gnome-software does not reload itself after being upgraded

This bug was inspired by
https://launchpad.net/ubuntu/+source/gnome-software/+bug/1573408/comments/40

What happens
============
After gnome-software itself is upgraded to a new version, a user needs to log out and log back in (or otherwise kill the background gnome-software service) to run the new version.

What should happen
==================
gnome-software should restart the background service when gnome-software is upgraded to a new version.

This issue could instead be mitigated if gnome-software was not *always* running in the background but only ran occasionally as suggested by bug 1592678.

How to reproduce
================
Let's test bug 1573408, the inability to install 3rd party apps issue.
1. Since this was a bug released with Ubuntu 16.04, start with a fresh Ubuntu 16.04 install. You can even use the live DVD/USB for this test.
2. Open Firefox and browse to https://www.google.com/chrome/
3. Click the Download now button then click Accept and install.
4. Click OK to open with Software Install.
5. After a few moments, the Software app opens with a basic info page about google-chrome-stable. Click Install.
6. It doesn't actually install.
7. Open a terminal and run sudo apt update; sudo apt install gnome-software
This will upgrade you to a version that fixes this bug.
8. Repeat steps 2-5. (Note that it doesn't matter whether you closed the Software app window or not after step 7.)
9. It still doesn't actually install.
10. Log out and log back in. (If you are using the live DVD/USB, the username is 'ubuntu'. Leave the password blank.). (Alternatively, you can run pkill gnome-software in your terminal.
11. Repeat steps 2-5. Google Chrome will successfully install.

ProblemType: Bug
DistroRelease: Ubuntu 16.10
Package: gnome-software 3.20.1+git20160617.1.0440874.ubuntu-xenial-0ubuntu1
ProcVersionSignature: Ubuntu 4.4.0-25.44-generic 4.4.13
Uname: Linux 4.4.0-25-generic x86_64
ApportVersion: 2.20.1-0ubuntu4
Architecture: amd64
CurrentDesktop: GNOME
Date: Sun Jun 19 04:08:56 2016
EcryptfsInUse: Yes
InstallationDate: Installed on 2016-04-09 (70 days ago)
InstallationMedia: Ubuntu-GNOME 16.04 LTS "Xenial Xerus" - Beta amd64 (20160408)
SourcePackage: gnome-software
UpgradeStatus: No upgrade log present (probably fresh install)