Prior work studies the question of ``fairly'' ordering transactions in a replicated state machine. Each of $n$ replicas receives transactions in a possibly different order, and the system must aggregate the observed orderings into a single order. We argue that this problem is best viewed through the lens of social choice theory, in which (in the preference aggregation problem) rankings on candidates are aggregated into an election result. Two features make this problem novel. First, the number of transactions is unbounded, and an ordering must be defined over a countably infinite set. And second, decisions must be made quickly, with only partial information. Additionally, some faulty replicas might alter their reported observations; their influence on the output should be bounded and well understood. Prior work studies a ``$\gamma$-batch-order-fairness'' property, which divides an ordering into contiguous batches. If a $\gamma$ fraction of replicas receive $\tau$ before $\tau^\prime$, then $\tau^\prime$ cannot be in an earlier batch than $\tau$. We strengthen this definition to require that batches have minimal size ($\gamma$-batch-order-fairness can be vacuously satisfied by large batches) while accounting for the possibility of faulty replicas. This social choice lens enables an ordering protocol with strictly stronger fairness and liveness properties than prior work. We study the Ranked Pairs method. Analysis of how missing information moves through the algorithm allows our streaming version to know when it can output a transaction. Deliberate construction of a tiebreaking rule ensures our algorithm outputs a transaction after a bounded time (in a synchronous network). Prior work relies on a fixed choice of $\gamma$ and bound on the number of faulty replicas $f$, but our algorithm satisfies our definition for every $\frac{1}{2}<\gamma\leq 1$ simultaneously and for any $f$.

翻译：先前的工作研究了在复制状态机中"公平"排序交易的问题。每个$n$个副本以可能不同的顺序接收交易，系统必须将观察到的顺序聚合为单一顺序。我们认为，这一问题最好通过社会选择理论的视角来审视（在偏好聚合问题中，候选人的排序被聚合成选举结果）。两个特征使该问题具有新颖性。首先，交易数量是无界的，必须在可数无限集上定义顺序。其次，决策必须快速做出，且信息不完整。此外，某些故障副本可能篡改其报告观测值；它们对输出的影响应受到约束且易于理解。先前工作研究了"$\gamma$批序公平性"性质，该性质将顺序划分为连续批次。如果$\gamma$比例的副本在$\tau^\prime$之前接收到$\tau$，则$\tau^\prime$不能出现在比$\tau$更早的批次中。我们强化了这一定义，要求在考虑故障副本可能性的同时，批次具有最小规模（$\gamma$批序公平性可通过大批次虚满足）。这种社会选择视角使得排序协议能够比先前工作具有更强的公平性和存活性属性。我们研究了排名配对方法。通过分析缺失信息在算法中的传递过程，我们的流式版本能够确定何时可以输出交易。刻意构建的打破平局规则确保算法（在同步网络中）能在有限时间内输出交易。先前工作依赖于固定的$\gamma$选择和故障副本数量上限$f$，但我们的算法能同时满足所有$\frac{1}{2}<\gamma\leq 1$及任意$f$下的定义。