Related papers: The Gerrymandering Jumble: Map Projections Permute…
By studying the effects of the shape moduli associated with toroidal compactifications, we demonstrate that Planck-sized extra dimensions can cast significant ``shadows'' over low-energy physics. These shadows can greatly distort our…
In recent decades, state legislatures have often drawn U.S. Congressional voting districts that look---to the human eye---to be rather twisted. In this paper, we propose a method to measure how much districts "meander" via a computation of…
Inverse optimization has received much attention in recent years, but little literature exists for solving generalized mixed integer inverse optimization. We propose a new approach for solving generalized mixed-integer inverse optimization…
Multiple-scale and broad-scale assessments often require rescaling the original data to a consistent grain size for analysis. Rescaling categorical raster data by spatial aggregation is common in large area ecological assessments. However,…
Several measures of partisan bias are reviewed for single member districts with two dominant parties. These include variants of the simple bias that considers only deviation of seats from 50% at statewide 50% vote. Also included are…
Packing disjoint subgraphs in a given graph is a fundamental problem with many applications. Motivated by political districting, we focus on connected subgraphs that are compact (e.g., having constant radius from a single center vertex) and…
Why not have a computer just draw a map? This is something you hear a lot when people talk about gerrymandering, and it's easy to think at first that this could solve redistricting altogether. But there are more than a couple problems with…
The splashback radius $R_{\rm sp}$ is a boundary of a halo that separates infalling and accreted matter. This results in a steep drop in the density profile at $R_{\rm st}$, which is a commonly adopted proxy for $R_{\rm sp}$.…
Every representative democracy must specify a mechanism under which voters choose their representatives. The most common mechanism in the United States -- Winner takes all single-member districts -- both enables substantial partisan…
We derive simple and unified closed-form expressions for projections with respect to fidelity (equivalently, the Bures and purified distances) onto several sets of interest. These include projections of bipartite positive semidefinite (PSD)…
This paper combines two ingredients in order to get a rather surprising result on one of the most studied, elegant and powerful tools for solving convex feasibility problems, the method of alternating projections (MAP). Going back to names…
The gerrymandering problem is a worldwide problem which sets great threat to democracy and justice in district based elections. Thanks to partisan redistricting commissions, district boundaries are often manipulated to benefit incumbents.…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
Composite indicators aggregate a set of variables using weights which are understood to reflect the variables' importance in the index. In this paper we propose to measure the importance of a given variable within existing composite…
Among recent developments centered around Randomized Kaczmarz (RK), a row-sampling iterative projection method for large-scale linear systems, several adaptions to the method have inspired faster convergence. Focusing solely on…
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…
We discuss difficulties of evaluating partisan gerrymandering in the congressional districts in Utah and the failure of many common metrics in Utah. We explain why the Republican vote share in the least-Republican district (LRVS) is a good…
Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect…
The classical notion of retraction map used to approximate geodesics is extended and rigorously defined to become a powerful tool to construct geometric integrators and it is called discretization map. Using the geometry of the tangent and…
Redistricting practitioners must balance many competing constraints and criteria when drawing district boundaries. To aid in this process, researchers have developed many methods for optimizing districting plans according to one or more…