Strategic sequential voting in multi-issue domains and multiple-election paradoxes

In many settings, a group of voters must come to a joint decision on multiple issues. In practice, this is often done by voting on the issues in sequence. We model sequential voting in multi-issue domains as a complete-information extensive-form game, in which the voters are perfectly rational and their preferences are common knowledge. In each step, the voters simultaneously vote on one issue, and the order of the issues is given exogenously before the process. We call this model strategic sequential voting. We focus on domains characterized by multiple binary issues, so that strategic sequential voting leads to a unique outcome under a natural solution concept. We show that under some conditions on the preferences, this leads to the same outcome as truthful sequential voting, but in general it can result in very different outcomes. In particular, sometimes the order of the issues has a strong influence on the winner. We also analyze the communication complexity of the corresponding social choice rule. Most significantly, we illustrate several multiple-election paradoxes in strategic sequential voting: there exists a profile for which the winner under strategic sequential voting is ranked nearly at the bottom in all voters' true preferences, and the winner is Pareto-dominated by almost every other alternative. We show that changing the order of the issues cannot completely prevent such paradoxes. We also study the possibility of avoiding the paradoxes for strategic sequential voting by imposing some constraints on the profile, such as separability, lexicographicity or O-legality.