Can sudo be reinstalled after being removed?

This seems to be a chicken-egg problem. The most common task using sudo is installing and removing software.

sudo apt-get purge <appname>

But sudo itself can be removed.

sudo apt-get purge sudo # Do not run this command on production computers!

This is where the fun comes

ubuntu@ubuntu:~$ sudo
bash: /usr/bin/sudo: No such file or directory

Although it's obvious that no person in his right mind will purge sudo (other than me), someone can be fooled to run this command (not directly, in its hex mode, or whatever it's called) or a person could SSH in disguised as tech guru and do the mess.

So is there a way of reinstalling sudo?

I can install applications using:

pkexec apt-get install <appname>

From man pkexec:

  pkexec allows an authorized user to execute PROGRAM as another user. If
  username is not specified, then the program will be executed as the
  administrative super user, root.

So, I suppose that pkexec apt-get install sudo should work as well.

Edit: now I can confirm: yes, sudo can be installed using using pkexec apt-get install sudo:

^{(click to enlarge)}

You can always boot into Recovery Mode, drop to root shell and install it without sudo.