scholarly journals Elections with Few Voters: Candidate Control Can Be Easy

2017 ◽  
Vol 60 ◽  
pp. 937-1002 ◽  
Author(s):  
Jiehua Chen ◽  
Piotr Faliszewski ◽  
Rolf Niedermeier ◽  
Nimrod Talmon
Keyword(s):  
Computational Complexity ◽  
Parameterized Complexity ◽  
Voting Rules ◽  
Standard Scenario ◽  
Candidate Control

We study the computational complexity of candidate control in elections with few voters, that is, we consider the parameterized complexity of candidate control in elections with respect to the number of voters as a parameter. We consider both the standard scenario of adding and deleting candidates, where one asks whether a given candidate can become a winner (or, in the destructive case, can be precluded from winning) by adding or deleting few candidates, as well as a combinatorial scenario where adding/deleting a candidate automatically means adding or deleting a whole group of candidates. Considering several fundamental voting rules, our results show that the parameterized complexity of candidate control, with the number of voters as the parameter, is much more varied than in the setting with many voters.

scholarly journals Computational Social Choice Meets Databases

2018 ◽  
Author(s):  
Benny Kimelfeld ◽  
Phokion G. Kolaitis ◽  
Julia Stoyanovich
Keyword(s):  
Computational Complexity ◽  
Social Choice ◽  
Relational Database ◽  
Database Management ◽  
Plurality Rule ◽  
Technical Level ◽  
Computational Social Choice ◽  
Conceptual Level ◽  
Voting Rules ◽  
Conjunctive Queries

We develop a novel framework that aims to create bridges between the computational social choice and the database management communities. This framework enriches the tasks currently supported in computational social choice with relational database context, thus making it possible to formulate sophisticated queries about voting rules, candidates, voters, issues, and positions. At the conceptual level, we give rigorous semantics to queries in this framework by introducing the notions of necessary answers and possible answers to queries. At the technical level, we embark on an investigation of the computational complexity of the necessary answers. In particular, we establish a number of results about the complexity of the necessary answers of conjunctive queries involving the plurality rule that contrast sharply with earlier results about the complexity of the necessary winners under the plurality rule.

scholarly journals Bribery and Control in Stable Marriage

2021 ◽  
Vol 71 ◽  
pp. 993-1048
Author(s):  
Niclas Boehmer ◽  
Robert Bredereck ◽  
Klaus Heeger ◽  
Rolf Niedermeier
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Parameterized Complexity ◽  
Complexity Analysis ◽  
Stable Solution ◽  
Stable Marriage ◽  
Np Hard ◽  
Natural Parameter ◽  
And Control ◽  
Comprehensive Study

We initiate the study of external manipulations in Stable Marriage by considering  several manipulative actions as well as several manipulation goals. For instance, one goal  is to make sure that a given pair of agents is matched in a stable solution, and this may be  achieved by the manipulative action of reordering some agents' preference lists. We present  a comprehensive study of the computational complexity of all problems arising in this way.  We find several polynomial-time solvable cases as well as NP-hard ones. For the NP-hard  cases, focusing on the natural parameter "budget" (that is, the number of manipulative  actions one is allowed to perform), we also conduct a parameterized complexity analysis  and encounter mostly parameterized hardness results. 

scholarly journals Computational complexity in the design of voting rules

2015 ◽  
Vol 80 (1) ◽  
pp. 33-41 ◽  
Author(s):  
Koji Takamiya ◽  
Akira Tanaka
Keyword(s):  
Computational Complexity ◽  
Voting Rules

scholarly journals Towards completing the puzzle: complexity of control by replacing, adding, and deleting candidates or voters

2021 ◽  
Vol 35 (2) ◽  
Author(s):  
Gábor Erdélyi ◽  
Marc Neveling ◽  
Christian Reger ◽  
Jörg Rothe ◽  
Yongjie Yang ◽  
...  
Keyword(s):  
Computational Complexity ◽  
Structural Changes ◽  
Voting Rules ◽  
Control Actions ◽  
Electoral Control ◽  
Range Voting

AbstractWe investigate the computational complexity of electoral control in elections. Electoral control describes the scenario where the election chair seeks to alter the outcome of the election by structural changes such as adding, deleting, or replacing either candidates or voters. Such control actions have been studied in the literature for a lot of prominent voting rules. We complement those results by solving several open cases for Copeland$$^{\alpha }$$ α , maximin, k-veto, plurality with runoff, veto with runoff, Condorcet, fallback, range voting, and normalized range voting.

scholarly journals Well-Structured Committees

2020 ◽  
Author(s):  
Sushmita Gupta ◽  
Pallavi Jain ◽  
Saket Saurabh
Keyword(s):  
Standard Model ◽  
Parameterized Complexity ◽  
Independent Set ◽  
Combinatorial Problems ◽  
Voting Rules ◽  
Voter Preferences ◽  
Candidate Network ◽  
Graph Properties ◽  
The Standard Model ◽  
The Given

In the standard model of committee selection, we are given a set of ordinal votes over a set of candidates and a desired committee size, and the task is to select a committee that relates to the given votes. Motivated by possible interactions and dependencies between candidates, we study a generalization of committee selection in which the candidates are connected via a network and the task is to select a committee that relates to the given votes while also satisfy certain properties with respect to this candidate network. To accommodate certain correspondences to the voter preferences, we consider three standard voting rules (in particular, $k$-Borda, Chamberlin-Courant, and Gehrlein stability); to model different aspects of interactions and dependencies between candidates, we consider two graph properties (in particular, Independent Set and Connectivity). We study the parameterized complexity of the corresponding combinatorial problems and discuss certain implications of our algorithmic results.

scholarly journals Fair Knapsack

2019 ◽  
Vol 33 ◽  
pp. 1941-1948 ◽  
Author(s):  
Till Fluschnik ◽  
Piotr Skowron ◽  
Mervin Triphaus ◽  
Kai Wilker
Keyword(s):  
Computational Complexity ◽  
Knapsack Problem ◽  
Parameterized Complexity ◽  
Fair Allocation ◽  
Total Cost ◽  
A Value ◽  
Restricted Domains

We study the following multiagent variant of the knapsack problem. We are given a set of items, a set of voters, and a value of the budget; each item is endowed with a cost and each voter assigns to each item a certain value. The goal is to select a subset of items with the total cost not exceeding the budget, in a way that is consistent with the voters’ preferences. Since the preferences of the voters over the items can vary significantly, we need a way of aggregating these preferences, in order to select the socially best valid knapsack. We study three approaches to aggregating voters’ preferences, which are motivated by the literature on multiwinner elections and fair allocation. This way we introduce the concepts of individually best, diverse, and fair knapsack. We study the computational complexity (including parameterized complexity, and complexity under restricted domains) of the aforementioned multiagent variants of knapsack.

scholarly journals Complexity of Shift Bribery in Committee Elections

2021 ◽  
Vol 13 (3) ◽  
pp. 1-25
Author(s):  
Robert Bredereck ◽  
Piotr Faliszewski ◽  
Rolf Niedermeier ◽  
Nimrod Talmon
Keyword(s):  
Computational Complexity ◽  
Voting Rules ◽  
Preference Orders ◽  
The Given

Given an election, a preferred candidate  p , and a budget, the S HIFT B RIBERY problem asks whether  p can win the election after shifting  p higher in some voters’ preference orders. Of course, shifting comes at a price (depending on the voter and on the extent of the shift) and one must not exceed the given budget. We study the (parameterized) computational complexity of S HIFT B RIBERY for multiwinner voting rules where winning the election means to be part of some winning committee. We focus on the well-established SNTV, Bloc, k -Borda, and Chamberlin-Courant rules, as well as on approximate variants of the Chamberlin-Courant rule. We show that S HIFT B RIBERY tends to be harder in the multiwinner setting than in the single-winner one by showing settings where S HIFT B RIBERY is computationally easy in the single-winner cases, but is hard (and hard to approximate) in the multiwinner ones.

Treewidth-aware Reductions of Normal ASP to SAT - Is Normal ASP Harder than SAT after All?

2020 ◽  
Author(s):  
Markus Hecher
Keyword(s):  
Graph Theory ◽  
Computational Complexity ◽  
Lower Bounds ◽  
Parameterized Complexity ◽  
No Reduction ◽  
Answer Set Programming ◽  
Propositional Satisfiability ◽  
Fine Grained ◽  
Problem Modeling ◽  
Structural Density

Answer Set Programming (ASP) is a paradigm and problem modeling/solving toolkit for KR that is often invoked. There are plenty of results dedicated to studying the hardness of (fragments of) ASP. So far, these studies resulted in characterizations in terms of computational complexity as well as in fine-grained insights presented in form of dichotomy-style results, lower bounds when translating to other formalisms like propositional satisfiability (SAT), and even detailed parameterized complexity landscapes. A quite generic and prominent parameter in parameterized complexity originating from graph theory is the so-called treewidth, which in a sense captures structural density of a program. Recently, there was an increase in the number of treewidth-based solvers related to SAT. While there exist several translations from (normal) ASP to SAT, yet there is no reduction preserving treewidth or at least being aware of the treewidth increase. This paper deals with a novel reduction from normal ASP to SAT that is aware of the treewidth, and guarantees that a slight increase of treewidth is indeed sufficient. Then, we also present a new result establishing that when considering treewidth, already the fragment of normal ASP is slightly harder than SAT (under reasonable assumptions in computational complexity). This also confirms that our reduction probably cannot be significantly improved and that the slight increase of treewidth is unavoidable.

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