Abstract
By using the Ising model formulation for combinatorial optimization with 0–1 binary variables, we investigated the extent to which partisan gerrymandering is possible from a random but even distribution of supporters. Assuming that an electoral district consists of square subareas and that each subarea shares at least one edge with other subareas in the district, it was possible to find the most tilted assignment of seats in most cases. However, in cases where supporters' distribution included many enclaves, the maximum tilted assignment was usually found to fail. We also discussed the proposed algorithm is applicable to other fields such as the redistribution of delivery destinations.
Highlights
By using the Ising model formulation for combinatorial optimization with 0–1 binary variables, we investigated the extent to which partisan gerrymandering is possible from a random but even distribution of supporters
By using combinatorial optimization based on the Ising model13, we investigated the extent to which partisan gerrymandering under a two-party system is possible to tilt seats in favor of one party starting from a random but even distribution of supporters for both parties
It requires at least 33 governing cells to set the number of assigned seats (Nseat) to Nmax(= 11 [in this study]) with 3 to 2 hard-won victories
Summary
By using the Ising model formulation for combinatorial optimization with 0–1 binary variables, we investigated the extent to which partisan gerrymandering is possible from a random but even distribution of supporters. Electoral districts are a unit of voters artificially defined by electoral legislation If this artificial demarcation is intentional, the neutrality of being a geographical division will disappear, and the problem of partisan gerrymandering arises. There are two techniques widely known in gerrymandering: cracking and p acking1 The former means the cracking of the opposing party’s voters’ concentration not to form a majority of the district. A voter who is assigned a wasted vote by gerrymandering effectively loses the opportunity to elect a representative. The concept of gerrymandering is expanding in recent times, and it becomes a research area that requires closer integration of social and mathematical science. Such mathematical studies on gerrymandering are still in the early stages. The combinatorial optimization based on the Ising model begins to be applied to various fields and problems such as logistics (delivery route planning), factories (automated guided vehicle operation), services (nurse scheduling), finance (risk management of financial assets), materials science (metamaterials design), and drug design (molecular similarity search)
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