A 3-string bass. For when 4 strings are just too confusing! (No bass-player jokes, please.)
I'd actually love to give that one a go. I've heard a bass balalaika at the local Russian restaurant and it sounds pretty cool, at least in the context of Russian acoustic music. It might, however, be an interesting substitute for standup bass for jazz. Or, you never know, maybe even run through an amp sim for prog rock.