永久投票中不满的最优界限
Optimal bounds for dissatisfaction in perpetual voting
AI总结：
本文研究永久投票中能否保证选民不满次数不过多，提出“有界冲突”条件，并借助 Kolmogorov 复杂性与专家预测技术给出次线性不满增长的紧界和投票方法。
摘要：
在永久投票中，多项决策是在不同时刻作出的。将以往决策的历史纳入考虑，使我们能够满足诸如跨时间段的比例代表性之类的性质。在本文中，我们思考如下问题：是否存在一种永久赞成投票方法，能够保证没有任何选民会有过多次数的不满？我们识别出一项关于选民行为的充分条件——我们称之为“有界冲突”条件——在该条件下，不满次数的次线性增长是可能的。我们利用 Kolmogorov 复杂性中的技术，给出了有界冲突下不满增长的一个紧上界。我们还观察到，带有二元选择的赞成投票模拟了借助专家建议进行预测的机器学习设定。这使我们能够基于借助专家建议进行预测的标准技术，提出一种在有界冲突下对不满具有次线性保证的投票方法。
英文摘要：
In perpetual voting, multiple decisions are made at different moments in time. Taking the history of previous decisions into account allows us to satisfy properties such as proportionality over periods of time. In this paper, we consider the following question: is there a perpetual approval voting method that guarantees that no voter is dissatisfied too many times? We identify a sufficient condition on voter behavior -- which we call 'bounded conflicts' condition -- under which a sublinear growth of dissatisfaction is possible. We provide a tight upper bound on the growth of dissatisfaction under bounded conflicts, using techniques from Kolmogorov complexity. We also observe that the approval voting with binary choices mimics the machine learning setting of prediction with expert advice. This allows us to present a voting method with sublinear guarantees on dissatisfaction under bounded conflicts, based on the standard techniques from prediction with expert advice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
