# Complexity of and Algorithms for Borda Manipulation

@article{Davies2011ComplexityOA, title={Complexity of and Algorithms for Borda Manipulation}, author={Jessica Davies and George Katsirelos and Nina Narodytska and Toby Walsh}, journal={ArXiv}, year={2011}, volume={abs/1105.5667} }

We prove that it is NP-hard for a coalition of two manipulators to compute how to manipulate the Borda voting rule. This resolves one of the last open problems in the computational complexity of manipulating common voting rules. Because of this NP-hardness, we treat computing a manipulation as an approximation problem where we try to minimize the number of manipulators. Based on ideas from bin packing and multiprocessor scheduling, we propose two new approximation methods to compute…

## 91 Citations

New Approximations for Coalitional Manipulation in Scoring Rules

- Computer ScienceJ. Artif. Intell. Res.
- 2019

Algorithms are provided that approximate the optimum score margin, which are applicable to any scoring rule, and for the specific case of the Borda protocol in the unweighted setting, the algorithm provides a superior approximation factor for lower values of k.

New Complexity Results on Coalitional Manipulation of Borda

- EconomicsArXiv
- 2020

A sharp contrast on computational complexity depending on the weight of the non-manipulator is demonstrated: the problem is NP-hard when the weight is larger than $1$ while there exists an efficient algorithm to find a manipulation when theWeight is at most $1.

Where are the hard manipulation problems?

- Computer Science, EconomicsJ. Artif. Intell. Res.
- 2011

Empirical studies are shown to be useful in improving the understanding of computational complexity in voting and manipulation, and two settings are considered which represent the two types of complexity results: manipulation with unweighted votes by a single agent, and manipulation with weighted Votes by a coalition of agents.

New Approximation for Borda Coalitional Manipulation

- Computer ScienceAAMAS
- 2017

The methods are novel and adapt techniques from multiprocessor scheduling by carefully rounding an exponentially-large configuration linear program that is solved by using the ellipsoid method with an efficient separation oracle, and believe that such methods could be beneficial in approximating coalitional manipulation in other election protocols as well.

Unweighted Coalitional Manipulation under the Borda Rule Is NP-Hard

- Computer ScienceIJCAI
- 2011

This work settles the open problem of can one add a certain number of additional votes to an election such that a distinguished candidate becomes a winner and shows NP-hardness even for two manipulators and three input votes.

Is computational complexity a barrier to manipulation?

- Computer ScienceAnnals of Mathematics and Artificial Intelligence
- 2011

This survey article summarizes the evidence for and against computational complexity being a barrier to manipulation, and looks both at techniques identified to increase complexity, as well as other features that may change the computational complexity of computing a manipulation.

Exact algorithms for weighted and unweighted Borda manipulation problems

- Computer ScienceTheor. Comput. Sci.
- 2016

Complexity of Manipulation with Partial Information in Voting

- Computer Science, EconomicsIJCAI
- 2016

Eliminating the Weakest Link: Making Manipulation Intractable?

- Computer Science, EconomicsAAAI
- 2012

It is shown here that it is NP-hard to compute how a single voter can manipulate the result of the elimination version of veto voting, of the closely related Coombs' rule, and of the Elimination versions of a general class of scoring rules.

Manipulation can be hard in tractable voting systems even for constant-sized coalitions

- Computer ScienceComput. Sci. Rev.
- 2012

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