Proportional Decisions in Perpetual Voting

Perpetual voting is a framework for long-term collective decision making. In this framework, we consider a sequence of subsequent approval-based elections and try to achieve a fair overall outcome. To achieve fairness over time, perpetual voting rules take the history of previous decisions into account and identify voters that were dissatisfied with previous decisions. In this paper, we look at perpetual voting rules from an axiomatic perspective. First, we define two classes of perpetual voting rules that are particularly easy to explain to voters and we explore the bounds imposed by this simplicity. Second, we study proportionality in the perpetual setting and identify two rules with strong proportionality guarantees. However, both rules yield different guarantees and we prove them to be incompatible with each other.