Justified Representation for Perpetual Voting

Abstract

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.

Temporal Fairness in Multiwinner Voting

“…The first (and one that is more common in the literature) is having a single winning candidate chosen at each timestep (i.e., o r ∈ P for each r ∈ [ℓ]). While one can view this variant of the model as a temporal extension of single-winner elections, the multiwinner interpretation is justified, too, as one can treat the (multi-)set O = {o r : r ∈ [ℓ]} as the winning committee and apply fairness concepts that originate in multiwinner voting literature to the entire set O; e.g., Bulteau et al (2021) and Page, Shapiro, and Talmon (2022) reason about justified representation provided by O. This model is considered in numerous existing works, including scheduling problems (Elkind, Kraiczy, and Teh 2022;Patro et al 2022), perpetual voting (Lackner 2020;, and public decision-making (Conitzer, Freeman, and Shah 2017;Fain, Munagala, and Shah 2018).…”

“…Approval preferences are relatively easy to elicit and reason about (Kilgour 1983;Brams and Fishburn 2005;Aragones, Gilboa, and Weiss 2011), yet they can capture a wide variety of scenarios from city budget planning to elections for the board of trustees. In temporal settings, approval ballots have been considered in the context of sequential committee elections (Bredereck, Kaczmarczyk, and Niedermeier 2020;Bredereck, Fluschnik, and Kaczmarczyk 2022;Deltl, Fluschnik, and Bredereck 2023) and scheduling (Bulteau et al 2021;Elkind, Kraiczy, and Teh 2022).…”

“…In this setting, each voter's preferences remain the same across the entire time horizon, and temporal considerations arise because of candidate availability issues or constraints on possible outcomes (see the Outcomes section for a discussion). For instance, Bulteau et al (2021) consider static preferences in perpetual voting, and obtain positive algorithmic results for achieving notions of proportionality in this setting.…”

The American Medical Association/Society of Vienna

“…The work of Lackner [26] and its follow-up by Lackner and Maly [27; 28] do not consider strategic issues. Further, Bulteau et al [14] move to a non-sequential (offline) model of perpetual voting and study proportional representation in this setting.…”

Welfare Maximization in Perpetual Voting (Student Abstract)

“…Perpetual voting was first studied by Lackner (2020), which looks into a formalism of the model, and studies several perpetual extensions of traditional voting rules and axioms. Bulteau et al (2021) subsequently looked into formalizing notions of proportionate representation in this context. This framework also captures several other scenarios, including fair scheduling (Elkind, Kraiczy, and Teh 2022).…”