DeepAI AI Chat
Log In Sign Up

Kemeny Consensus Complexity

05/18/2021
by   Zack Fitzsimmons, et al.
0

The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus). We study the complexity of consensus-related questions, with a particular focus on Kemeny and its qualitative version Slater. The simplest of these questions is the problem of determining whether a ranking is a consensus, and we show that this problem is coNP-complete. We also study the natural question of the complexity of manipulative actions that have a specific consensus as a goal. Though determining whether a ranking is a Kemeny consensus is hard, the optimal action for manipulators is to simply vote their desired consensus. We provide evidence that this simplicity is caused by the combination of election system (Kemeny), manipulative action (manipulation), and manipulative goal (consensus). In the process we provide the first completeness results at the second level of the polynomial hierarchy for electoral manipulation and for optimal solution recognition.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/13/2017

Consensus Halving is PPA-Complete

We show that the computational problem CONSENSUS-HALVING is PPA-complete...
05/31/2018

The Complexity of Splitting Necklaces and Bisecting Ham Sandwiches

We resolve the computational complexity of two problems known as NECKLAC...
02/02/2018

A Simple Object that Spans the Whole Consensus Hierarchy

This paper presents a simple generalization of the basic atomic read/wri...
03/07/2019

Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem

We study the problem of finding an exact solution to the consensus halvi...
09/30/2022

Broadening the Complexity-theoretic Analysis of Manipulative Attacks in Group Identification

In the Group Identification problem, we are given a set of individuals a...
07/14/2020

Consensus Halving for Sets of Items

Consensus halving refers to the problem of dividing a resource into two ...
03/30/2022

Manipulative Attacks and Group Identification

The group identification problem asks to identify a socially qualified s...