We study the election control problem with multi-votes, where each voter can present a single vote according different views (or layers, we use "layer" to represent "view"). For example, according to the attributes of candidates, such as: education, hobby or the relationship of candidates, a voter may present different preferences for the same candidate set. Here, we consider a new model of election control that by assigning different rules to the votes from different layers, makes the special candidate p being the winner of the election (a rule can be assigned to different layers). Assuming a set of candidates C among a special candidate "p", a set of voters V, and t layers, each voter gives t votes over all candidates, one for each layer, a set of voting rules R, the task is to find an assignment of rules to each layer that p is acceptable for voters (possible winner of the election). Three models are considered (denoted as sum-model, max-model, and min-model) to measure the satisfaction of each voter. In this paper, we analyze the computational complexity of finding such a rule assignment, including classical complexity and parameterized complexity. It is interesting to find out that 1) it is NP-hard even if there are only two voters in the sum-model, or there are only two rules in sum-model and max-model; 2) it is intractable with the number of layers as parameter for all of three models; 3) even the satisfaction of each vote is set as dichotomous, 1 or 0, it remains hard to find out an acceptable rule assignment. Furthermore, we also get some other intractable and tractable results.

翻译：我们研究了多票投票场景下的选举控制问题，其中每位投票者可根据不同视角（或层次，本文使用"层次"表示"视角"）提交单张选票。例如，根据候选人的属性（如教育背景、兴趣爱好或人际关系），投票者可能对同一候选集呈现不同的偏好顺序。本文提出一种新型选举控制模型：通过为不同层次的选票分配不同规则，使特定候选人p成为选举胜出者（同一规则可被分配至多个层次）。假设存在包含特殊候选人p的候选集C、投票者集V、t个层次（每位投票者对全体候选人提交t张选票，每层一张）以及投票规则集R，任务是为每个层次分配规则，使得候选人p获得投票者认可（即成为可能的选举胜出者）。本文考虑三种衡量投票者满意度的模型（分别称为求和模型、最大值模型和最小值模型）。我们分析了寻找此类规则分配方案的计算复杂度，包括经典复杂度与参数复杂度。有趣发现包括：1）在求和模型中仅存在两名投票者时，或在求和模型与最大值模型中仅存在两种规则时，问题即为NP困难；2）对三种模型而言，以层次数量为参数时问题均难以处理；3）即使将每张选票的满意度简化为二值（1或0），寻找可接受的规则分配方案仍具难度。此外，我们还获得了其他可解性与不可解性结论。