The existence of the bifurcation makes it useless to estimate linear or generalized linear models of the relationships among most of the variables of interest in studies of congressional elections. The inherently nonlinear dynamics associated with the bifurcation imply that each congressional campaign evolves in a manner that resembles motion around a loop. Around the loop the relationship between a pair of variables will cycle among all possible orientations, sometimes increasing, sometimes decreasing. It is impossible to map such covariation faithfully into a linear model. A line segment cannot model a circle. The existence of the bifurcation means that linear models of congressional election phenomena such as campaign contributions, district service and votes are necessarily misspecified. If the bifurcation exists, such models must necessarily fail to produce correct results.
Both the current theoretical models and the claim that the bifurcation is inherent in congressional politics have many more testable implications than I have discussed. To get a sense of the range of such implications, consider that the ``campaign'' of the game model is not restricted to any particular time period within a legislator's term in office, and that the actions of the model such as the incumbent's choosing a service type may reach deep into the legislative process. Arguably, for instance, choosing a service type includes securing one's portfolio of committee assignments. On the most capacious interpretation, the game model should be read as predicting that the bifurcation pattern occurs in some form in the committee assignment process. Because the provision of district service often involves coordinated action across the federal, state and local levels of government, traces of the bifurcation pattern ought to be found as well in actions taken by nonlegislators at many levels of the federal system. The 4DH model can be extended in various ways to support many of the forms of data and particular hypotheses that would be most appropriate for empirical tests in these and other areas. Statistical models quite different from the 4DH model may also prove useful.