Related papers: Measuring Congressional District Meandering
Over the years, American politics have become increasingly polarized. In the current political landscape, a president cannot easily collaborate with the opposite party and pass legislature. Ideologies between parties have drifted apart to…
Spatial voting models of legislators' preferences are used in political science to test theories about their voting behavior. These models posit that legislators' ideologies as well as the ideologies reflected in votes for and against a…
Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…
Liquid democracy is the principle of making collective decisions by letting agents transitively delegate their votes. Despite its significant appeal, it has become apparent that a weakness of liquid democracy is that a small subset of…
The Political Districting Problem is mapped to a $q$-state Potts model in which the constraints can be written as interactions between sites or external fields acting on the system. Districting into $q$ voter districts is equivalent to…
We compute exactly the mean perimeter <L(T)> and the mean area <A(T)> of the convex hull of a random acceleration process of duration T in two dimensions. We use an exact mapping that relates, via Cauchy's formulae, the computation of the…
We propose and analyze the moving median absolute deviation (MMAD) as a robust depth construction based on the median absolute distance functional with particular emphasis on its local geometry and probabilistic structure. In the univariate…
We consider the median dynamics process in general graphs. In this model, each vertex has an independent initial opinion uniformly distributed in the interval [0,1] and, with rate one, updates its opinion to coincide with the median of its…
Local time is the measure of how much time a random walk has visited a given position. In multiple scattering media, where waves are diffuse, local time measures the sensitivity of the waves to the local medium's properties. Local…
How to elect the representatives in legislative bodies is a question that every modern democracy has to answer. This design task has to consider various elements so as to fulfill the citizens' expectations and contribute to the maintenance…
Finding outlying elements in probability distributions can be a hard problem. Taking a real example from Voting Rights Act enforcement, we consider the problem of maximizing the number of simultaneous majority-minority districts in a…
Depth is a concept that measures the `centrality' of a point in a given data cloud or in a given probability distribution. Every depth defines a family of so-called trimmed regions. For statistical applications it is desirable that with…
Results of deploying a Differential Image Motion Monitor (DIMM) and a DIMM combined with a Multi-Aperture Scintillation Sensor (MASS/DIMM) are reported for campaigns in 2011 and 2012 on the roof of the Polar Environment Atmospheric Research…
Motivated by the problem of partisan gerrymandering, we introduce an electoral system for a representative democracy called democratic cellular voting, designed to make modern packing and cracking strategies irrelevant by allowing districts…
In previous work [arXiv:1608.02014], we developed a rigorous statistical test for outlier status in a reversible Markov Chain, and demonstrated its utilization with an application to detecting gerrymandering in Pennsylvania's Congressional…
In this paper I show that any $m$th-degree polynomial function of the elements of the density matrix $\rho$ can be determined by finding the expectation value of an observable on $m$ copies of $\rho$, without performing state tomography.…
The paper deals with state estimation of a spatially distributed system given noisy measurements from pointwise-in-time-and-space threshold sensors spread over the spatial domain of interest. A Maximum A posteriori Probability (MAP)…
Computing entanglement of an arbitrary bipartite or multipartite mixed state is in general not an easy task as it usually involves complex optimization. Here we show that exploiting symmetries of certain mixed states, we can compute a…
Accurately measuring street dimensions is essential to evaluating how their design influences both travel behavior and safety. However, gathering street-level information at city scale with precision is difficult given the quantity and…
Volume approximation is an important problem found in many applications of computer graphics, vision, and image processing. The problem is about computing an accurate and compact approximate representation of 3D volumes using some simple…