Representation through Legislative Redistricting: A Stochastic Model

Gary King
1989 American Journal of Political Science  
This paper builds a stochastic model of the processes that give rise to observed patterns of representation and bias in congressional and state legislative elections. The analysis demonstrates that partisan swing and incumbency voting, concepts from the congressional elections literature, have determinate effects on representation and bias, concepts from the redistrictihg literature. The model shows precisely how incumbency and increased variability of partisan swing reduce the responsiveness
more » ... the electoral system and how partisan swing affects whether the system is biased toward one party or the other. Incumbency, and other causes of unresponsive representation, also reduce the effect of partisan swing on current levels of partisan bias. By relaxing the restrictive portions of the widely applied "uniform partisan swing" assumption, the theoretical analysis leads directly to an empirical model enabling one more reliably to estimate responsiveness and bias from a single year of electoral data. Applying this to data from seven elections in each of six states, the paper demonstrates that redistricting has effects in predicted directions in the short run: partisan gerrymandering biases the system in favor of the party in control and, by freeing up seats held by opposition party incumbents, increases the system's responsiveness. Bipartisan-controlled redistricting appears to reduce bias somewhat and dramatically to reduce responsiveness. Nonpartisan redistricting processes substantially increase responsiveness but do not have as clear an effect on bias. However, after only two elections, prima facie evidence for redistricting effects evaporate in most states. Finally, across every state and type of redistricting process, responsiveness declined significantly over the course of the decade. This is clear evidence that the phenomenon of "vanishing marginals," recognized first in the U.S. Congress literature, also applies to these different types of state legislative assemblies. It also strongly suggests that redistricting could not account for this pattern. *Thanks to Rosenthal for many helpful discussions and comments. Robert Browning also made significant contributions at an early stage in this research. Thanks also to the National Science Foundation for research support grants SES-87-22715 and SES-89-09201. Now integrate out e to leave the new time 2 mean voter preference distribution: By the application of assumption 5 , the corresponding seats-votes curve is then: Note that E does not appear directly in either the modified mean voter preference distribution or this corresponding seats-votes curve. However, the mean (7) and the dispersion ( 0 ) of the distribution of E are included. By this procedure, then, the model has one additional parameter.
doi:10.2307/2111110 fatcat:ouqu6he6mfaihoqfdbjj6alzeq