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A Bisection Protocol for Political Redistricting
Political redistricting in the United States is the process of drawing congressional and state legislative district boundaries. This work introduces the bisection protocol, a two-player, zero-sum, extensive-form game motivated by political redistricting in which two players alternately divide pieces of a region in half (up to rounding) to obtain a district plan. A subgame perfect Nash equilibrium is presented for the protocol in a relaxed continuous nongeometric setting, and a recurrence is given for the optimal strategies. The bisection protocol is compared with the recently proposed I-cut-you-freeze protocol across a variety of standard fairness metrics. A hardness result is presented for the bisection protocol in the more realistic discrete geometric setting along with exact equilibrium strategies for small grid graphs. Because equilibrium computation is intractable for practical instances, heuristics are developed for both protocols that model players’ drawing strategies as mixed-integer linear programs. When the heuristics are applied to congressional redistricting in Iowa with counties preserved, both protocols produce district plans that are fairer (according to three popular metrics) than Iowa’s 115th congressional districts. Finally, the bisection heuristic is used to generate congressional district plans from census tracts for 18 states, demonstrating its potential for practical use.
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