How Hard Is the Manipulative Design of Scoring Systems?

Abstract

In an election, votes are often given as ordered lists over candidates. A common way of determining the winner is then to apply some scoring system, where each position is associated with a specific score. This setting is also transferable to other situations, such as sports tournaments. The design of such systems, i.e.,  the choice of the score values, may have a crucial influence on the outcome. We study the computational complexity of two related decision problems. In addition, we provide a case study of data from Formula 1 using ILP formulations. Our results show that under some mild conditions there are cases where the actual scoring system has no influence, whereas in other cases very small changes may lead to a different winner. This may be seen as a measure of robustness of the winning candidate.