Redistricting efforts have gathered contemporary attention in both popular and scholarly debates, particularly in the United States where efforts to redraw congressional districts to favor either of the two major parties in 12 states -- such as California, Texas, and Ohio -- have captured the public eye. The treatment of redistricting in computational social choice has essentially focused on the process of determining "appropriate" districts. In this work, we are interested in understanding the gamut of options left for the "losing" party, and so we consider the flip side of the problem: Given fixed/predetermined districts, can a given party still make their candidates win by strategically placing them in certain districts? We dub this as "recampaigning" to capture the intuition that a party would redirect their campaigning efforts from one district to another. We model recampaigning as a computational problem, consider natural variations of the model, and study those new models through the lens of (1) (polynomial-time many-one) interreducibilities, (2) separations/collapses (both unconditional and axiomatic-sufficient), and (3) both worst-case and parametrized complexity.

翻译：重新划分选区这一努力已引起大众和学术界的广泛关注，尤其是在美国，12个州（如加利福尼亚、得克萨斯和俄亥俄）为偏向两大政党之一而重新绘制国会选区的举动已吸引公众目光。计算社会选择学中对重新划分选区的处理主要集中在确定"适当"选区的过程上。本文旨在理解"失败"党所剩选项的范围，因此我们考虑问题的另一面：在给定/预设的选区下，某个政党是否仍能通过策略性地将其候选人安排在某些选区中使其获胜？我们将此称为"重新竞选"，以捕捉一个政党将其竞选努力从一个选区转向另一个选区的直觉。我们将重新竞选建模为计算问题，考虑该模型的自然变体，并从以下角度研究这些新模型：(1)（多项式时间多对一）互归约性，(2)分离/坍缩（无条件和公理充分性均可），以及(3)最坏情形和参数化复杂性。