The translation of citizen votes into legislative seats is of central importance in democratic electoral systems. It has been a longstanding concern among scholars in political science and in numerous other disciplines. Through this literature, two fundamental tenets of democratic theory, partisan bias and democratic representation, have often been confused. We develop a general statistical model of the relationship between votes and seats and separate these two important concepts theoretically and empirically. In so doing, we also solve several methodological problems with the study of seats, votes and the cube law. An application to U.S. congressional districts provides estimates of bias and representation for each state and deomonstrates the model’s utility. Results of this application show distinct types of representation coexisting in U.S. states. Although most states have small partisan biases, there are some with a substantial degree of bias.
Three articles, published in the leading journals of three disciplines over the last five decades, have each used the Poisson probability distribution to help describe the frequency with which presidents were able to appoint United States Supreme Court Justices. This work challenges these previous findings with a new model of Court appointments. The analysis demonstrates that the number of appointments a president can expect to make in a given year is a function of existing measurable variables.
The Davis v. Bandemer case focused much attention on the problem of using statistical evidence to demonstrate the existence of political gerrymandering. In this paper, we evaluate the uses and limitations of measures of the seat-votes relationship in the Bandemer case. We outline a statistical method we have developed that can be used to estimate bias and the form of representation in legislative redistricting. We apply this method to Indiana State House and Senate elections for the period 1972 to 1984 and demonstrate a maximum bias 6.2% toward the Republicans in the House and a 2.8% bias in the Senate.