On the Hardness of Bribery Variants in Voting with CP-Nets

TL;DR

This paper investigates the computational complexity of bribery problems in voting systems where voters have CP-net preferences, extending previous results to weighted voters and negative bribery scenarios.

Contribution

It solves two open cases of bribery complexity in CP-net voting and generalizes results to weighted voters and negative bribery.

Findings

Two previously open bribery cases are solved.

Results extended to weighted voters.

Negative bribery scenarios analyzed.

Abstract

We continue previous work by Mattei et al. (Mattei, N., Pini, M., Rossi, F., Venable, K.: Bribery in voting with CP-nets. Ann. of Math. and Artif. Intell. pp. 1--26 (2013)) in which they study the computational complexity of bribery schemes when voters have conditional preferences that are modeled by CP-nets. For most of the cases they considered, they could show that the bribery problem is solvable in polynomial time. Some cases remained open---we solve two of them and extend the previous results to the case that voters are weighted. Moreover, we consider negative (weighted) bribery in CP-nets, when the briber is not allowed to pay voters to vote for his preferred candidate.