An algorithmic approach to legislative apportionment bases and redistricting

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.