12 citations · 39 across the 6 of their papers we have counts for
14 papers
Metric geometry for ranking-based voting: Tools for learning electoral structure
Moon Duchin, Kristopher Tapp
In this paper, we develop the metric geometry of ranking statistics, proving that the two major permutation distances in the statistics literature -- Kendall tau and Spearman footr…
Census TopDown: The Impacts of Differential Privacy on Redistricting
Aloni Cohen, Moon Duchin, JN Matthews +1
The 2020 Decennial Census will be released with a new disclosure avoidance system in place, putting differential privacy in the spotlight for a wide range of data users. We conside…
Implementing partisan symmetry: Problems and paradoxes
Daryl DeFord, Natasha Dhamankar, Moon Duchin +4
We consider the measures of partisan symmetry proposed for practical use in the political science literature, as clarified and developed in Katz, King, and Rosenblatt (2020). Eleme…
The (homological) persistence of gerrymandering
Moon Duchin, Tom Needham, Thomas Weighill
We apply persistent homology, the dominant tool from the field of topological data analysis, to study electoral redistricting. Our method combines the geographic information from a…
Mathematics of Nested Districts: The Case of Alaska
Sophia Caldera, Daryl DeFord, Moon Duchin +2
In eight states, a "nesting rule" requires that each state Senate district be exactly composed of two adjacent state House districts. In this paper we investigate the potential imp…
Locating the representational baseline: Republicans in Massachusetts
Moon Duchin, Taissa Gladkova, Eugene Henninger-Voss +3
Republican candidates often receive between 30 and 40 percent of the two-way vote share in statewide elections in Massachusetts. For the last three Census cycles, MA has held 9-10…
You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces
Moon Duchin, Viveka Erlandsson, Christopher J. Leininger +1
We give a complete characterization of the relationship between the shape of a Euclidean polygon and the symbolic dynamics of its billiard flow. We prove that the only pairs of tab…
Gerrymandering metrics: How to measure? What's the baseline?
Moon Duchin
This note outlines three intellectually distinct but not mutually exclusive strategies for measuring partisan gerrymandering: partisan symmetry, efficiency gap, and algorithmic sam…
A formula goes to court: Partisan gerrymandering and the efficiency gap
Mira Bernstein, Moon Duchin
Recently, a proposal has been advanced to detect unconstitutional partisan gerrymandering with a simple formula called the efficiency gap. The efficiency gap is now working its way…
A sharper threshold for random groups at density one-half
Moon Duchin, Kasia Jankiewicz, Shelby C. Kilmer +3
In the density model of random groups, we consider presentations with any fixed number m of generators and many random relators of length l, sending l to infinity. If d is a "densi…
Fine asymptotic geometry in the Heisenberg group
Moon Duchin, Christopher Mooney
For every finite generating set on the integer Heisenberg group H(Z), Pansu showed that the word metric has the large-scale structure of a Carnot-Caratheodory Finsler metric on the…
Statistical hyperbolicity in groups
Moon Duchin, Samuel Lelièvre, Christopher Mooney
In this paper, we introduce a geometric statistic called the "sprawl" of a group with respect to a generating set, based on the average distance in the word metric between pairs of…
The geometry of spheres in free abelian groups
Moon Duchin, Samuel Lelièvre, Christopher Mooney
We study word metrics on Z^d by developing tools that are fine enough to measure dependence on the generating set. We obtain counting and distribution results for the words of leng…
Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry
Moon Duchin
We show that, in the Teichmüller metric, "thin-framed triangles are thin"---that is, under suitable hypotheses, the variation of geodesics obeys a hyperbolic-like inequality. This…