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. We also show that this definition is related to the ‘smoothness’ of a function over the symmetric group in a variety of settings and that, from this definition and some basic observations, we recover a number of results from the literature.

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