[ubuntu] No module named repository

I have started getting messages like these for a couple of applications lately. The first one I noticed was Deja-Dup when it quit working. I get the error

I googled and found a few references to other problems where the module name was gi.repository, and to resolve it I should install python-gi. My error just says repository, and python-gi and python3-gi are already installed anyway.

Today, I noticed that software center would not start. When starting it from a terminal I see this:

This one DOES say gi.repository. So something has broken, but what???

Wayne

P.S. I should maybe note that Deja Dup was working perfectly as of July 28, but broken August 4 when it tried to do a weekly backup. As for software center, I haven't used it in a long time so I can only assume it broke at the same time.

Ubuntu 16.04 (upgraded from 15.10)
Intel I-7 processor with 16GB RAM
1TB esata disk for / filesystem
1TB esata disk for /home