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In the context of modern sampling methods for redistricting, we define a natural measurement of the clustering of a political party, and we study how clustering affects the expected election outcome. We first prove general results and then…
We show how voting may be viewed naturally from an algebraic perspective by viewing voting profiles as elements of certain well-studied $\mathbb{Q}S_n$-modules. By using only a handful of simple combinatorial objects (e.g., tabloids) and…
We analyse a preferential urn model with randomness using the replica method. The preferential urn model is a stochastic model based on the concept "the rich get richer." The replica analysis clarifies that the preferential urn model with…
The task of parametric model selection is cast in terms of a statistical mechanics on the space of probability distributions. Using the techniques of low-temperature expansions, we arrive at a systematic series for the Bayesian posterior…
Decisions about how the population of the United States should be divided into legislative districts have powerful and not fully understood effects on the outcomes of elections. The problem of understanding what we might mean by "fair…
We propose a deep learning approach to probabilistic forecasting of macroeconomic and financial time series. Being able to learn complex patterns from a data rich environment, our approach is useful for a decision making that depends on…
We investigate the distribution of partisanship in a cross-section of ten diverse States to elucidate how votes translate into seats won and other metrics. Markov chain simulations taking into account partisanship distribution agree…
Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the…
We study in details the turnout rate statistics for 77 elections in 11 different countries. We show that the empirical results established in a previous paper for French elections appear to hold much more generally. We find in particular…
The Schulze voting method aggregates voter preference data using maxmin-weight graph paths, achieving the Condorcet property that a candidate who would win every head-to-head contest will also win the overall election. Once the voter…
In elections, the vote shares or turnout rates show a strong spatial correlation. The logarithmic decay with distance suggests that a 2D noisy diffusive equation describes the system. Based on the study of U.S. presidential elections data,…
We seek to extract a small number of representative scenarios from large panel data that are consistent with sample moments. Among two novel algorithms, the first identifies scenarios that have not been observed before, and comes with a…
When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
We give an overview of the diverse electoral systems used in local, national, or super-national elections around the world. We discuss existing methods for selecting single and multiple winners and give real-world examples for some more…
Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
Criteria for a good voting system have been given particularly careful scrutiny in recent years, with general agreement that the core values are fair results, voter power and choice, and local representation. This paper reexamines the basic…
The increasing cost of electoral campaigns raises the need for effective campaign planning and a precise understanding of the return of such investment. Interestingly, despite the strong impact of elections on our daily lives, how this…