Miner extractable value (MEV) refers to any excess value that a transaction validator can realize by manipulating the ordering of transactions. In this work, we introduce a simple theoretical definition of the 'cost of MEV', prove some basic properties, and show that the definition is useful via a number of examples. In a variety of settings, this definition is related to the 'smoothness' of a function over the symmetric group. From this definition and some basic observations, we recover a number of results from the literature.

翻译：矿工可提取价值（Miner Extractable Value，MEV）指交易验证者通过操纵交易排序所能获取的任何超额价值。本文提出“MEV成本”的简洁理论定义，证明其基本性质，并通过多个实例展示该定义的实用性。在不同情境下，这一定义与对称群上函数的“平滑性”相关联。基于该定义与若干基本观察，我们重新推导出文献中的一系列结论。