Parliamentary voting procedures: Agenda control, manipulation, and uncertainty

Abstract

We study computational problems for two popular parliamentary voting procedures: the amendment procedure and the successive procedure. They work in multiple stages where the result of each stage may influence the result of the next stage. Both procedures proceed according to a given linear order of the alternatives, an agenda. We obtain the following results for both voting procedures: On the one hand, deciding whether one can make a specific alternative win by reporting insincere preferences by the fewest number of voters, the Coalitional Manipulation problem, or whether there is a suitable ordering of the agenda, the Agenda Control problem, takes polynomial time. On the other hand, our experimental studies with real-world data indicate that most preference profiles cannot be manipulated by only few voters and a successful agenda control is typically impossible. If the voters' preferences are incomplete, then deciding whether an alternative can possibly win is NP-hard for both procedures. Whilst deciding whether an alternative necessarily wins is coNP-hard for the amendment procedure, it is polynomial-time solvable for the successive procedure.