More Ngram fun: carrots and sticks

Carrot and stick, or carrot on a stick? In my last go-round with this one -- when I found "turnips on a stick" in the 1840s -- I decided they might well be two independent creations, rather than an original and a variant. Michael Quinion also covers the issue pretty exhaustively at World Wide words. And here's the Google graph, showing that "carrot and stick," if no more respectable than its stablemate, is a lot more common.