Redistricting efforts have gathered contemporary attention in both quotidian 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：选区重划工作已在日常讨论与学术辩论中引起广泛关注，尤其在美国，加利福尼亚州、德克萨斯州和俄亥俄州等12个州为偏袒两大政党之一而重划国会选区的行动已成为公众焦点。计算社会选择领域对选区重划的研究主要集中于确定“合适”选区的过程。本研究旨在探讨“失败”政党剩余的选择范围，因此我们关注该问题的另一面：在选区固定/预先确定的情况下，特定政党是否仍能通过将其候选人战略性部署于特定选区而使其获胜？我们将此称为“重新竞选”，以体现政党将竞选资源从一个选区重新调配至另一选区的策略意图。我们将重新竞选建模为计算问题，考虑该模型的自然变体，并通过以下视角研究这些新模型：(1)（多项式时间多一）互归约性，(2) 分离/坍缩现象（包括无条件性与公理充分性），以及(3) 最坏情况与参数化复杂度分析。