This paper identifies four paradoxes of parties. These paradoxes illustrate
not only substantive problems in their own right but also diverse ways tha
t formal models can help to define and address problems in legislative rese
arch. Models are shown to clarify key concepts (such as majority party stre
ngth), to sharpen the definition of important problems of inference (observ
ational equivalence of theories), to evaluate widely used measures (party v
oting), and to derive and test competing hypotheses (majoritarian versus ma
jority-party determinants of legislative organization).