A popular model of preference in the context of recommendation systems is the so-called ideal point model. In this model, a user is represented as a vector u together with a collection of items x N in a common low-dimensional space. The vector u represents the user's ideal point, or the ideal combination of features that represents a hypothesized most preferred item. The underlying assumption in this model is that a smaller distance between u and an item x j. In the vast majority of the existing work on learning ideal point models, the underlying distance has been assumed to be Euclidean. However, this eliminates any possibility of interactions between features and a user's underlying preferences.

A popular model of preference in the context of recommendation systems is the so-called ideal point model. In this model, a user is represented as a vector u together with a collection of items x1 ... xN in a common low-dimensional space. The vector u represents the user's "ideal point," or the ideal combination of features that represents a hypothesized most preferred item. The underlying assumption in this model is that a smaller distance between u and an item xj indicates a stronger preference for xj. In the vast majority of the existing work on learning ideal point models, the underlying distance has been assumed to be Euclidean. However, this eliminates any possibility of interactions between features and a user's underlying preferences.

We develop a probabilistic model of legislative data that uses the text of the bills to uncover lawmakers' positions on specific political issues. Our model can be used to explore how a lawmaker's voting patterns deviate from what is expected and how that deviation depends on what is being voted on. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout predictive performance and the model's utility in interpreting an inherently multi-dimensional space.

Ideal point models analyze lawmakers' votes to quantify their political positions, or ideal points. But votes are not the only way to express a political position. Lawmakers also give speeches, release press statements, and post tweets. In this paper, we introduce the text-based ideal point model (TBIP), an unsupervised probabilistic topic model that analyzes texts to quantify the political positions of its authors. We demonstrate the TBIP with two types of politicized text data: U.S. Senate speeches and senator tweets. Though the model does not analyze their votes or political affiliations, the TBIP separates lawmakers by party, learns interpretable politicized topics, and infers ideal points close to the classical vote-based ideal points. One benefit of analyzing texts, as opposed to votes, is that the TBIP can estimate ideal points of anyone who authors political texts, including non-voting actors. To this end, we use it to study tweets from the 2020 Democratic presidential candidates. Using only the texts of their tweets, it identifies them along an interpretable progressive-to-moderate spectrum.

Suppose that we wish to estimate a vector $\mathbf{x}$ from a set of binary paired comparisons of the form "$\mathbf{x}$ is closer to $\mathbf{p}$ than to $\mathbf{q}$" for various choices of vectors $\mathbf{p}$ and $\mathbf{q}$. The problem of estimating $\mathbf{x}$ from this type of observation arises in a variety of contexts, including nonmetric multidimensional scaling, "unfolding," and ranking problems, often because it provides a powerful and flexible model of preference. We describe theoretical bounds for how well we can expect to estimate $\mathbf{x}$ under a randomized model for $\mathbf{p}$ and $\mathbf{q}$. We also present results for the case where the comparisons are noisy and subject to some degree of error. Additionally, we show that under a randomized model for $\mathbf{p}$ and $\mathbf{q}$, a suitable number of binary paired comparisons yield a stable embedding of the space of target vectors. Finally, we also that we can achieve significant gains by adaptively changing the distribution for choosing $\mathbf{p}$ and $\mathbf{q}$.

We develop a probabilistic model of legislative data that uses the text of the bills to uncover lawmakers' positions on specific political issues. Our model can be used to explore how a lawmaker's voting patterns deviate from what is expected and how that deviation depends on what is being voted on. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout predictive performance and the model's utility in interpreting an inherently multi-dimensional space.

Legislative behavior centers around the votes made by lawmakers. These votes are captured in roll call data, a matrix with lawmakers in the rows and proposed legislation in the columns. We illustrate a sample of roll call votes for the United States Senate in Figure 1. The seminal work of Poole and Rosenthal (1985) introduced the ideal point model, using roll call data to infer the latent political positions of the lawmakers. The ideal point model is a latent factor model of binary data and an application of item-response theory (Lord 1980) to roll call data. It gives each lawmaker a latent political position along a single dimension and then uses these points (called the ideal points) in a model of the votes.