This paper analyzes the use of ideal point estimates for testing pivot theories of lawmaking such as Krehbiel's (1998, Pivotal politics: A theory of U.S. lawmaking. Chicago, IL: University of Chicago) pivotal politics and Cox and McCubbins's (2005, Setting the Agenda: Responsible Party Government in the U.S. House of Representations. New York: Cambridge University Press) party cartel model. Among the prediction of pivot theories is that all pivotal legislators will vote identically on all successful legislation. Clinton (2007, Lawmaking and roll calls. Journal of Politics 69:455–67) argues that the estimated ideal points of the pivotal legislators are therefore predicted to be statistically indistinguishable and false when estimated from the set of successful final passage roll call votes, which implies that ideal point estimates cannot logically be used to test pivot theories. I show using Monte Carlo simulation that when pivot theories are augmented with probabilistic voting, Clinton's prediction only holds in small samples when voting is near perfect. I furthermore show that the predicted bias is unlikely to be consequential with U.S. Congressional voting data. My analysis suggests that the methodology of estimating ideal points to compute theoretically relevant quantities for empirical tests is not inherently flawed in the case of pivot theories.
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