A Note on the Welfare Gap in Fair Ordering

In this short note, we show a gap between the welfare of a traditionally '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 an '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.