选举中的节俭贿赂
Frugal Bribery in Voting
摘要：
选举中的贿赂问题是计算社会选择理论中的一个重要问题。然而，在选举中，金钱贿赂往往是非法的。基于此，我们引入节俭贿赂的概念，并提出了两个新的相关计算问题，我们称之为节俭贿赂和节俭- $贿赂，以捕捉在选举中没有钱的贿赂。在拟议的模型中，贿赂者本质上是节俭的，这是因为她无法贿赂某种选票，即非弱势选票。在节俭贿赂问题中，目标是通过只改变弱势选票来使某个候选人赢得选举。在节俭贿赂问题中，弱势选票有价格，目标是通过改变弱势选票来使某个候选人赢得选举，但要受到贿赂者的预算约束。我们进一步制定两个自然变种的节俭-{美元}贿赂问题，即均匀节俭-{美元}贿赂和非均匀节俭-{美元}贿赂的弱势选票的价格，分别是相同或不同的。我们研究了几种常用的投票规则的无权和加权选举的上述问题的计算复杂性。我们观察到，即使我们只有少量的候选人，问题是棘手的加权选举这里研究的所有投票规则，唯一的例外的节俭贿赂问题的多数投票规则。相比之下，我们有多项式时间算法的节俭贿赂问题的多数，否决权，k-批准，k-否决权，和多数与径流投票规则的未加权选举。然而，节俭-{美元}贿赂问题是棘手的所有的投票规则，这里研究，除了多数和否决权的投票规则不加权选举。
英文摘要：
Bribery in elections is an important problem in computational social choice theory. However, bribery with money is often illegal in elections. Motivated by this, we introduce the notion of frugal bribery and formulate two new pertinent computational problems which we call Frugal-bribery and Frugal- $bribery to capture bribery without money in elections. In the proposed model, the briber is frugal in nature and this is captured by her inability to bribe votes of a certain kind, namely, non-vulnerable votes. In the Frugal-bribery problem, the goal is to make a certain candidate win the election by changing only vulnerable votes. In the Frugal-{dollar}bribery problem, the vulnerable votes have prices and the goal is to make a certain candidate win the election by changing only vulnerable votes, subject to a budget constraint of the briber. We further formulate two natural variants of the Frugal-{dollar}bribery problem namely Uniform-frugal-{dollar}bribery and Nonuniform-frugal-{dollar}bribery where the prices of the vulnerable votes are, respectively, all the same or different. We study the computational complexity of the above problems for unweighted and weighted elections for several commonly used voting rules. We observe that, even if we have only a small number of candidates, the problems are intractable for all voting rules studied here for weighted elections, with the sole exception of the Frugal-bribery problem for the plurality voting rule. In contrast, we have polynomial time algorithms for the Frugal-bribery problem for plurality, veto, k-approval, k-veto, and plurality with runoff voting rules for unweighted elections. However, the Frugal-{dollar}bribery problem is intractable for all the voting rules studied here barring the plurality and the veto voting rules for unweighted elections.
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