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Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting

dc.contributor.author Autry, Eric A
dc.contributor.author Carter, Daniel
dc.contributor.author Herschlag, Gregory
dc.contributor.author Hunter, Zach
dc.contributor.author Mattingly, Jonathan C
dc.date.accessioned 2020-08-29T16:32:28Z
dc.date.available 2020-08-29T16:32:28Z
dc.identifier.uri https://hdl.handle.net/10161/21351
dc.description.abstract We develop a Multi-Scale Merge-Split Markov chain on redistricting plans. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts to dividing a graph into a partition with a specified number of elements which each correspond to a different district. The districts satisfy a collection of hard constraints and the measure may be weighted with regard to a number of other criteria. The multi-scale algorithm is similar to our previously developed Merge-Split proposal, however, this algorithm provides improved scaling properties and may also be used to preserve nested communities of interest such as counties and precincts. Both works use a proposal which extends the ReCom algorithm which leveraged spanning trees merge and split districts. In this work we extend the state space so that each district is defined by a hierarchy of trees. In this sense, the proposal step in both algorithms can be seen as a "Forest ReCom." We also expand the state space to include edges that link specified districts, which further improves the computational efficiency of our algorithm. The collection of plans sampled by the MCMC algorithm can serve as a baseline against which a particular plan of interest is compared. If a given plan has different racial or partisan qualities than what is typical of the collection of plans, the given plan may have been gerrymandered and is labeled as an outlier.
dc.subject math.PR
dc.subject math.PR
dc.subject cs.NA
dc.subject math.NA
dc.subject 60j22, 62p25, 91f10, 65c05
dc.title Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting
dc.type Journal article
duke.contributor.id Mattingly, Jonathan C|0297691
dc.date.updated 2020-08-29T16:32:24Z
pubs.organisational-group Trinity College of Arts & Sciences
pubs.organisational-group Mathematics
pubs.organisational-group Duke
duke.contributor.orcid Mattingly, Jonathan C|0000-0002-1819-729X


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