask:
Why do candidates fail to position at the location of the median voter? An array of
answers has been posited.
Some, such as Calvert (1985) and Wittman (1977, 1983), contend that candidates,
like voters, possess policy preferences and that this may lead to divergence – though
candidates may moderate the positions offered in an effort to capture a larger segment of
the electorate.
Others, like Palfrey (1984), have demonstrated that the potential entry of third
party candidates can provide the incentive for candidates to become more extreme so as
to minimize the possible section of the electorate which an entrant can capture. The
established candidate may not be able to become sufficiently extreme so as to prevent the
entrance of the minor candidate; this is because he must also compensate for the impact
that this outward shift in position will have on the behavior of the other established
candidate – who will shift in towards the median in an effort to gain a higher percentage
of votes and, therefore, a higher probability of winning the election. While most of the
literature has limited its focus to a single potential entrant, there is nothing to say that
there must be just one entrant. Osborne and Slivinski (1996) and Besley and Coate
(1997) have provided a series of conditions which make the number of entrants in an
election endogenous to the model.
An additional direction that scholarly research has taken regards valence
advantages. Valence refers to any non-policy advantage that increases the utility voters
receive from a specific candidate. Valence can be any positive quality, such as party
identification, good looks, charisma, honesty, and the like. Both Groseclose (2001) and
Aragones and Palfrey (2002) study models of this type. The general finding of these
studies is that, while pure strategies typically fail to exist, the advantaged candidate tends
to moderate his policy position towards that of the median voter, while the disadvantaged
one shifts away from the median in an effort to distinguish himself and, therefore,
maintain some probability of winning the election. These theoretical predictions are also
consistent with the findings of empirical studies on Congressional elections (Fiorina 1973
and Ansolabehere, Snyder, and Stewart 2001).
While the literatures on entry and valence advantage each have certain predictions
for equilibrium candidate behavior, I believe that the interaction of these two
considerations will lead to different equilibria. Therefore, in this paper, I will develop a
spatial model of candidate competition which includes both the potential entrance of third
party candidates and the fact that the established parties possess partisans in electorate
(or, in the terms of our previous discussion, the parties possess a valence advantage
among portions of the electorate).
The paper will follow in the following manner. In the second section, I will lay
out the assumptions and definitions which my model relies on. Following this, I will
discuss the results I have been able to develop. The main findings are that: 1) when the
major parties have equal levels of valance, the equilibrium is the same as that in Palfrey’s
work without valence, and 2) when valence asymmetries exist, the equilibrium will be
that the entrant enters to the exterior of the major party with lower valance. The fourth
section will include a brief discussion of ways to extend my analysis once the basic
model has been fully solved. Finally, I conclude the paper with a brief recap.