On the complexity of Winner Verification and Candidate Winner for Multiwinner Voting Rules

Proportionally Representative Participatory Budgeting with Ordinal Preferences

Participatory budgeting (PB) is a democratic paradigm whereby voters decide on a set of projects to fund with a limited budget. We consider PB in a setting where voters report ordinal preferences over projects and have (possibly) asymmetric weights. We propose proportional representation axioms and clarify how they fit into other preference aggregation settings, such as multi-winner voting and approval-based multi-winner voting. As a result of our study, we also discover a new solution concept for approval-based multi-winner voting, which we call Inclusion PSC (IPSC). IPSC is stronger than pro…

The Complexity of the Possible Winner Problem over Partitioned Preferences

The Possible-Winner problem asks, given an election where the voters' preferences over the set of candidates is partially specified, whether a distinguished candidate can become a winner. In this work, we consider the computational complexity of Possible-Winner under the assumption that the voter preferences are $partitioned$. That is, we assume that every voter provides a complete order over sets of incomparable candidates (e.g., candidates are ranked by their level of education). We consider elections with partitioned profiles over positional scoring rules, with an unbounded number of candid…

加权二元投票下的孔多塞赢家与安斯康姆悖论

Condorcet Winners and Anscombes Paradox Under Weighted Binary Voting

研究多个独立二元议题的加权投票问题，分析议题式多数提案的孔多塞赢家属性与安斯康姆悖论，证明无权重时孔多塞赢家存在性判定为co-NP难，提出单切换条件等理论结果并扩展瓦格纳规则至加权场景。

Triadic Consensus：一种群体投票的随机算法

Triadic Consensus: A Randomized Algorithm for Voting in a Crowd

典型的投票规则在有许多候选人的情况下不起作用。如果只有几百个候选人，那么即使是一个简单的任务，如选择一个最好的候选人变得不切实际。出于在互联网上发展群体共识机制的希望，候选人的数量可以很容易地数以千计，我们研究了一个基于瓮的投票规则，每个参与者作为选民和候选人。我们证明，当参与者躺在一个一维的空间，这个投票协议发现一个$(1-ε/sqrt{n})$近似的孔多塞赢家具有很高的概率，而只需要一个预期的$O(\frac{1}{ε^2}\log^2 \frac{n}{ε^2})$平均每个选民的比较。此外，该投票协议被证明有一个准真实的纳什均衡：即，一个纳什均衡存在，这可能不是真实的，但产生一个赢家具有相同的概率分布的真实的策略。

Proportional Approval Voting, Harmonic k-median, and Negative Association

We study a generic framework that provides a unified view on two important classes of problems: (i) extensions of the k-median problem where clients are interested in having multiple facilities in their vicinity (e.g., due to the fact that, with some small probability, the closest facility might be malfunctioning and so might not be available for using), and (ii) finding winners according to some appealing multiwinner election rules, i.e., election system aimed for choosing representatives bodies, such as parliaments, based on preferences of a population of voters over individual candidates. E…

关于控制修正案程序与连续程序胜者的参数化复杂性

On the Parameterized Complexity of Controlling Amendment and Successive Winners

本文研究修正案程序与连续程序中通过增删选民或候选人进行建设性/破坏性控制的参数化复杂性，并推广修正案程序，给出多参数下的完整复杂性图景。

On the Exact Amount of Missing Information that makes Finding Possible Winners Hard

We consider election scenarios with incomplete information, a situation that arises often in practice. There are several models of incomplete information and accordingly, different notions of outcomes of such elections. In one well-studied model of incompleteness, the votes are given by partial orders over the candidates. In this context we can frame the problem of finding a possible winner, which involves determining whether a given candidate wins in at least one completion of a given set of partial votes for a specific voting rule. The possible winner problem is well-known to be NP-complete …

Sample Complexity for Winner Prediction in Elections

Predicting the winner of an election is a favorite problem both for news media pundits and computational social choice theorists. Since it is often infeasible to elicit the preferences of all the voters in a typical prediction scenario, a common algorithm used for winner prediction is to run the election on a small sample of randomly chosen votes and output the winner as the prediction. We analyze the performance of this algorithm for many common voting rules. More formally, we introduce the $(ε, δ)$-winner determination problem, where given an election on $n$ voters and $m$ candidates in whic…

Fine-Grained Complexity and Algorithms for the Schulze Voting Method

We study computational aspects of a well-known single-winner voting rule called the Schulze method [Schulze, 2003] which is used broadly in practice. In this method the voters give (weak) ordinal preference ballots which are used to define the weighted majority graph (WMG) of direct comparisons between pairs of candidates. The choice of the winner comes from indirect comparisons in the graph, and more specifically from considering directed paths instead of direct comparisons between candidates. When the input is the WMG, to our knowledge, the fastest algorithm for computing all winners in the …

从投票流中钓出获胜者

Fishing out Winners from Vote Streams

我们从计算社会选择理论的数据流模型中的赢家决定的问题。具体来说，我们认为总结任意顺序的流$n$投票$m$候选人到一个小空间数据结构，以便能够获得流行的投票规则确定的赢家的任务。正如我们所展示的，找到确切的获胜者需要存储基本上所有的选票。因此，我们关注的问题是找到一个{ \em $\eps$ -winner}，一个候选人谁可以赢得最多$\eps$分数的选票变化。我们展示了非平凡的上界和下界的空间复杂度的$\eps$ -赢家确定几个投票规则，包括$k$ -批准，$k$ -否决，评分规则，批准，最大，Bucklin，Copeland，和运行的多。

一个寻找Dodgson选举获胜者的算法的成功频率的保证

Guarantees for the Success Frequency of an Algorithm for Finding Dodgson-Election Winners

1876年，数学家查尔斯·道奇森（Charles Dodgson）设计了一个美丽的投票系统，长期以来一直吸引着政治学家。然而，已知确定道奇森选举的获胜者对于多项式层次的Θ_2^p水平是完全的。这意味着除非P=NP，否则这个问题不存在多项式时间解，除非多项式层次崩溃为NP，否则这个问题甚至不是NP。尽管如此，我们证明，当选民的数量远远大于候选人的数量-虽然选民的数量可能仍然是多项式的候选人的数量-一个简单的贪心算法非常频繁地发现道奇森赢家在这样一种方式，它"知道“，它已经找到他们，而且算法从来没有错误地宣布一个nonwinner是赢家。