Congressional Campaign Contributions, District Service and Electoral Outcomes
in the United States: Statistical Tests of a Formal Game Model with Nonlinear
Dynamics 
by
Walter R. Mebane, Jr. 
October 23, 1998
Forthcoming, Diana Richards, ed., Political Complexity: Nonlinear
Models of Politics. Ann Arbor: University of Michigan Press.
Associate Professor, Department of Government, 121 McGraw
Hall, Cornell University, Ithaca, New York 14853-4601, phone 607/255-3868,
fax 607/255-4530, email wrm1@macht.arts.cornell.edu.
Congressional Campaign Contributions, District Service and Electoral Outcomes
in the United States: Statistical Tests of a Formal Game Model with Nonlinear
Dynamics
Using a two-stage game model, with the second stage being a system of ordinary differential equations, I argue that candidates, political parties and financial contributors interact strategically in American congressional elections in a way that is inherently nonlinear. The nonlinearity explains longstanding anomalies in the congressional elections literature regarding candidate finances, district service and votes for the incumbent. Congressional races in which the incumbent faces a challenge are generated by dynamical systems that have Hopf and saddle connection bifurcations. A small change in the challenger's quality or in the type of district service can change a stable incumbent advantage into a race with growing oscillations in which the incumbent's chances are uncertain. Normal form equations from local bifurcation theory, and topological considerations, motivate a statistical model that can recover qualitative features of the dynamics from cross-sectional data. I estimate and test the model using district-level data from the 1984 and 1986 U.S. House election periods for political action committee campaign contributions, intergovernmental transfers and general election vote shares.