Towards a Dichotomy of Finding Possible Winners in Elections Based on Scoring Rules

Abstract. To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the POSSIBLE WINNER problem that asks, given a set of partial votes, if a distinguished candidate can still become a winner. In this work, we consider the computational complexity of POSSIBLE WINNER for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, k-approval, and Borda. Generalizing previous NP-hardness results for some special cases and providing new many-one reductions, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that POSSI-BLE WINNER is NP-complete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2,1,..., 1, 0), while it is solvable in polynomial time for plurality and veto.

Approval-Based Shortlisting

Shortlisting is the task of reducing a long list of alternatives to a (smaller) set of best or most suitable alternatives from which a final winner will be chosen. Shortlisting is often used in the nomination process of awards or in recommender systems to display featured objects. In this paper, we analyze shortlisting methods that are based on approval data, a common type of preferences. Furthermore, we assume that the size of the shortlist, i.e., the number of best or most suitable alternatives, is not fixed but determined by the shortlisting method. We axiomatically analyze established and new shortlisting methods and complement this analysis with an experimental evaluation based on biased voters and noisy quality estimates. Our results lead to recommendations which shortlisting methods to use, depending on the desired properties

The Complexity of Online Manipulation of Sequential Elections

Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We introduce a framework, in which manipulators can see the past votes but not the future ones, to model online coalitional manipulation of sequential elections, and we show that in this setting manipulation can be extremely complex even for election systems with simple winner problems. Yet we also show that for some of the most important election systems such manipulation is simple in certain settings. This suggests that when using sequential voting, one should pay great attention to the details of the setting in choosing one's voting rule. Among the highlights of our classifications are: We show that, depending on the size of the manipulative coalition, the online manipulation problem can be complete for each level of the polynomial hierarchy or even for PSPACE. We obtain the most dramatic contrast to date between the nonunique-winner and unique-winner models: Online weighted manipulation for plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive case) and NP-hard (destructive case) in the unique-winner model. And we obtain what to the best of our knowledge are the first P^NP[1]-completeness and P^NP-completeness results in the field of computational social choice, in particular proving such completeness for, respectively, the complexity of 3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition manipulation of veto elections.Comment: 24 page

Computational aspects of voting: a literature survey

Preference aggregation is a topic of study in different fields such as philosophy, mathematics, economics and political science. Recently, computational aspects of preference aggregation have gained especial attention and “computational politics” has emerged as a marked line of research in computer science with a clear concentration on voting protocols. The field of voting systems, rooted in social choice theory, has expanded notably in both depth and breadth in the last few decades. A significant amount of this growth comes from studies concerning the computational aspects of voting systems. This thesis comprehensively reviews the work on voting systems (from a computing perspective) by listing, classifying and comparing the results obtained by different researchers in the field. This survey covers a wide range of new and historical results yet provides a profound commentary on related work as individual studies and in relation to other related work and to the field in general. The deliverables serve as an overview where students and novice researchers in the field can start and also as a depository that can be referred to when searching for specific results. A comprehensive literature survey of the computational aspects of voting is a task that has not been undertaken yet and is initially realized here. Part of this research was dedicated to creating a web-depository that contains material and references related to the topic based on the survey. The purpose was to create a dynamic version of the survey that can be updated with latest findings and as an online practical reference

How Hard is Bribery in Elections with Randomly Selected Voters

Many research works in computational social choice assume a fixed set of voters in an election and study the resistance of different voting rules against electoral manipulation. In recent years, however, a new technique known as random sample voting has been adopted in many multi-agent systems. One of the most prominent examples is blockchain. Many proof-of-stake based blockchain systems like Algorand will randomly select a subset of participants of the system to form a committee, and only the committee members will be involved in the decision of some important system parameters. This can be viewed as running an election where the voter committee (i.e., the voters whose votes will be counted) is randomly selected. It is generally expected that the introduction of such randomness should make the election more resistant to electoral manipulation, despite the lack of theoretical analysis. In this paper, we present a systematic study on the resistance of an election with a randomly selected voter committee against bribery. Since the committee is randomly generated, by bribing any fixed subset of voters, the designated candidate may or may not win. Consequently, we consider the problem of finding a feasible solution that maximizes the winning probability of the designated candidate. We show that for most voting rules, this problem becomes extremely difficult for the briber as even finding any non-trivial solution with non-zero objective value becomes NP-hard. However, for plurality and veto, there exists a polynomial time approximation scheme that computes a near-optimal solution efficiently. The algorithm builds upon a novel integer programming formulation together with techniques from n-fold integer programming, which may be of a separate interest