相关论文: Implementing partisan symmetry: Problems and parad…

Classical spatial models of two-party competition typically predict convergence to the median voter, yet real-world party systems often exhibit persistent and asymmetric polarization. We develop a spatial model of two-party competition in…

Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…

Consider an election where N seats are distributed among parties with proportions p_1,...,p_m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a…

In recent years, in an effort to promote fairness in the election process, a wide variety of techniques and metrics have been proposed to determine whether a map is a partisan gerrymander. The most accessible measures, requiring easily…

Understanding political phenomena requires measuring the political preferences of society. We introduce a model based on mixtures of spatial voting models that infers the underlying distribution of political preferences of voters with only…

Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…

Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of…

Partisan gerrymandering, i.e., manipulation of electoral district boundaries for political advantage, is one of the major challenges to election integrity in modern day democracies. Yet most of the existing methods for detecting partisan…

Defying the median voter theorem, party polarization has spread globally, especially in the United States. As concerns grow over its risks to democracy, political science has probed its causes, revealing two paradoxes: while polarization…

Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical…

When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…

We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this…

This preprint offers a detailed look, both qualitative and quantitative, at districting with respect to recent voting patterns in one state: Pennsylvania. We investigate how much the partisan playing field is tilted by political geography.…

Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…

The process of legislative redistricting in New Hampshire, along with many other states across the country, was particularly contentious during the 2020 census cycle. In this paper we present an ensemble analysis of the enacted districts to…

Partisan gerrymandering poses a threat to democracy. Moreover, the complexity of the districting task may exceed human capacities. One potential solution is using computational models to automate the districting process by optimizing…

Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric $\bar{d}_1$ that combines…

Algorithmic and statistical approaches to congressional redistricting are becoming increasingly valuable tools in courts and redistricting commissions for quantifying gerrymandering in the United States. While there is existing literature…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

The Schmidt number is of crucial importance in characterizing the bipartite pure states. We explore and propose here a generalization of Schmidt number for states in multipartite systems. It is shown to be entanglement monotonic and valid…