Swap Bribery

TL;DR

This paper introduces and analyzes the complexity of swap bribery in voting systems, where the cost depends on the sequence of candidate swaps needed to alter voters' preferences.

Contribution

It models swap bribery with variable swap costs and provides complexity results across multiple election systems, expanding understanding of manipulation difficulty.

Findings

Complexity results vary across different voting rules.

Swap bribery is computationally hard for many common election systems.

The model captures realistic bribery scenarios with variable costs.

Abstract

In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that the voter is asked to implement. Specifically, in our model the briber can change a voter's preference list by paying for a sequence of swaps of consecutive candidates. Each swap may have a different price; the price of a bribery is the sum of the prices of all swaps that it involves. We prove complexity results for this model, which we call swap bribery, for a broad class of election systems, including variants of approval and k-approval, Borda, Copeland, and maximin.