sudo apt-get install --no-install-recommends libpolkit-gobject-elogind-1-0 policykit-1
sed -i -r -e '/session\s+optional\s+pam_systemd\.so/s/systemd/elogind/;' /etc/pam.d/lightdm-greeter

Unfortunately my normal mitigations for automating the apt-get are not recommended, because of the propensity for policykit and the elogind packages to conflict with major packages, and the admin should always review what is about to be removed.
If you truly want an unattended process for this task:

sudo apt-get install -y -q -o Dpkg::Options::="--force-confdef" -o Dpkg::Options::="--force-confold" -o Dpkg::Options::="--force-overwrite" --no-install-recommends libpolkit-gobject-elogind-1-0 policykit-1
sed -i -r -e '/session\s+optional\s+pam_systemd\.so/s/systemd/elogind/;' /etc/pam.d/lightdm-greeter

To reiterate, this solution worked for me:

# aptitude update
# aptitude install policykit-1

That's it!

That systemd-free Debian Jessie was installed in a VM, and later on it was dist-upgraded to Devuan ASCII. The upgrade went smoothly, and afterward LightDM continued to work normally. I don't know what the best solution to this problem is, but I thought I should chime in with my experience in case the information is helpful to someone.

Phil

 ,------+-----.  
 |   Please   |  
 | wiki this. |  
 `------+-----´   
     _  |  _
    ò.ó/|\°v°
   (|_|   |_|\
----^-^---^-^---

Step 1:
Check that
   libpam-elogind, elogind, libelogind0, libpolkit-backend-elogind-1-0,
   libpolkit-gobject-elogind-1-0 and policykit-1 is *installed*.

I am using LightDM and I don't have those packages installed, except for policykit-1. I am also using Xfce, and the "Restart" and "Shut Down" buttons work fine. Is there something else broken that I've missed?

Phil

I installed Devuan 2 + MATE, which defaults to Slim display manager.
To see users list at the graphic login interface, I needed to switch to LightDM, and it worked with only this command:

sudo apt-get install lightdm libpolkit-backend-elogind-1-0

(reboot and shutdown work)
Today I've edited /etc/pam.d/lightdm-greeter to replace the use of pam_systemd.so by pam_elogind.so , although I don't know what it is necessary for.

Devuan 2 needs some packages fix to allow a cleaner switch between Slim and LightDM:

• lightdm should deped on libpolkit-backend-elogind-1-0

• slim should deped on libpolkit-backend-consolekit-1-0

• task-mate-desktop should depend on any of libpolkit-backend-consolekit-1-0 | libpolkit-backend-elogind-1-0

Without this last fix, installing libpolkit-backend-elogind-1-0 it's also removed task-mate-desktop and some other packages are suggested for autoremoval: gnome-orca speech-dispatcher libreoffice-gtk3 etc.

Hello fred43 and all
fred43, you are a genius, your solution works perfectly well on a fresh ascii-install. I tested it with Cinnamon and OpenRC. I'm delighted the lightdm is the display manager by default now.
Thank you, well done!

It is the default for Cinnamon.  Xfce uses slim etc.

Yes, it would be nice and helpful if a MATE user could verify that the outlined procedure also works for that environment.

I have tested both LightDM + elogind with KDE as well as XFCE and both work.  I wonder if LightDM + elogind works with MATE, anyone test it?  From looking at the release notes, it appears slim is who likes consolekit.  It would be nice to completely replace consolekit with elogind.

Hope you don't mind that I played a bit with the formatting to make it easier to read.

IMHO, using "elogind and friends" has the potential of making life a
little bit easier for the Devuan nosystemd-DE developers/maintainers.

Have you swapped out 'slim' for 'lightdm' (with libpam-elogind) and
consequently the reboot and shutdown does not work as advertised?

Don't despair, it can be fixed in 3 easy steps.

-----
Do the following as Root

Step 1:
Check that
   libpam-elogind, elogind, libelogind0, libpolkit-backend-elogind-1-0,
   libpolkit-gobject-elogind-1-0 and policykit-1 is *installed*.

and make sure that
   consolekit, libpolkit-backend-consolekit-1-0,
   libpolkit-gobject-consolekit-1-0, libck-connector0 and
   libpam-ck-connector is *uninstalled*

Step 2:
Then go to /etc/pam.d/ and edit the file lightdm-greeter to look thus:

   #added '#'
   #session   optional pam_systemd.so
   #added a new line
   session   optional pam_elogind.so

Step 3:
Reboot the system
-----

You can now reboot or shutdown from the Lighdm or from the Xfce4 DE just
like in the olden days but now with "elogind and friends" in place. BTW,
the command 'who' is also working correctly.