不完全投票更难操纵
Manipulation is Harder with Incomplete Votes
摘要：
联盟操纵（CM）问题已经在许多投票规则的文献中得到了广泛的研究。然而，CM问题，只研究了在完全信息设置，也就是说，当操纵者知道非操纵者的投票。更现实的场景是不完全信息设置，其中操纵者不知道非操纵者的确切投票，但可能具有投票的一些部分知识。在本文中，我们研究了一个设置中的操纵者知道一个偏序为每个选民，这是一致的，该选民的投票。在此背景下，我们引入并研究了两个自然的计算问题：（1）弱操纵（Weak Manipulation，WM）问题，其中操纵者希望以一种方式进行投票，使得他们的首选候选人在非操纵者的部分投票的至少一个扩展中获胜;（2）强操纵（SM）操纵者希望投票的方式，使他们的首选候选人赢得所有可能的扩展的非操纵者的部分选票的问题。我们研究了WM和SM问题的计算复杂性，适用于常用的投票规则，例如多元化、否决权、k-批准、k-否决、最大化、Copeland和Bucklin。我们的主要发现是，除了少数例外，操纵成为一个显着更难的问题，在设置不完整的选票。
英文摘要：
The Coalitional Manipulation (CM) problem has been studied extensively in the literature for many voting rules. The CM problem, however, has been studied only in the complete information setting, that is, when the manipulators know the votes of the non-manipulators. A more realistic scenario is an incomplete information setting where the manipulators do not know the exact votes of the non- manipulators but may have some partial knowledge of the votes. In this paper, we study a setting where the manipulators know a partial order for each voter that is consistent with the vote of that voter. In this setting, we introduce and study two natural computational problems - (1) Weak Manipulation (WM) problem where the manipulators wish to vote in a way that makes their preferred candidate win in at least one extension of the partial votes of the non-manipulators; (2) Strong Manipulation (SM) problem where the manipulators wish to vote in a way that makes their preferred candidate win in all possible extensions of the partial votes of the non-manipulators. We study the computational complexity of the WM and the SM problems for commonly used voting rules such as plurality, veto, k-approval, k-veto, maximin, Copeland, and Bucklin. Our key finding is that, barring a few exceptions, manipulation becomes a significantly harder problem in the setting of incomplete votes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
