Synaptic not launching on Ubuntu 17.10

You can use Synaptic (or any other application that needs to run as root) under Wayland by first entering this command in the terminal:

xhost +si:localuser:root

You probably logged in using the default Wayland session. Wayland does not allow gui applications to run in superuser mode like Synaptic. If you really want to use this tool you have to login using the Xorg session.