Most theoretical definitions about the complexity of manipulating elections focus on the decision problem of recognizing which instances can be successfully manipulated, rather than the search problem of finding the successful manipulative actions. Since the latter is a far more natural goal for manipulators, that definitional focus may be misguided if these two complexities can differ. Our main result is that they probably do differ: If integer factoring is hard, then for election manipulation, election bribery, and some types of election control, there are election systems for which recognizing which instances can be successfully manipulated is in polynomial time but producing the successful manipulations cannot be done in polynomial time.
Shortlisting of candidates--selecting a group of "best" candidates--is a special case of multiwinner elections. We provide the first in-depth study of the computational complexity of strategic voting for shortlisting based on the perhaps most basic voting rule in this scenario, l-Bloc (every voter approves l candidates). In particular, we investigate the influence of several tie-breaking mechanisms (e.g., pessimistic versus optimistic) and group evaluation functions (e.g., egalitarian versus utilitarian). Among other things, conclude that in an egalitarian setting strategic voting may indeed b…
Integrity of elections is vital to democratic systems, but it is frequently threatened by malicious actors. The study of algorithmic complexity of the problem of manipulating election outcomes by changing its structural features is known as election control. One means of election control that has been proposed is to select a subset of issues that determine voter preferences over candidates. We study a variation of this model in which voters have judgments about relative importance of issues, and a malicious actor can manipulate these judgments. We show that computing effective manipulations in…
Complexity of voting manipulation is a prominent topic in computational social choice. In this work, we consider a two-stage voting manipulation scenario. First, a malicious party (an attacker) attempts to manipulate the election outcome in favor of a preferred candidate by changing the vote counts in some of the voting districts. Afterwards, another party (a defender), which cares about the voters' wishes, demands a recount in a subset of the manipulated districts, restoring their vote counts to their original values. We investigate the resulting Stackelberg game for the case where votes are …
We study the problem of election control through social influence when the manipulator is allowed to use the locations that she acquired on the network for sending \emph{both} positive and negative messages on \emph{multiple} candidates, widely extending the previous results available in the literature that study the influence of a single message on a single candidate. In particular, we provide a tight characterization of the settings in which the maximum increase in the margin of victory can be efficiently approximated and of those in which any approximation turns out to be impossible. We als…
By the Gibbard--Satterthwaite theorem, every reasonable voting rule for three or more alternatives is susceptible to manipulation: there exist elections where one or more voters can change the election outcome in their favour by unilaterally modifying their vote. When a given election admits several such voters, strategic voting becomes a game among potential manipulators: a manipulative vote that leads to a better outcome when other voters are truthful may lead to disastrous results when other voters choose to manipulate as well. We consider this situation from the perspective of a boundedly …
The computational study of elections generally assumes that the preferences of the electorate come in as a list of votes. Depending on the context, it may be much more natural to represent the list succinctly, as the distinct votes of the electorate and their counts, i.e., high-multiplicity representation. We consider how this representation affects the complexity of election problems. High-multiplicity representation may be exponentially smaller than standard representation, and so many polynomial-time algorithms for election problems in standard representation become exponential-time. Surpri…
The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus). We study the complexity of consensus-related questions, with a particular focus on Kemeny and its qualitative version Slater. The simplest of these questions is the problem of determining whether a ranking is a consensus, and we show that this problem is coNP-complete. We also study the natural question of the complexity of manipulative actions that have a sp…
We consider the problem of protecting and manipulating elections by recounting and changing ballots, respectively. Our setting involves a plurality-based election held across multiple districts, and the problem formulations are based on the model proposed recently by~[Elkind et al, IJCAI 2019]. It turns out that both of the manipulation and protection problems are NP-complete even in fairly simple settings. We study these problems from a parameterized perspective with the goal of establishing a more detailed complexity landscape. The parameters we consider include the number of voters, and the…
While manipulative attacks on elections have been well-studied, only recently has attention turned to attacks that account for geographic information, which are extremely common in the real world. The most well known in the media is gerrymandering, in which district border-lines are changed to increase a party's chance to win, but a different geographical manipulation involves influencing the election by selecting the location of polling places, as many people are not willing to go to any distance to vote. In this paper we initiate the study of this manipulation. We find that while it is easy …
Lu and Boutilier proposed a novel approach based on "minimax regret" to use classical score based voting rules in the setting where preferences can be any partial (instead of complete) orders over the set of alternatives. We show here that such an approach is vulnerable to a new kind of manipulation which was not present in the classical (where preferences are complete orders) world of voting. We call this attack "manipulative elicitation." More specifically, it may be possible to (partially) elicit the preferences of the agents in a way that makes some distinguished alternative win the electi…
Exact Algorithms for Weighted and Unweighted Borda Manipulation Problems
加权和非加权Borda操作问题都被证明是$\mathcal{NP}$ -困难的。然而，没有确切的组合算法已知这些问题。在本文中，我们开始研究的精确组合算法的加权和非加权Borda操作问题。更准确地说，我们提出了$O^*((m\cdot 2^m)^{t+1})$时间和$O^*(t^{2m})$时间\footnote{$O^*()$ is the $O()$ notation with suppressed factors polynomial in the size of the input.}组合算法的加权和未加权的Borda操作问题，分别，其中$t$是机械手的数量和$m$是候选人的数量。因此，对于$t=2$，我们解决了Betzler等人[IJCAI 2011]提出的一个未决问题。作为我们的结果的副产品，我们表明，{未加权Borda操作}问题承认运行时间的算法$O^*(2^{9m^2\log{m}})$，基于整数线性规划技术。最后，我们研究了{unweighted Borda操纵}问题下的单峰选举和目前的多项式时间算法的问题的情况下，两个机械手，在对比$\mathcal{NP}$ -硬度的情况下，在一般设置。
