Related papers: Alleviating partisan gerrymandering: can math and …

We consider a distributed voting problem with a set of agents that are partitioned into disjoint groups and a set of obnoxious alternatives. Agents and alternatives are represented by points in a metric space. The goal is to compute the…

While manipulative attacks on elections have been well-studied, only recently has attention turned to attacks that account for geographic information, which are extremely common in the real world. The most well known in the media is…

Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…

Political fragmentation in Africa poses to a significant challenge to effective governance and stability. Traditional measures of party system fragmentation, such as the Effective Number of Parties (ENP) index, often fail to capture the…

In an election in which each voter ranks all of the candidates, we consider the head-to-head results between each pair of candidates and form a labeled directed graph, called the margin graph, which contains the margin of victory of each…

Mutual coherence is a measure of similarity between two opinions. Although the notion comes from philosophy, it is essential for a wide range of technologies, e.g., the Wahl-O-Mat system. In Germany, this system helps voters to find…

The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier across these groups. Constraints of this…

Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities. In recent years, the use of randomized methods to sample from the vast space…

It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…

This preprint is an exploration in how a single mathematical idea - entropy - can be applied to redistricting in a number of ways. It's meant to be read not so much as a call to action for entropy, but as a case study illustrating one of…

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…

The problem of how to allocate to states the seats in the US House of Representatives is the most studied instance of what is termed the `apportionment problem'. We propose a new method of apportionment which is stochastic, which meets the…

Many democratic political parties hold primary elections, which nicely reflects their democratic nature and promote, among other things, the democratic value of inclusiveness. However, the methods currently used for holding such primary…

The space of connected graph partitions underlies statistical models used as evidence in court cases and reform efforts that analyze political districting plans. In response to the demands of redistricting applications, researchers have…

Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…

Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice,…

The paper considers the problem of finding the number of dominant voters in two-level voting procedures. At the first stage, voting is conducted among local groups of voters, and at the second stage, the results are aggregated to form a…

Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this…

Apportionment is the act of distributing the seats of a legislature among political parties (or states) in proportion to their vote shares (or populations). A famous impossibility by Balinski and Young (2001) shows that no apportionment…

We study computational aspects of a well-known single-winner voting rule called the Schulze method [Schulze, 2003] which is used broadly in practice. In this method the voters give (weak) ordinal preference ballots which are used to define…