Triage is a model of one person
Inbox management is the highest-volume task in the role, and the thing being automated is not sorting. It is a model of what one specific person needs to see.
A useful triage produces four outcomes. Needs the executive, now. Needs the executive, not urgently. Handle without them. And nothing required.
What determines which bucket a message lands in is almost never the message alone. It is the sender's relationship to the executive, what is happening this week, what the executive already knows, and whether this thread has history. The same message from two different senders belongs in two different buckets.
Generic importance filtering fails for exactly this reason. It sorts on properties of the email rather than on properties of the relationship.
What does work is calibration from your own decisions. If the system can learn from how you have historically routed messages from particular senders and topics, it becomes useful, because you are the model being approximated.
And the practical arrangement is a queue rather than an action. The system proposes a bucket, you confirm or move it, and the corrections are the training signal.
One asymmetry to design around. The costs of the two errors are wildly different. Wrongly escalating something unimportant wastes a minute of the executive's attention. Wrongly suppressing something urgent can cost a deal or a relationship. So triage should be biased toward escalation, and any automated suppression needs to be conservative in a way that feels inefficient and is correct.

