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Political scientists increasingly analyze multimodal data. However, the effective analysis of such data requires aligning information across different modalities. In our paper, we demonstrate the significance of such alignment. Informed by…
The concept of ``ideology" is central to political discourse and dynamics, and is often cast as falling primarily on a one-dimensional scale from ``left-wing/liberal" to ``right-wing/conservative", but the validity of this simple…
To understand and summarize approval preferences and other binary evaluation data, it is useful to order the items on an axis which explains the data. In a political election using approval voting, this could be an ideological left-right…
Sports tracking data are the high-resolution spatiotemporal observations of a competitive event. The growing collection of these data in professional sport allows us to address a fundamental problem of modern sport: how to attribute value…
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…
The voter model is a toy model of consensus formation based on nearest-neighbor interactions. A voter sits at each vertex in a hypercubic lattice (of dimension $d$) and is in one of two possible opinion states. The opinion state of each…
In many settings people must give numerical scores to entities from a small discrete set. For instance, rating physical attractiveness from 1--5 on dating sites, or papers from 1--10 for conference reviewing. We study the problem of…
Representative democracy in the United States relies on election systems that transmit votes into representatives in three key bodies: the two chambers of the federal legislature (House of Representatives and Senate) and the Electoral…
Elections, the cornerstone of democratic societies, are usually regarded as unpredictable due to the complex interactions that shape them at different levels. In this work, we show that voter turnouts contain crucial information that can be…
Existing approaches to estimating politicians' latent positions along specific dimensions often fail when relevant data is limited. We leverage the embedded knowledge in generative large language models (LLMs) to address this challenge and…
We give three algebraic equations which allow a geometric classification of all spectral types of equilibria of a given $m$-dimensional dynamical system, and we analyse them thoroughly in dimension 3 and 4. The loci defined by these…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
Planning in high-dimensional decision spaces is increasingly being studied through the lens of learned representations. Rather than training policies or value heads, we investigate whether planning can be carried out directly in an…
Recently, Peter Doyle and Curt McMullen devised an iterative solution to the fifth degree polynomial. At the method's core is a rational mapping of the Riemann sphere with the icosahedral symmetry of a general quintic. Moreover, this map…
Cumulative and quadratic voting are two distributional voting methods that are expressive, promoting fairness and inclusion, particularly in the realm of participatory budgeting. Despite these benefits, graphical voter interfaces for…
We propose a new single-winner election method ("Schulze method") and prove that it satisfies many academic criteria (e.g. monotonicity, reversal symmetry, resolvability, independence of clones, Condorcet criterion, k-consistency,…
Estimating effects of spatially structured exposures is complicated by unmeasured spatial confounders, which undermine identifiability in spatial linear regression models unless structural assumptions are imposed. We develop a general…
In this article, we review and compare a number of methods of spatial prediction. To demonstrate the breadth of available choices, we consider both traditional and more-recently-introduced spatial predictors. Specifically, in our exposition…
We visualize aggregate outputs of popular multiwinner voting rules--SNTV, STV, Bloc, k-Borda, Monroe, Chamberlin--Courant, and HarmonicBorda--for elections generated according to the two-dimensional Euclidean model. We consider three…
We introduce a single-winner perspective on voting on matchings, in which voters have preferences over possible matchings in a graph, and the goal is to select a single collectively desirable matching. Unlike in classical matching problems,…