Drawing Competitive Districts in Redistricting
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914758091866112 |
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| author | Chuang, Gabriel Hanguir, Oussama Stein, Clifford |
| author_facet | Chuang, Gabriel Hanguir, Oussama Stein, Clifford |
| contents | In the process of redistricting, one important metric is the number of competitive districts, that is, districts where both parties have a reasonable chance of winning a majority of votes. Competitive districts are important for achieving proportionality, responsiveness, and other desirable qualities; some states even directly list competitiveness in their legally-codified districting requirements. In this work, we discuss the problem of drawing plans with at least a fixed number of competitive districts. In addition to the standard, ``vote-band'' measure of competitivenesss (i.e., how close was the last election?), we propose a measure that explicitly considers ``swing voters'' - the segment of the population that may choose to vote either way, or not vote at all, in a given election. We present two main, contrasting results. First, from a computational complexity perspective, we show that the task of drawing plans with competitive districts is NP-hard, even on very natural instances where the districting task itself is easy (e.g., small rectangular grids of population-balanced cells). Second, however, we show that a simple hill-climbing procedure can in practice find districtings on real states in which all the districts are competitive. We present the results of the latter on the precinct-level graphs of the U.S. states of North Carolina and Arizona, and discuss trade-offs between competitiveness and other desirable qualities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_10964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Drawing Competitive Districts in Redistricting Chuang, Gabriel Hanguir, Oussama Stein, Clifford Data Structures and Algorithms Computers and Society F.2.2 In the process of redistricting, one important metric is the number of competitive districts, that is, districts where both parties have a reasonable chance of winning a majority of votes. Competitive districts are important for achieving proportionality, responsiveness, and other desirable qualities; some states even directly list competitiveness in their legally-codified districting requirements. In this work, we discuss the problem of drawing plans with at least a fixed number of competitive districts. In addition to the standard, ``vote-band'' measure of competitivenesss (i.e., how close was the last election?), we propose a measure that explicitly considers ``swing voters'' - the segment of the population that may choose to vote either way, or not vote at all, in a given election. We present two main, contrasting results. First, from a computational complexity perspective, we show that the task of drawing plans with competitive districts is NP-hard, even on very natural instances where the districting task itself is easy (e.g., small rectangular grids of population-balanced cells). Second, however, we show that a simple hill-climbing procedure can in practice find districtings on real states in which all the districts are competitive. We present the results of the latter on the precinct-level graphs of the U.S. states of North Carolina and Arizona, and discuss trade-offs between competitiveness and other desirable qualities. |
| title | Drawing Competitive Districts in Redistricting |
| topic | Data Structures and Algorithms Computers and Society F.2.2 |
| url | https://arxiv.org/abs/2404.10964 |