We study the question of "fairly" ordering transactions in a replicated state machine. Each replica receives transactions over a network from clients in a possibly different order, and the system aggregates these orderings into a single, total order. This problem is akin to the classic problem of social choice theory, where rankings on candidates are aggregated into an election result. Three features make this problem novel and distinct. First, the number of transactions is unbounded, so an ordering must be defined over a countably infinite set. Second, decisions must be made quickly and with only partial information. Finally, some faulty replicas might alter reported observations; their influence should be bounded. We study the Ranked Pairs algorithm. Analysis of how missing information propagates through the algorithm enables our streaming version to know when it can output a transaction. Manipulation of a tiebreaking rule gives a protocol that (in a synchronous network) always outputs a transaction after a bounded time. Prior work proposes a "$\gamma$-batch-order-fairness" property on an output ordering, which divides the output into contiguous batches. If a $\gamma$ fraction of replicas receive a transaction $tx$ before another transaction $tx^\prime$, then $tx^\prime$ cannot be in an earlier batch than $tx$. We strengthen this definition to require that batches have minimal size, which must be handled carefully in the presence of faulty replicas. This gives the first notion of order-fairness that cannot be vacuously satisfied by arbitrarily large batches and that is satisfiable in the presence of faulty replicas. Prior work relies on a fixed choice of $\gamma$ and bound on the number of faulty replicas $f$, but we show that Ranked Pairs satisfies our definition for every $\gamma$ simultaneously and for any $f$, where fairness guarantees linearly degrade as $f$ increases.

翻译：我们研究在复制状态机中“公平地”排序交易的问题。每个副本通过网络从客户端接收交易，交易到达顺序可能不同，系统将这些排序聚合为一个全局总序。该问题类似于经典的社会选择理论问题——将候选人排序聚合为选举结果。三个特征使该问题具有新颖性和独特性。首先，交易数量无界，因此必须在可数无限集上定义排序。其次，决策必须快速做出且仅基于部分信息。最后，部分恶意副本可能篡改报告观测结果，其影响应受限制。我们研究了Ranked Pairs算法。通过分析缺失信息在算法中的传播方式，我们的流式版本能够确定何时可以输出交易。对平局打破规则的操控设计出一种协议，该协议（在同步网络中）总能在有界时间内输出交易。既有工作提出了输出排序的“γ-批序公平性”属性，该属性将输出划分为连续批次。如果γ比例的副本在另一笔交易tx′之前收到交易tx，则tx′不能出现在比tx更早的批次中。我们强化该定义要求批次规模最小化，这在存在恶意副本时需谨慎处理。这首次给出了序公平性概念，既不会因任意大批次而空洞满足，又能在存在恶意副本时仍可满足。既有工作依赖固定的γ值及恶意副本数量上限f的约束，但我们证明Ranked Pairs同时满足每个γ值及任意f下的定义，且公平性保障随f增加线性退化。