Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting
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 corresp...
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creator | Autry, Eric A Carter, Daniel Herschlag, Gregory Hunter, Zach Mattingly, Jonathan C |
description | 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. |
doi_str_mv | 10.48550/arxiv.2008.08054 |
format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.2008.08054</identifier><language>eng</language><subject>Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis ; Mathematics - Probability</subject><creationdate>2020-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2008.08054$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2008.08054$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Autry, Eric A</creatorcontrib><creatorcontrib>Carter, Daniel</creatorcontrib><creatorcontrib>Herschlag, Gregory</creatorcontrib><creatorcontrib>Hunter, Zach</creatorcontrib><creatorcontrib>Mattingly, Jonathan C</creatorcontrib><title>Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting</title><description>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.</description><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz71OwzAYhWEvHVDLBTDhG3BwnM-xM7YRf1IjJNo9svPZxaqbVK6p4O6B0uHo3Y70EHJX8gK0lPzBpK9wLgTnuuCaS7ghq-4z5sA2g4mOdi7tHNscY8i0M2k_nWn7YcJIu2nMjrYmxYn6KdF3h-GUUxhyGHcLMvMmntzttXOyfXrcti9s_fb82i7XzNQKmBOotDNWuXIA9L-TZd0o7a306EVlG6ltDQC2tBIBEZVAqBoB4FFJqObk_v_2guiPKRxM-u7_MP0FU_0AfIREew</recordid><startdate>20200818</startdate><enddate>20200818</enddate><creator>Autry, Eric A</creator><creator>Carter, Daniel</creator><creator>Herschlag, Gregory</creator><creator>Hunter, Zach</creator><creator>Mattingly, Jonathan C</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20200818</creationdate><title>Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting</title><author>Autry, Eric A ; Carter, Daniel ; Herschlag, Gregory ; Hunter, Zach ; Mattingly, Jonathan C</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-e2d78eab7e1c4dfc4d516978fb5fdf23b958b6444b1b5d4ddd72d439244fd7543</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Autry, Eric A</creatorcontrib><creatorcontrib>Carter, Daniel</creatorcontrib><creatorcontrib>Herschlag, Gregory</creatorcontrib><creatorcontrib>Hunter, Zach</creatorcontrib><creatorcontrib>Mattingly, Jonathan C</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Autry, Eric A</au><au>Carter, Daniel</au><au>Herschlag, Gregory</au><au>Hunter, Zach</au><au>Mattingly, Jonathan C</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting</atitle><date>2020-08-18</date><risdate>2020</risdate><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.</abstract><doi>10.48550/arxiv.2008.08054</doi><oa>free_for_read</oa></addata></record> |
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title | Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting |
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