[...the earliest (1916) citation for the phrase listed by the OED seems to refer to a carrot dangling from a stick attached to and moving forward with the donkey itself: "The spectacle of an otherwise intellectual individual engaged in trying to plumb the depths of duplicity to which dealers can descend in faking old furniture is like that of the donkey pressing eagerly forward after the dangling carrot. It would ... be very pleasant to possess the carrot of complete knowledge, but the conditions render it impossible."
My guess is that the "perpetual motion" sense of the phrase was the original, probably inspired by a fanciful cartoon (real donkeys, unlike voters, are not stupid enough to fall for such a trick for very long). But the world being what it is, the "reward and punishment" meaning took over rather rapidly, and is thus the one heard most often today.]
There, I think we have made a lot of progress today. How does the group feel about that?