Justified Representation for Perpetual Voting

We study the social choice setting of perpetual voting where, based on voter preferences, decisions have to be taken over a finite horizon of consecutive points in time (e.g, days). We consider two complementary settings: a
Static
setting, in which voter preferences remain static over time, and a
Dynamic
setting, in which voter preferences may change over time. We adapt the well-established Justified Representation and Proportional Justified Representation axioms, commonly used in the social choice literature, to perpetual voting, resulting in two axiomatic variants for the static setting and four variants for the dynamic setting. We show that all of the axioms are always satisfiable, and that simple preference aggregation methods can be used to satisfy the axioms in both cases. We then conduct a large human study (
$N=190$
) aimed at identifying what potential voters (i.e., ordinary people) deem as desirable outcomes in simple perpetual voting settings. Our results show that approximately half of our participants consider different interpretations of fairness that correspond to our axiomatic framework. Taken jointly, our results can be used to help the research community identify appropriate aggregation methods to use in practice.