Browsing by Author "Fravel, Jamie"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Black Representation and District Compactness in Southern Congressional Districts
    Goedert, Nicholas; Hildebrand, Robert; Pierson, Matthew; Travis, Laurel; Fravel, Jamie (2024-04-01)
    This paper explores the assumed trade-off between district compactness and Black representation in legislative districts in the American South. We perform analysis both on heuristically generated districts using current US demographics, and on historical congressional maps since the 1970s. Computations are performed using an iterative heuristic to find feasible solutions guided by multiple objectives. We find that while the trade-off has been strongly observed historically, it is possible to effectively address both goals simultaneously in most cases. We are able to demonstrate maps substantially superior to the present enacted maps on both dimensions in at least seven of nine states analyzed. Nevertheless, the trade-off appears more necessary in states with larger and/or more heavily rural Black populations than in more urbanized states, where the drawing of compact Blackinfluence districts is easier.
  • Thumbnail Image
    Continuous Equality Knapsack with Probit-Style Objectives
    Fravel, Jamie; Hildebrand, Robert; Travis, Laurel (2022-11-04)
    We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, strictly increasing, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple allocation problem with the goal of optimizing an expected value where the objective is a sum of cumulative distribution functions of identically distributed normal distributions (i.e., a sum of inverse probit functions). We prove structural results of this model under general assumptions and provide two algorithms for efficient optimization: (1) running in linear time and (2) running in a constant number of operations given preprocessing of the objective function.