Manipulative Design of Scoring Systems

Scoring systems give points to candidates according to their positions and are, for example, used in elections and sports tournaments. We study the influence that the design of such systems has on the outcome by introducing two related decision problems. The problem Scoring System Existence asks whether for a given set of profiles there exists a scoring system that makes some distinguished candidate win, whereas Closest Scoring System bounds the choice of an alternative scoring system by some given distance.