Redistricting and the Personal Vote : When Natural Experiments are Neither Natural nor Experiments

Natural experiments are increasingly prominent in the social sciences. However, natural experiments often have more in common with traditional observational studies than with randomized experiments. We illustrate our argument by examining the case of using redistricting to estimate the personal vote. Strikingly, even if voters were redistricted randomly, previous uses of redistricting would not identify the causal effect of interest. We also find that the redistricting process is sufficiently nonrandom as to require significant covariate adjustment to overcome confounding. To overcome these difficulties, we propose a new design for estimating the personal vote and the partisan incumbency advantage that relies on the implementation of multiple redistricting plans. Analyzing data from U.S. House elections in California and Texas, we find that there is a large partisan incumbency advantage in both states but that the effect of the personal vote is zero in Texas and small in California