A Retarded Cousin is that one slice of pizza that is cut smaller than the rest, and is usually left-over, until drastic measures are used.
If left at a party, the host will usually try to trick someone into taking the Retarded Cousin home.
Host: There's still a piece of pizza left if anyone wants it.
Tim: I'll take it... wait a second, is it the Retarded Cousin?
John: I am still kinda hungry... I'm going to get another piece of pizza. Ohh, never mind...
John: There's only the Retarded Cousin left.