V.O.Key Formalized:
Retrospective Voting as Adaptive Behavior
Jon Bendor
Sunil Kumar
David Siegel
Abstract
Since V. O. Key’s seminal work, retrospective voting been regarded as a major component of voting theory,
spawning a rich variety of models of voter choice utilizing Key’s basic idea that the incumbent’s
performance influences citizens’ votes. However, these models often assume that voters are fully rational
and, for example, update their beliefs in accord with Bayes’ rule. We suspect that Key had a less heroic
view of voter cognition, and we propose a formalization of his verbal theory that we believe is closer to the
spirit of his ideas. Our model is based on two fundamental axioms of aspiration-based retrospective voting:
if an incumbent performed “well” (i.e., above voter A’s aspiration level) then A’s propensity to vote for the
incumbent will rise; if an incumbent performed “poorly” (below A’s aspiration level) then A’s propensity to
vote for the incumbent falls. These two assumptions, together with some postulates about how aspirations
adjust, form the core of our model. We show analytically that citizens endogenously develop partisan
voting tendencies, even though they lack overt political ideologies and instead simply vote retrospectively
in the above manner. Further, this result is robust against perceptual errors (citizens evaluating an
incumbent’s performance incorrectly), given the conventional benchmark assumptions of independent and
identically distributed errors. Lastly, we supplement this analytical model, which is spare in several
respects, with a computational model that enables us to examine richer voting contexts.
I. Introduction
Two of the most robust findings about American voters is that few of them have coherent,
detailed ideologies and few know much about politics.
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Donald Kinder summarizes decades of
survey research on ideology: “Precious few Americans make sophisticated use of political abstrac-
tion. Most are mystified by or at least indifferent to standard ideological concepts, and not many
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We thank Jim Fearon, Alan Gerber, Bob Luskin, Terry Moe and Ken Schultz for helpful comments on earlier
versions of this paper. Bendor thanks the Fellows of the Center for Advanced Study in the Behavioral Sciences and
CASBS itself for providing a wonderful work environment.
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