Perpetual voting was recently introduced as 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 and study two main questions. First, we ask how simple such rules can be while still meeting basic desiderata. For two simple but natural classes, we fully characterize the axiomatic possibilities. Second, we ask how proportionality can be formalized in perpetual voting. We study proportionality on simple profiles that are equivalent to the apportionment setting and show that lower and upper quota axioms can be used to distinguish (and sometimes characterize) perpetual voting rules. Furthermore, we show a surprising connection between a perpetual rule called Perpetual Consensus and Frege's apportionment method.
Optimal bounds for dissatisfaction in perpetual voting
Centro Nacional de Inteligencia Artificial（国家人工智能中心）；LIRMM（蒙彼利埃计算机科学、机器人学、微电子与电力实验室）；Univ Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；Institute of Fundamental Technological Research, Polish Academy of Sciences（波兰科学院基础技术研究所）
Voting with Partial Orders: The Plurality and Anti-Plurality Classes
Institute for Logic, Language and Computation (ILLC), University of Amsterdam（阿姆斯特丹大学逻辑、语言与计算研究所）；Université Jean Monnet Saint-Étienne, CNRS, Université Lyon 2, emlyon business school, GATE（圣艾蒂安让·莫内大学，法国国家科学研究中心，里昂第二大学，emlyon商学院，GATE）
