相关论文: An impossibility theorem for gerrymandering

Individual fairness, proposed by Dwork et al., is a fairness measure that is supposed to prevent the unfair treatment of individuals on the subgroup level, and to overcome the problem that group fairness measures are susceptible to…

Consider elections where the set of candidates is partitioned into parties, and each party must nominate exactly one candidate. The Possible President problem asks whether some candidate of a given party can become the winner of the…

We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…

We study the problem of a partisan gerrymanderer who assigns voters to equipopulous districts so as to maximize his party's expected seat share. The designer faces both aggregate uncertainty (how many votes his party will receive) and…

The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…

Over the last few years, researchers have put significant effort into understanding of the notion of proportional representation in committee election. In particular, recently they have proposed the notion of proportionality degree. We…

The Condorcet criterion (CC) is a classical and well-accepted criterion for voting. Unfortunately, it is incompatible with many other desiderata including participation (Par), half-way monotonicity (HM), Maskin monotonicity (MM), and…

Arrow's Impossibility Theorem establishes bounds on what we can require from voting systems. Given satisfaction of a small collection of "fairness" axioms, it shows votes can only exist as dictatorships in which one voter determines all…

We prove some constructive results that on first and maybe even on second glance seem impossible.

We study extensions of the Election Isomorphism problem, focused on the existence of isomorphic subelections. Specifically, we propose the Subelection Isomorphism and the Maximum Common Subelection problems and study their computational…

We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…

Using an ensemble of redistricting plans, we evaluate whether a given political districting faithfully represents the geo-political landscape. Redistricting plans are sampled by a Monte Carlo algorithm from a probability distribution that…

Divided Government is nowadays a common feature of the U.S. political system. The voters can cast partisan ballots for two political powers the executive (Presidential elections) and the legislative (the Congress election). Some recent…

We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…

Various ways for decision making with imprecise probabilities (admissibility, maximal expected utility, maximality, E-admissibility, $\Gamma$-maximax, $\Gamma$-maximin, all of which are well-known from the literature) are discussed and…

Gerrymandering is a pervasive problem within the US political system. In the past decade, methods based on Markov Chain Monte Carlo (MCMC) sampling and statistical outlier tests have been proposed to quantify gerrymandering and were used as…

Since Downs proposed that the act of voting is irrational in 1957, myriad models have been proposed to explain voting and account for observed turnout patterns. We propose a model in which partisans consider both the instrumental and…

Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the…

Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose…

Congressional district lines in many U.S. states are drawn by partisan actors, raising concerns about gerrymandering. To separate the partisan effects of redistricting from the effects of other factors including geography and redistricting…