What is the "Precedence" email header?
This email header originated in the RFC 3834. It suggested that autoresponders (such as for out-of-office or vacation situations) should not be sent in response to emails with a precedence of "list", "junk", or "bulk". This helps to avoid autoresponder loops.
How is "bulk" used?
In Google's Bulk Senders Guidelines they mention that
Messages should indicate that they are bulk mail, using the 'Precedence: bulk' header field.
This triggers Google's Smart Labels feature to label the messages as bulk. If you fail to label bulk emails with this header, it's more likely that Google will send your messages to the recipient's Spam folder.
How do I set it up?
In whichever system or software you use to send bulk/broadcast messages to your subscribers, you need to edit its email header area and include a new field: