A new theoretical method for examining gerrymandering is presented based on lattice models of voters, in which districts are constructed by partitioning the lattice. We propose three novel algorithms for constructing equal-population, connected districts which favor the gerrymanderer and incorporate the spatial distribution of voters. Due to the probabilistic population fluctuations inherent to our voter models, Monte Carlo techniques can be applied to study the impact of gerrymandering. We use the method developed here to compare our different gerrymandering algorithms, show approaches which ignore spatial data lead to (legally prohibited) disconnected districts, and examine the effectiveness of isoperimetric quotient tests.

Information about the ideological positions of different political actors is crucial in answering questions regarding political representation, polarization, and voting behavior. One way to obtain such information is to ask survey respondents to place actors on a common ideological scale, but, unfortunately, respondents typically display a set of biases when performing such placements. Key among these are rationalization bias and differential item functioning (DIF). While Aldrich–McKelvey (AM) scaling offers a useful solution to DIF, it ignores the issue of rationalization bias, and this study presents Monte Carlo simulations demonstrating that AM-type models thus can give inaccurate results. As a response to this challenge, this study develops an alternative Bayesian scaling approach, which simultaneously estimates DIF and rationalization bias, and therefore performs better when the latter bias is present.

We introduce a model that extends the standard vote choice model to encompass text. In our model, votes and speech are generated from a common set of underlying preference parameters. We estimate the parameters with a sparse Gaussian copula factor model that estimates the number of latent dimensions, is robust to outliers, and accounts for zero inflation in the data. To illustrate its workings, we apply our estimator to roll call votes and floor speech from recent sessions of the US Senate. We uncover two stable dimensions: one ideological and the other reflecting to Senators’ leadership roles. We then show how the method can leverage common speech in order to impute missing data, recovering reliable preference estimates for rank-and-file Senators given only leadership votes.