We study the plurality consensus problem in distributed systems where a population of extremely simple agents, each initially holding one of $k$ opinions, aims to agree on the initially most frequent one. In this setting, $h$-majority is arguably the simplest and most studied protocol, in which each agent samples the opinion of $h$ neighbors uniformly at random and updates its opinion to the most frequent value in the sample. We propose a new, extremely simple mechanism called DéjàVu: an agent queries neighbors until it encounters an opinion for the second time, at which point it updates its own opinion to the duplicate value. This rule does not require agents to maintain counters or estimate frequencies, nor to choose any parameter (such as a sample size $h$); it relies solely on the primitive ability to detect repetition. We provide a rigorous analysis of DéjàVu that relies on several technical ideas of independent interest and demonstrates that it is competitive with $h$-majority and, in some regimes, substantially more communication-efficient, thus yielding a powerful primitive for plurality consensus.

翻译：我们研究了分布式系统中的多元共识问题，其中一群极其简单的智能体，每个初始持有$k$种意见之一，旨在就初始最频繁的意见达成一致。在此设定下，$h$-多数协议可以说是最简单且研究最广泛的协议，其中每个智能体均匀随机地采样$h$个邻居的意见，并将其意见更新为样本中出现频率最高的值。我们提出了一种称为DéjàVu的新颖极简机制：智能体查询邻居，直到第二次遇到某个意见，此时它将自己的意见更新为该重复值。该规则无需智能体维护计数器或估计频率，也无需选择任何参数（例如样本大小$h$），仅依赖于检测重复的基本能力。我们对DéjàVu进行了严格分析，该分析依赖于若干具有独立价值的技术性思想，并证明其与$h$-多数协议相比具有竞争力，在某些情况下在通信效率上显著更优，从而为多元共识提供了一种强大的原语。