A Note on the Welfare Gap in Fair Ordering

Abstract: Public blockchains group submitted transactions into batches, called blocks. A natural question is how to determine which transactions are included in these batches. In this note, we show a gap between the welfare of so-called fair' ordering, namely first-in-first-out (an ideal that a number of blockchain protocols strive to achieve), where the first transactions to arrive are the ones put into the block, and the welfare ofoptimal' inclusion that is, at least approximately, welfare-maximizing, such as choosing which transactions are included in a block via an auction. We show this gap is positive under a simple model with mild assumptions where we assume transactions are, roughly speaking, uniformly drawn from a reasonable distribution. Our results formalize a performance metric for blockchain inclusion rules and consequently provide a framework to help design and compare these rules. The results can be directly extended to ordering mechanisms as well.