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Bibliographic Details
Main Authors: Cannon, Sarah, Duchin, Moon, Randall, Dana, Rule, Parker
Format: Preprint
Published: 2022
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Online Access:https://arxiv.org/abs/2210.01401
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author Cannon, Sarah
Duchin, Moon
Randall, Dana
Rule, Parker
author_facet Cannon, Sarah
Duchin, Moon
Randall, Dana
Rule, Parker
contents Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now signed on to decisions that find that computational methods can provide key evidence. Today, the leading approaches for benchmarking districting plans are based on the use of spanning trees for sampling graph partitions. We present a new *reversible recombination* algorithm and rigorously prove its fundamental properties. Furthermore, we argue for a canonical sampling distribution called the *spanning tree distribution* that is well adapted to redistricting and provides a principled foundation for comparing and validating methods. Together with a highly efficient (and open-source) implementation that can generate and handle large datasets, this work provides the most powerful null model to date for the gerrymandering problem, meeting an urgent democratic challenge with sound scientific methodology.
format Preprint
id arxiv_https___arxiv_org_abs_2210_01401
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Spanning Trees and Redistricting: New Methods for Sampling and Validation
Cannon, Sarah
Duchin, Moon
Randall, Dana
Rule, Parker
Physics and Society
Computers and Society
60J10, 62P25, 05C85
Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now signed on to decisions that find that computational methods can provide key evidence. Today, the leading approaches for benchmarking districting plans are based on the use of spanning trees for sampling graph partitions. We present a new *reversible recombination* algorithm and rigorously prove its fundamental properties. Furthermore, we argue for a canonical sampling distribution called the *spanning tree distribution* that is well adapted to redistricting and provides a principled foundation for comparing and validating methods. Together with a highly efficient (and open-source) implementation that can generate and handle large datasets, this work provides the most powerful null model to date for the gerrymandering problem, meeting an urgent democratic challenge with sound scientific methodology.
title Spanning Trees and Redistricting: New Methods for Sampling and Validation
topic Physics and Society
Computers and Society
60J10, 62P25, 05C85
url https://arxiv.org/abs/2210.01401