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：我们研究分布式系统中的多数共识问题，其中由极端简单个体组成的群体，每个个体初始持有k种意见之一，目标是达成对初始最频繁意见的一致同意。在此设定下，h-多数协议可以说是最简单且研究最充分的协议：每个个体均匀随机地采样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。我们提出一种称为DéjàVu的新型极简机制：个体持续查询邻居，直到第二次遇到某个意见，此时将其自身意见更新为该重复值。该规则无需个体维护计数器或估计频率，也无需选择任何参数（如样本大小h）；它仅依赖检测重复的原始能力。我们提供了DéjàVu的严格分析，该分析依赖于若干具有独立意义的技术思路，并证明其与h-多数协议竞争力相当，且在某些场景下通信效率显著更高，从而为多数共识提供了一种强有力的原始方法。