Mailman Archiving Options

I just moved a client to Dreamhost from another provider where they also had a Mailman discussion list.

Everything is working at Dreamhost, but they have a strange request. They want all original posts to go to all subscribers as normal. BUT, they want all replies to ONLY go to the original poster. But they also want those replies to be archived so the entire list can choose to view them or not.

I’ve looked through all of the Mailman config options and cannot find a way to achieve what they want, even though they swear this is the way it worked with their old host.

Is this possible, or are they on crack?