Will Baude, at the prompting of Jacob T. Levy, ponders the Three-Fifths Compromise. I don’t have a better theory than Will’s; I always just figured that’s the offer the southern delegates proffered after a few rounds and that’s what stuck.
I suppose another possibility is that it reflected the assumed ratios of voting populations around 1787—so as to balance voting between relatively free North with the more populous but part-slave South—but I don’t have the numbers in front of me to prove it.