相关论文: Taming the Gerrymander--Statistical Physics Approa…

We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…

We show that the Potts model on a graph can be approximated by a sequence of independent and identically distributed spins in terms of Wasserstein distance at high temperatures. We prove a similar result for the Curie--Weiss--Potts model on…

To assess the presence of gerrymandering, one can consider the shapes of districts or the distribution of votes. The "efficiency gap," which does the latter, plays a central role in a 2016 federal court case on the constitutionality of…

We present a new approach to the analysis of entanglement in smooth bipartite continuous-variable states. One or both parties perform projective filterings via preliminary measurements to determine whether the system is located in some…

We expand the substantive terrain of QI's reach by illuminating a body of political theory that to date has been elaborated in strictly classical language and formalisms but has complex features that seem to merit generalizations of the…

Integrity of elections is vital to democratic systems, but it is frequently threatened by malicious actors. The study of algorithmic complexity of the problem of manipulating election outcomes by changing its structural features is known as…

We examine a global disorder transition when identifying community structure in an arbitrary complex network. Earlier, we illustrated [Phil. Mag. 92, 406 (2012)] that "community detection" (CD) generally exhibits disordered (or unsolvable)…

In the process of redistricting, one important metric is the number of competitive districts, that is, districts where both parties have a reasonable chance of winning a majority of votes. Competitive districts are important for achieving…

We describe a general strategy for sampling configurations from a given (Gibbs-Boltzmann or other) distribution. It is {\it not} based on the Metropolis concept of establishing a Markov process whose stationary state is the wanted…

The local equilibrium thermodynamics is a basic assumption of macroscopic descriptions of the out of equilibrium dynamics for Hamiltonian systems. We numerically analyze the Hamiltonian Potts model in two dimensions to study the violation…

Accurate modeling of opinion dynamics has the potential to help us understand polarization and what makes effective political discourse possible or impossible. Here, we use physics-based methods to model the evolution of political opinions…

We investigate efficient ways for the incorporation of liquid democracy into election settings in which voters submit cumulative ballots, i.e., when each voter is assigned a virtual coin that she can then distribute as she wishes among the…

We consider n identically prepared qubits and study the asymptotic properties of the joint state \rho^{\otimes n}. We show that for all individual states \rho situated in a local neighborhood of size 1/\sqrt{n} of a fixed state \rho^0, the…

Voting theory has become increasingly integrated with computational social choice and multiagent systems. Computational complexity has been extensively used as a shield against manipulation of voting systems, however for several voting…

The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered.…

We consider the heavy-dense limit of QCD at finite fermion density in the canonical formulation and approximate it by a 3-state Potts model. In the strong coupling limit, the model is free of the sign problem. Away from the strong coupling,…

We show that an excellent approximation to the exact quantum solution of the ground state of the Tavis-Cummings model is obtained by means of a semi-classical projected state. This state has an analytical form in terms of the model…

Elections constitute a paradigm of decision-making problems that have puzzled experts of different disciplines for decades. We study two decision-making problems, where groups make decisions that impact only themselves as a group. In both…

Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…

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…