Control of the ordering of transactions in modern blockchains can be extremely profitable. Rather than allow one central actor to control this revenue source, recent research has studied mechanisms for decentralizing the process of computing an ordering among multiple, distributed replicas. This problem is akin to the classic problem from social choice theory of aggregating ordinal votes, applied to a streaming setting. Prior work proposes a ``$\gamma$-batch-order-fairness'' requirement on the aggregate ordering. Under this requirement, the ordering should be divisible into contiguous batches, and when a $\gamma$ fraction of replicas receive $tx$ before $tx^\prime$, then $tx^\prime$ cannot be in an earlier batch than $tx$. We extend this definition to formalize the notion that these batches should have minimal size, thereby giving the first notion of order fairness that cannot be vacuously satisfied (by arbitrarily large batches) and that can be satisfied in the presence of faulty replicas. We then show that the Ranked Pairs aggregation method produces an ordering that satisfies our fairness definition for every choice of parameter $\gamma$ simultaneously and for any number of faulty replicas (where fairness guarantees linearly degrade as the fraction of faulty replicas increases). We then instantiate our protocol in the streaming setting. Careful analysis of the interactions between ordering dependencies enables our protocol to simulate Ranked Pairs voting in this setting, and adjustments to ordering algorithm give a protocol that (under synchronous network assumptions) always appends a transaction to the output ordering after a bounded amount of time.

翻译：现代区块链中交易排序的控制权可能带来极高的利润。为避免让单一中心角色掌控这一收益来源，近期研究探讨了如何在多个分布式副本间实现排序过程的去中心化机制。该问题类似于社会选择理论中将序数投票聚合的经典问题，但需应用于流式场景。先前研究提出了聚合排序的“γ批量顺序公平”约束条件：在此要求下，排序应能划分为连续批次，且当γ比例的副本先接收到交易tx而后收到tx'时，则tx'不能出现在早于tx的批次中。我们将该定义扩展，形式化要求这些批次应具有最小规模，从而首次提出一种既不能被空洞满足（通过任意大的批次），又能在存在故障副本时得以实现的排序公平性概念。进而证明，秩对聚合方法可同时针对参数γ的所有取值及任意数量的故障副本（公平性保证随故障副本比例增加而线性衰减）生成满足公平性定义的排序。随后将该协议实例化于流式场景中。通过精细分析排序依赖关系间的交互，我们的协议可在该场景下模拟秩对投票过程，并对排序算法进行调节，使得协议（在同步网络假设下）始终在有限时间后将交易追加至输出排序中。