The problem of election control through social influence consists in finding a set of nodes in a social network of voters to be the starters of a political campaign aimed at supporting a particular target candidate. The voters reached by the campaign change their views on the candidates. The goal is to model the spread of the campaign in such a way as to maximize the chances of winning for the target candidate. Herein, differently from previous work, we consider that each voter is associated with a probability distribution over the candidates modeling the likelihood of the voter to vote for each candidate. In a first model we propose, we prove that, under the Gap-ETH, the problem cannot be approximated to within a factor better than \(1/n^{o(1)}\), where n is the number of voters. In a second model, which is a slight relaxation of the first one, the problem instead admits a constant-factor approximation algorithm. Finally, we present simulations on both synthetic and real networks, comparing the results of our algorithm with those obtained by a standard greedy algorithm for Influence Maximization.

通过社会影响控制选举的问题在于在选民的社交网络中找到一组节点，作为旨在支持特定目标候选人的政治运动的发起者。竞选活动所吸引的选民改变了他们对候选人的看法。目标是以最大化目标候选人获胜机会的方式对竞选的传播进行建模。在这里，与以前的工作不同，我们认为每个选民都与候选人的概率分布相关联，该概率分布模拟了选民投票给每个候选人的可能性。在我们提出的第一个模型中，我们证明，在 Gap-ETH 下，问题不能被近似到比\(1/n^{o(1)}\)更好的因子内，其中n是选民人数。在第二个模型中，它是第一个模型的轻微放松，该问题改为采用常数因子近似算法。最后，我们在合成网络和真实网络上进行了模拟，将我们算法的结果与通过影响最大化的标准贪心算法获得的结果进行了比较。