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:
Pin: release a=utopic
Finally, install the mailman package, explicitly instructing apt-get to use the utopic version:
apt-get update && apt-get install mailman/utopic
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.
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.
These are based on the Ubuntu Backport instructions, substituting "utopic" for "trusty-backports"
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.