On manipulation in multi-winner elections based on scoring rules

Multi-winner elections model scenarios where voters must select a fixed-size group of candidates based on their individual preferences. In such scenarios, it is often the case that voters are incentivized to manipulate, i.e.~misreport their preferences in order to obtain a better outcome. In this paper, we study the complexity of manipulating multi-winner elections under scoring rules, with a particular focus on the role of tie-breaking rules. We consider both lexicographic tie-breaking rules, which break ties according to a fixed ordering of the candidates, and a natural randomized tie-breaking rule. We describe polynomial-time manipulation algorithms for several special cases of our problem. Specifically, we show that finding a successful manipulation is easy if the underlying voting rule is k-Approval or the number of candidates to be elected is bounded by a constant (for both types of tie-breaking rules), as well as if the manipulator's utility function only takes values in {0, 1} and the ties are broken in the manipulator's favor.