相关论文: An impossibility theorem for gerrymandering

A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption…

Redistricting efforts have gathered contemporary attention in both popular and scholarly debates, particularly in the United States where efforts to redraw congressional districts to favor either of the two major parties in 12 states --…

Currently, there is currently no effective, standardized way to identify the presence of partisan gerrymandering. A relatively newly proposed method of identification is ensemble analysis. This is done by generating a large neutral ensemble…

We consider two symmetry metrics commonly used to analyze partisan gerrymandering: the Mean-Median Difference (MM) and Partisan Bias (PB). Our main results compare, for combinations of seats and votes achievable in districted elections, the…

The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often…

In several decision-making problems, alternatives should be ranked on the basis of paired comparisons between them. We present an axiomatic approach for the universal ranking problem with arbitrary preference intensities, incomplete and…

We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given…

Quadratic irrationals posses a periodic continued fraction expansion. Much less is known about cubic irrationals. We do not even know if the partial quotients are bounded, even though extensive computations suggest they might follow…

In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR. First, we find a natural obstruction in a finite group for not admitting a bipartite GRR. Then we give a complete…

We study the problem of designing multiwinner voting rules that are candidate monotone and proportional. We show that the set of committees satisfying the proportionality axiom of proportionality for solid coalitions is candidate monotone.…

Switching from one electoral system to another one is frequently criticized by the opposition and is viewed as a means for the ruling party to stay in power. In particular, when the new electoral system is a parallel voting (or a…

Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis of the problem without such constraints yields mathematical insights that can inform real-world…

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.…

Gerrymandering, the deliberate manipulation of electoral district boundaries for political advantage, is a persistent issue in U.S. redistricting cycles. This paper introduces and analyzes a new phenomenon, 'votemandering'- a strategic…

We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…

Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections' outcomes, no matter how paradoxical it may appear. On this purpose…

"Compactness," or the use of shape as a proxy for fairness, has been a long-running theme in the scrutiny of electoral districts; badly-shaped districts are often flagged as examples of the abuse of power known as gerrymandering. The most…

Quadratic irrationals posses a periodic continued fraction expansion. Much less is known about cubic irrationals. We do not even know if the partial quotients are bounded, even though extensive computations suggest they might follow…

In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…