Comment 10 for bug 977069

Dont know if that helps:

As far as i recall from when i experienced this bug, installing lightdm-gtk-greeter triggered an update-alternative when installing, not when removing tho.

when installing lightdm-gtk-greeter i had to manually edit lightdm.conf to greater-session=lightdm-gtk-greeter to usethe lightdm greeter, when removing the greeter and changing the key back to greeter-session=unity-greeter lightdm failed to start.
i have no clue about lightdm internals, nor how greeter actually work, thats purely from an users POV but having a key in the config file and partially ignoring it and having redundant update-alternatives which partly work seems very very confusing and irritating to me. there may be a technical reason behind it, or something i dont get/understand, but well, i am just a user