Related papers: Don't Trust A Single Gerrymandering Metric
Using the recently introduced declination function, we estimate the net number of seats won in the US House of Representatives due to asymmetries in vote distributions. Such asymmetries can arise from combinations of partisan gerrymandering…
Manipulation, bribery, and control are well-studied ways of changing the outcome of an election. Many voting rules are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to…
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…
We consider a social choice setting with agents that are partitioned into disjoint groups, and have metric preferences over a set of alternatives. Our goal is to choose a single alternative aiming to optimize various objectives that are…
Divergence functions are interesting discrepancy measures. Even though they are not true distances, we can use them to measure how separated two points are. Curiously enough, when they are applied to random variables, they lead to a notion…
Mapping political party systems to metric policy spaces is one of the major methodological problems in political science. At present, in most political science project this task is performed by domain experts relying on purely qualitative…
Hedonic games are fundamental models for investigating the formation of coalitions among a set of strategic agents, where every agent has a certain utility for every possible coalition of agents it can be part of. To avoid the…
We study how electoral rules shape polarization dynamics when voters and candidates both adapt to repeated election outcomes. We introduce two geometric primitives for comparing rules under this feedback: the \emph{winner radius} $R_t =…
As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for…
Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure \emph{intersectional fairness} -- i.e., that no subgroup is discriminated against. It is known that…
In this paper, we apply techniques of ensemble analysis to understand the political baseline for Congressional representation in Colorado. We generate a large random sample of reasonable redistricting plans and determine the partisan…
In a district-based election, we apply a voting rule $r$ to decide the winners in each district, and a candidate who wins in a maximum number of districts is the winner of the election. We present efficient sampling-based algorithms to…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
Elections for public offices in democratic nations are large-scale examples of collective decision-making. As a complex system with a multitude of interactions among agents, we can anticipate that universal macroscopic patterns could emerge…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
Generative adversarial networks (GANs) have been extremely effective in approximating complex distributions of high-dimensional, input data samples, and substantial progress has been made in understanding and improving GAN performance in…
The median voter theorem has long been the default model of voter behavior and candidate choice. While contemporary work on the distribution of political opinion has emphasized polarization and an increasing gap between the "left" and the…
Measure what is measurable, and make measurable what is not so (Galileo Galilei). According to the above sentence we do not ask why we need to measure democracy but if it is possible to measure something which is not unequivocally defined.…
Socioeconomic segregation is considered one of the main factors behind the emergence of large-scale inequalities in urban areas, and its characterisation is an active area of research in urban studies. There are currently many available…
Distortion-based analysis has established itself as a fruitful framework for comparing voting mechanisms. m voters and n candidates are jointly embedded in an (unknown) metric space, and the voters submit rankings of candidates by…