How to install Cinnamon desktop environment on top of Ubuntu?
Solution 1:
Because Linux Mint isn't related to Ubuntu the way Kubuntu and the like are, (Direct offshoots etc...) you unfortunately cannot install the Linux Mint environment on top of the Ubuntu DE like you can with say, Kubuntu/Xubuntu/Lubuntu etc...You can do a second partition and install Linux Mint on that and subsequently choose between them at system boot with the GRUB menu but that's the extent of what you can do in regards to running Linux Mint on Ubuntu...
Solution 2:
It's not possible to switch like Gnome and KDE. You need to make a fresh install for Linux Mint and in the end of the installation, grub (boot loader) will do the things in spite of you.
You can select the Operating Systems after the BIOS section on Grub window.
Solution 3:
As the others have said, you can't do it like that. However, you can modify your Ubuntu to ACT like Linux Mint. To get the Mint Menu, and other Mint tools, add the WebUpd8 PPAs for each one. it's a slog, but you probably don't need all of them