An integrated perspective on the three potential sources of partisan bias: Malapportionment, turnout differences, and the geographic distribution of party vote shares

Partisan bias refers to an asymmetry in the way party vote share is translated into seats, i.e., a situation where some parties are able to win a given share of seats with a lesser (share of the) vote than is true for other parties. Any districted system is potentially subject to partisan biases. We show that there are three potential sources of partisan bias: (1) differences in the nature of the vote shares of the winning candidates of different parties that give rise to differences in the proportion of each party's votes that come to be ‘wasted’—differences which arise because of the nature of the geographic distribution of partisan support; (2) turnout rate differences across districts that are linked to the partisan vote shares in those districts, such that certain parties are more likely to have ‘cheap seats’ vis-à-vis turnout; and (3) malapportionment. In the context of two-party competition over single-member districts we provide a simple formulation to calculate the independent effect of each of these three factors. We illustrate our analysis with a calculation of the magnitude and direction of effects of the three determinants of partisan bias in elections to the US House and the US Senate in 1984, 1986 and 1988; then we consider how to extend the approach to a system with a mix of single- and multi-member districts or to a weighted voting system such as the US electoral college. We then apply the method to calculate the nature and sources of partisan bias in the 1984 and 1988 US presidential elections.