# A minimax procedure for electing committees

@article{Brams2007AMP, title={A minimax procedure for electing committees}, author={Steven J. Brams and D. Marc Kilgour and M. Remzi Sanver}, journal={Public Choice}, year={2007}, volume={132}, pages={401-420} }

Abstract
A new voting procedure for electing committees, called the minimax procedure, is described. Based on approval balloting, it chooses the committee that minimizes the maximum Hamming distance to voters’ ballots, where these ballots are weighted by their proximity to other voters’ ballots. This minimax outcome may be diametrically opposed to the outcome obtained by aggregating approval votes in the usual manner, which minimizes the sum of the Hamming distances and is called the minisum…

## 151 Citations

Winner Determination and Manipulation in Minisum and Minimax Committee Elections

- Computer ScienceADT
- 2015

It is shown that winner determination is possible in polynomial time for all minisum rules the authors consider, whereas it is $$\mathrm{NP}$$-complete for three of the minimax rules.

Does Choosing Committees from Approval Balloting Fulfill the Electorate's Will?

- Education
- 2010

An approval ballot is a voting ballot where voters indicate the candidates they approve among finitely many ones running for elections. We review below some recent studies of procedures that select…

Approximation Algorithms and Mechanism Design for Minimax Approval Voting

- Computer Science, EconomicsAAAI
- 2010

A polynomial-time 2-approximation algorithm that uses a natural linear programming relaxation for the underlying optimization problem and deterministically rounds the fractional solution in order to compute the outcome improves upon the previously best known algorithm that has an approximation ratio of 3.

Social Choice and Welfare Justified Representation in Approval-Based Committee Voting

- Economics, Computer Science
- 2016

A stronger version of the JR axiom is introduced, which is called extended justified representation (EJR), and it is shown that PAV satisfies EJR, while other rules the authors consider do not; indeed, EJR can be used to characterize PAV within the class of weighted PAV rules.

A Generalization of the Minisum and Minimax Voting Methods

- Computer ScienceArXiv
- 2016

A family of approval voting-schemes for electing committees based on the preferences of voters and suggests that using a small value of p, such as 2 or 3, provides a good compromise between the minisum and minimax voting methods with regard to the weightage given to approvals and disapprovals.

Manipulation of Hamming-based Approval Voting for Multiple Referenda and Committee Elections

- Computer ScienceAAMAS
- 2017

This paper proves that all rules parameterized by fair (non-increasing) weight vectors are manipulable, except minisum, if they are either resolute with a tie-breaking mechanism or irresolute with classic extension principles, and conducts an empirical study of the proportion of elections that are manipULable.

Multiple Referenda and Multiwinner Elections Using Hamming Distances: Complexity and Manipulability

- Computer Science, EconomicsAAMAS
- 2015

It is exhibited that for many rules, it is NP-hard to find a winning committee, and cases where the problem is either efficiently solvable, or approximable with a small approximation factor are identified.

What Do We Elect Committees For? A Voting Committee Model for Multi-Winner Rules

- EconomicsIJCAI
- 2015

It is shown that if not only a committee, but also an election rule used to make final decisions, to depend on the voters' preferences, the authors can obtain an even better representation of the voters.

College Senior Thesis Mathematics Fall , 2009 Research Proposal : Electing Committees

- Economics
- 2009

Extensive work has been done to expose and analyze the flaws in common single-candidate election procedures. Arrow’s Theorem states that there exists no perfect voting procedure, so the existing…

OWA-Based Extensions of the Chamberlin-Courant Rule

- EconomicsADT
- 2015

A family of multiwinner voting rules based on the concept of ordered weighted average OWA are proposed and it is shown that under moderate constraints on the weight vector many of the algorithmic results known for the egalitarian and the utilitarian version of Chamberlin---Courant's rule can be recovered.

## References

SHOWING 1-10 OF 34 REFERENCES

Voter Sovereignty and Election Outcomes

- Economics
- 2003

Voters are sovereign to the degree that they can express their approval for any set of candidates. While voter sovereignty is maximized under approval voting (AV), AV can lead to a plethora of…

Some startling inconsistencies when electing committees

- EconomicsSoc. Choice Welf.
- 2003

Two methods to measure how far a set of m candidates is from being the Condorcet committee are adapted, and Kemeny’s method, which gives a complete transitive ranking, is generalized to the selection of committees and it is shown that it is closely related to the first method.

Voting By Quota And Committee

- Economics
- 1988

The main result of this paper characterizes voting by committees. There are n voters and K objects. Voters must choose a subset of K. Voting by committees is defined by one monotone family of winning…

Voting by Committees

- Economics, Computer Science
- 1991

The main result of the paper is a characterization of voting by committees, which is the class of all voting schemes that satisfy voter sovereignty and non-manipulability on the domain of separable preferences.

Voting for Voters: A Model of Electoral Evolution

- Economics
- 1998

We model the decision problems faced by the members of societies whose new members are determined by vote. We adopt a number of simplifying assumptions: the founders and the candidates are fixed; the…

The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules

- Economics, Business
- 1987

It is found that certain elements of multistage procedures promote departures from purely sincere strategies, including, in some instances, strictly insincere voting, which is especially likely under certain threshold rules.

How to Elect a Representative Committee Using Approval Balloting

- Computer Science
- 2006

It is shown that a general class of voting systems based on approval ballots can be implemented through analysis of appropriate tables, and a by-product of this procedure is a clarification of the complexity of these systems.

Going from theory to practice: the mixed success of approval voting

- Political ScienceSoc. Choice Welf.
- 2005

Ballot data from some of the societies that adopted AV are used to compare theoretical results with experience, including the nature of voting under AV and the kinds of candidates that are elected.

The paradox of multiple elections

- Economics
- 1998

Abstract. Assume that voters must choose between voting yes (Y) and voting no (N) on three propositions on a referendum. If the winning combination is NYY on the first, second, and third…