  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.
