The methods for measuring partisan bias and electoral responsiveness, and related quantities, that first relaxed the assumptions of exact uniform partisan swing and the exact correspondence between statewide electoral results and legislative electoral results, among other improvements:
The first attempt to eliminate the exact uniform partisan swing assumption, using data from a single election. . 1989. “Representation Through Legislative Redistricting: A Stochastic Model.” American Journal of Political Science, 33, Pp. 787–824.Abstract
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 redistricting literature. The model shows precisely how incumbency and increased variability of partisan swing reduce the responsiveness of 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.