On Choosing Committees Based on Approval Votes in the Presence of Outliers

11/13/2015
by   Palash Dey, et al.
0

We study the computational complexity of committee selection problem for several approval-based voting rules in the presence of outliers. Our first result shows that outlier consideration makes committee selection problem intractable for approval, net approval, and minisum approval voting rules. We then study parameterized complexity of this problem with five natural parameters, namely the target score, the size of the committee (and its dual parameter, the number of candidates outside the committee), the number of outliers (and its dual parameter, the number of non-outliers). For net approval and minisum approval voting rules, we provide a dichotomous result, resolving the parameterized complexity of this problem for all subsets of five natural parameters considered (by showing either FPT or W[1]-hardness for all subsets of parameters). For the approval voting rule, we resolve the parameterized complexity of this problem for all subsets of parameters except one. We also study approximation algorithms for this problem. We show that there does not exist any alpha(.) factor approximation algorithm for approval and net approval voting rules, for any computable function alpha(.), unless P=NP. For the minisum voting rule, we provide a pseudopolynomial (1+eps) factor approximation algorithm.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/09/2021

Parameterized Complexity of Multi-winner Determination: More Effort Towards Fixed-Parameter Tractability

We study winner determination for three prevalent k-committee selection ...
research
11/17/2017

The Complexity of Multiwinner Voting Rules with Variable Number of Winners

We consider the approval-based model of elections, and undertake a compu...
research
12/05/2018

Voting and Bribing in Single-Exponential Time

We introduce a general problem about bribery in voting systems. In the R...
research
01/29/2018

A Unifying Framework for Manipulation Problems

Manipulation models for electoral systems are a core research theme in s...
research
01/07/2016

Complexity of Shift Bribery in Committee Elections

We study the (parameterized) complexity of SHIFT BRIBERY for multiwinner...
research
05/02/2023

Ties in Multiwinner Approval Voting

We study the complexity of deciding whether there is a tie in a given ap...
research
12/14/2013

Achieving Fully Proportional Representation: Approximability Results

We study the complexity of (approximate) winner determination under the ...

Please sign up or login with your details

Forgot password? Click here to reset