I think it is worth revisiting BIP 125's replace-by-fee policy for when to
replace transactions.

The current policy can be problematic. As noted earlier by Rhavar,
sometimes one's transaction becomes pinned making it infeasible to fee bump
with RBF.  This happens when one makes a normal payment to a large
commercial service, and, while the transaction remains unconfirmed, the
commercial service creates a low-fee-rate sweep of one's payment, among a
collection of others.  If one wants to RBF this original payment, for
example to get confirmation of the change output for use in further
transactions, the current BIP 125 rules require that you make a fee bump
that exceeds the combined total fees of the original transaction and the
low-fee-rate sweep of the commercial service.

The problem is that, while the fee rate of the sweep is low, the absolute
size of the fee can still be large, making it infeasible to RBF the
original transaction.  BIP 125 was defined back in 2015, when perhaps
rational miners did care about absolute fee amounts. However, today we are
in an era where rational miners care about fee-rates more than absolute
fees.  The fee-rate of the large sweep transaction is low enough that we do
not expect that miners will be mining it in the same block as the original
transaction.  Today, a rational miner will prefer a fee-bumped version of
original transaction without consideration of the low-fee sweep transaction
(or at least discounting the low-fee sweep in proportion to the miner's
hash-rate fraction).

Let me quote the five rules that define the current BIP 125 policy:

One or more transactions currently in the mempool (original transactions)
> will be replaced by a new transaction (replacement transaction) that spends
> one or more of the same inputs if,
>    1. The original transactions signal replaceability explicitly or
>    through inheritance as described in the above Summary section.
>    2. The replacement transaction does not contain any new unconfirmed
>    inputs that did not previously appear in the mempool. (Unconfirmed inputs
>    are inputs spending outputs from currently unconfirmed transactions.)
>    3. The replacement transaction pays an absolute fee of at least the
>    sum paid by the original transactions.
>    4. The replacement transaction must also pay for its own bandwidth at
>    or above the rate set by the node's minimum relay fee setting. For example,
>    if the minimum relay fee is 1 satoshi/byte and the replacement transaction
>    is 500 bytes total, then the replacement must pay a fee at least 500
>    satoshis higher than the sum of the originals.
>    5. The number of original transactions to be replaced and their
>    descendant transactions which will be evicted from the mempool must not
>    exceed a total of 100 transactions.
> To address the new reality of rational miners' consideration, I propose
changing rules 3 and 4 to something like the following.

3'. The replacement transaction pays a fee rate of at least the effective
fee rate of any chain of transactions from the set of original transactions
that begins with the root of the original transaction set.

4'. The replacement transaction must also pay for replacing the original
transactions at or above the rate set by the node's minimum relay fee
setting. For example, if the minimum relay fee is 1 satoshi/byte and the
replacement transaction and the original transactions are 1000 bytes total,
then the replacement must pay a fee at least 1000 satoshis higher than the
fee of the root transaction of the original transactions.

Rule 3' is a fancy way of saying that the replacement transaction must have
a fee rate that is larger than the package fee rate of the root of the set
of transactions it replaces, where the package fee rate is the fee rate
implied by considering CPFP.

Rule 4' is an amended anti-spam rule that is intended to avoid DOS attacks
from churning the mempool. I don't know if it is really necessary to pay
for the size of the original transactions being evicted, but some people I
chatted with thought it could be important.

Other people on the mailing list have been thinking about RBF policy for
far longer than I have, so I wouldn't be surprised if my proposal above is
naive.  However, I think it can start a conversation about addressing the
problems with the current RBF policy.
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