You can use utopic's Mailman 2.1.18 package on trusty. (Source: I am using it, for precisely this reason, see Background below.)
To install it via apt-get, do the following:
- First, configure the utopic repository by creating a file /etc/apt/sources.list.d/utopic.list with these contents: - deb http://archive.ubuntu.com/ubuntu utopic main restricted universe multiverse
 
- Next, configure the system so that it does not automatically install packages from utopic (since otherwise you will upgrade to utopic the next time you run dist-upgrade). Create a file /etc/apt/preferences.d/utopic with these contents: - Package: *
Pin: release a=utopic
Pin-Priority: 100
 
- Finally, install the mailman package, explicitly instructing apt-get to use the utopic version: - apt-get update && apt-get install mailman/utopic
 
Caution
Using packages from a newer release on an older release is not supported. If something goes wrong with this process you will likely be on your own bug-wise. However, I can confirm that my Mailman lists work after doing this.
Upgrading
You should remove the /etc/apt/sources.list.d/utopic.list and /etc/apt/preferences.d/utopic files before attempting any upgrade to a new version of Ubuntu from trusty.
Sources
These are based on the Ubuntu Backport instructions, substituting "utopic" for "trusty-backports"
Background
I also wanted 2.1.18, because the "ALLOW_FROM_IS_LIST = Yes" feature in 2.1.16 is list-wide. I don't want to re-write everyone as "from is list", just Yahoo users and others with a DMARC p=reject policy. 2.1.18 has a per-sender feature accessible from Privacy options → Sender filters in an individual list's admin interface.