集体决策的一种自然自适应过程
A Natural Adaptive Process for Collective Decision-Making
AI总结：
研究提出一种基于瓮模型的自适应集体决策过程，通过随机投票者抽球比较并更新标签，证明其经验分布逼近极大彩票这一概率投票规则，且收敛概率随轮次呈指数级增长。
摘要：
考虑一个装满球的瓮，每个球标有几种可能的集体决策之一。现在，让一名随机投票者从瓮中抽出两个球，并选择她更偏好的作为集体决策。将落败的球重新标记为该集体决策，把两个球都放回瓮中，并重复此过程。偶尔，将随机抽出的一个球重新标记为随机的集体决策。我们证明，由此过程产生的集体决策的经验分布逼近极大彩票，这是 Peter C. Fishburn（Rev. Econ. Stud., 51(4), 1984）提出的一种著名的概率投票规则。事实上，第 n 轮中集体决策根据极大彩票做出的概率随 n 呈指数级增长。所提出的过程比传统投票规则更灵活，并且与生物学、物理学和化学中研究的自然过程以及机器学习中提出的算法具有高度的相似性。
英文摘要：
Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the collective decision, put both balls back into the urn, and repeat. Once in a while, relabel a randomly drawn ball with a random collective decision. We prove that the empirical distribution of collective decisions produced by this process approximates a maximal lottery, a celebrated probabilistic voting rule proposed by Peter C. Fishburn (Rev. Econ. Stud., 51(4), 1984). In fact, the probability that the collective decision in round $n$ is made according to a maximal lottery increases exponentially in $n$. The proposed procedure is more flexible than traditional voting rules and bears strong similarities to natural processes studied in biology, physics, and chemistry as well as algorithms proposed in machine learning.
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。
