Setting up a moderated mailing list in mailman
Copied from https://answers.stanford.edu/solution/i-want-allow-only-owners-post-my-mailman-list
If you want to only allow owners to post to my list, but you don't want to moderate any posts to the list. Use the Sender Filters under Privacy settings for you Mailman list.
Mailman offers a great many options for managing who can post messages to a list, and how the list owner can moderate messages.
Go to https://mailman.stanford.edu/mailman/admin/LISTNAME (where LISTNAME is the name of your list). Note that you have to use the 'full administrative interface' to set these options. If you see 'Mailing Lists Basic Options' at the top of the page, click on the 'full administrative interface' link at the bottom of the page.
Select Privacy > Sender filters. Select Yes to By default, should new list member posting be moderated? Select Reject or Discard to Action to take when a moderated member posts to the list. Optionally, you can customize the rejection notice in Text to include in any reject notice to be sent to moderated members who post to this list. In the No-member filters section, put your address in List of non-member addrresses whose postings should be automatically accepted. If the owners are also members of the list, go to the Membership Management section and make sure the mod (moderated) option is not selected for the owner addresses.