Computational Social Choice: The First Ten Years and Beyond

Aziz, Haris; Brandt, Felix; Elkind, Edith; Skowron, Piotr

doi:10.1007/978-3-319-91908-9_4

Cited by 16 publications

(21 citation statements)

References 112 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our paper is the first to bring fine-grained complexity into the field of computational social choice (see [2,9,19] for a description of computational social choice topics). Related areas such as Fixed Parameter Tractability (FPT) 7 and hardness of approximation 8 have already gained significant traction in computational social choice.…”

Section: Our Contributionmentioning

confidence: 99%

See 1 more Smart Citation

Fine-Grained Complexity and Algorithms for the Schulze Voting Method

Sornat

Williams

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

View full text Add to dashboard Cite

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 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 weighted majority graph, to our knowledge, the fastest algorithm for computing all winners in the Schulze method uses a folklore reduction to the All-Pairs Bottleneck Paths (APBP) problem and runs in O(m 2.69 ) time, where m is the number of candidates. It is an interesting open question whether this can be improved. Our first result is a combinatorial algorithm with a nearly quadratic running time for computing all winners. This running time is essentially optimal as it is nearly linear in the size of the weighted majority graph.If the input to the Schulze winners problem is not the weighted majority graph but the preference profile, then constructing the weighted majority graph is a bottleneck that increases the running time significantly; in the special case when there are m candidates and n = O(m) voters, the running time is O(m 2.69 ), or O(m 2.5 ) if there is a nearly-linear time algorithm for multiplying dense square matrices.To address this bottleneck, we prove a formal equivalence between the well-studied Dominance Product problem and the problem of computing the weighted majority graph. As the Dominance Product problem is believed to require at least time r 2.5−o(1) on r × r matrices, our equivalence implies that constructing the weighted majority graph in O(m 2.499 ) time for m candidates and n = O(m) voters would imply a breakthrough in the study of "intermediate" problems [Lincoln et al., 2020] in fine-grained complexity. We prove a similar connection between the so called Dominating Pairs problem and the problem of verifying whether a given candidate is a winner.Our paper is the first to bring fine-grained complexity into the field of computational social choice. Previous approaches say nothing about lower bounds for problems that already have polynomial time algorithms. By bringing fine-grained complexity into the picture we can identify voting protocols that are unlikely to be practical for large numbers of candidates and/or voters, as their complexity is likely, say at least cubic. CCS Concepts: • Theory of computation → Algorithmic game theory and mechanism design; Graph algorithms analysis; • Applied computing → Voting / election technologies.

show abstract

Section: Our Contributionmentioning

confidence: 99%

“…The method appears under different names such as Beatpath Method/Winner, Path Voting, (Cloneproof) Schwartz Sequential Dropping-see discussion in[39] 2. Also referred to as the Minimax method and the Simpson-Kramer method[40] 3.…”

mentioning

confidence: 99%

Fine-Grained Complexity and Algorithms for the Schulze Voting Method

Sornat

Williams

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

View full text Add to dashboard Cite

show abstract

“…Given a a set of alternatives and a set of agents who possess preference relations over the alternatives, social choice theory focuses on how to yield a collective choice that appropriately reflects the agents' individual preferences (Aziz et al 2017). With this aim, social choice theory has extensively explored many ways of aggregating agents' individual preferences (Gaertner 2009).…”

Section: Social Choice Theorymentioning

confidence: 99%

Combining Social Choice Theory and Argumentation: Enabling Collective Decision Making

et al. 2018

View full text Add to dashboard Cite

Argumentation-based debates are mechanisms that a group can use to resolve conflicting opinions and hence reach agreement. They have many potential applications in on-line communities and other open environments. In this paper, we provide computational infrastructure to support argumentation-based debates, in particular focusing on the problem of how participants in a debate can reach agreement about the outcome of the debate, given all the statements that have been made. Our approach makes it possible to represent arguments that are put forward by the participants in a debate, allows both positive and negative relationships between the arguments to be represented, and makes it possible for participants to express opinions about both the arguments and the outcome of the debate. Our main contribution is to provide a novel method-indeed the first method-for computing the collective decision that emerges from the combination of a set of arguments and a set of opinions about whether the arguments hold or not. To do this, we carry out a formal investigation of a family of aggregation functions. This family starts with a function that is firmly rooted in the social choice literature, and is extended with functions that are more oriented towards the use of argumentation. We prove that to ensure that the collective decision is coherent, a property that we think is essential, an aggregation function needs to take into account the dependencies between arguments. We also provide an empirical analysis of the performance of our approach to reaching a collective decision, showing that a collective decision can be reached for debates, of the size that one currently finds online, in reasonable time.

show abstract

“…Recent work has addressed the computational complexity of many choice procedures (see for example: [14] [15]) and the literature is full of choice procedures that are difficult to compute [15] [16]. It is assumed that if computing a choice set is infeasible, the applicability of the corresponding solution concept is seriously undermined [17].…”

Section: Introductionmentioning

confidence: 99%

The Computational Complexity of Untrapped Choice Procedures

Sanni¹

2019

View full text Add to dashboard Cite

In this paper, we define two versions of Untrapped set (weak and strong Untrapped sets) over a finite set of alternatives. These versions, considered as choice procedures, extend the notion of Untrapped set in a more general case (i.e. when alternatives are not necessarily comparable). We show that they all coincide with Top cycle choice procedure for tournaments. In case of weak tournaments, the strong Untrapped set is equivalent to Getcha choice procedure and the Weak Untrapped set is exactly the Untrapped set studied in the litterature. We also present a polynomial-time algorithm for computing each set.

show abstract

Computational Social Choice: The First Ten Years and Beyond

Cited by 16 publications

References 112 publications

Fine-Grained Complexity and Algorithms for the Schulze Voting Method

Fine-Grained Complexity and Algorithms for the Schulze Voting Method

Combining Social Choice Theory and Argumentation: Enabling Collective Decision Making

The Computational Complexity of Untrapped Choice Procedures

Contact Info

Product

Resources

About