An algorithmic approach to legislative apportionment bases and redistricting

Christian Haas*, Peter Miller, Steven O. Kimbrough

*Corresponding author for this work

Publication: Scientific journalJournal articlepeer-review


The apportionment process that precedes redistricting is generally a staid American political ritual. Recent debates about who should be included in the apportionment basis, however, have raised new questions about representation in the apportionment process. To estimate the effects of excluding non-citizens and children from apportionment, we describe an algorithm to simulate drawing of state legislative districts, based on a previously published algorithm, Seed-Fill-Shift-Repair (SFSR), designed to draw congressional districts. To account for the larger number of districts to draw we implement an adapted search heuristic that is able to efficiently create contiguous and population-balanced maps for state legislative districts, which we call SFSR-G. We use SFSR-G to simulate 1000 maps of upper and lower legislative chambers in 12 states to demonstrate that a shift from total population to citizen voting age population as the apportionment basis will reduce minority–majority and minority-opportunity districts. The paper presents findings for all 12 states investigated, and discusses the important case of Texas at greater length.

Original languageEnglish
Article number102520
Number of pages17
JournalElectoral Studies
Publication statusPublished - Oct 2022

Bibliographical note

Publisher Copyright:
© 2022 The Authors


  • Apportionment
  • Automated redistricting
  • Minority representation
  • Redistricting
  • State legislative districts

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