Related papers: Impartial Redistricting: A Markov Chain Approach

This note outlines three intellectually distinct but not mutually exclusive strategies for measuring partisan gerrymandering: partisan symmetry, efficiency gap, and algorithmic sampling.

We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…

Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…

Judgment aggregation problems form a class of collective decision-making problems represented in an abstract way, subsuming some well known problems such as voting. A collective decision can be reached in many ways, but a direct one-step…

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…

We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…

Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…

Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to…

Partially observable Markov decision processes (POMDPs) are a natural model for planning problems where effects of actions are nondeterministic and the state of the world is not completely observable. It is difficult to solve POMDPs…

Computer-aided decision making--where a human decision-maker is aided by a computational classifier in making a decision--is becoming increasingly prevalent. For instance, judges in at least nine states make use of algorithmic tools meant…

Significant efforts are being spent on building a quantum computer. At the same time, developments in quantum software are rapidly progressing. Insufficient quantum resources often are the problem when running quantum algorithms. New…

Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…

We create 4200 synthetic cities which vary in percent minority population and their residential segregation patterns. Of these, 1200 are modeled on existing cities, and 3000 are rectangular grid cities. In each city, we consider…

The Political Districting Problem is mapped to a $q$-state Potts model in which the constraints can be written as interactions between sites or external fields acting on the system. Districting into $q$ voter districts is equivalent to…

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…

We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…

We introduce an algorithm for generating a random sequence of fragmentation trees, which we call the ancestral branching algorithm. This algorithm builds on the recursive partitioning structure of a tree and gives rise to an associated…

The gradient boosting machine is a powerful ensemble-based machine learning method for solving regression problems. However, one of the difficulties of its using is a possible discontinuity of the regression function, which arises when…

For many probability distributions of interest, it is quite difficult to obtain samples efficiently. Often, Markov chains are employed to obtain approximately random samples from these distributions. The primary drawback to traditional…

We develop a theory of distributive competition under redistricting that explains both electoral outcomes and the equilibrium allocation of policy benefits by endogenizing voter pivotality. In a multi-district model with primaries, general…