Coalitional manipulation in voting is considered to be any scenario in which a group of voters decide to misrepresent their votes in order to secure an outcome they all prefer to the outcome of the election when they vote honestly. The present paper is devoted to studying coalitional manipulability within the class of scoring voting rules. For any such rule and any number of alternatives, we introduce a new approach allowing us to characterize all the outcomes that are manipulable by a coalition of voters. This then opens the possibility of determining the probability of manipulable outcomes for some well-studied scoring voting rules in the case of small number of alternatives and large electorates, under a well-known assumption on individual preference profiles.

投票中的联盟操纵被认为是一群选民决定歪曲其选票，以确保他们诚实地投票时都倾向于选举结果的结果。本文致力于在计分投票规则类别中研究联盟的可操纵性。对于任何这样的规则和任何其他选择，我们引入一种新方法，使我们能够表征由选民联盟操纵的所有结果。这样，就可以在众所周知的个人喜好假设的情况下，在备选方案数量少而选民人数众多的情况下，为一些经过仔细研究的计分投票规则确定可操纵结果的可能性。