As for who invented the Carrot Stick in particular, that would be PP, but it's really nothing more than his own take and some speshul name he slapped on something that has been used for millennia in the horse-handling arena.
Or has the whip always been all stick & no carrot, as it were, B.P.? When I was a kid, the longe whip or crop were just whips, which the horses would've been shocked to find us stroking them with! Au contraire, the horses were always leery & overly aware that one had a crop. Yet that was considered normal horsemanship. I find the cs concept much better for the horse.