A Note on the Welfare Gap in Fair Ordering

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 of `optimal' 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.