Matthew Poole and continuators on Numbers 17:3

3 And thou shalt write Aarons name upon the rod of Levi, for one rod shall be for the head of the house of their fathers .

Rather than Levi's name, for that would have left the controversie undecided between Aaron and the other Levites, whereas this would justifie the appropriation of the Priesthood to Aarons family.

(i. e.) There shall be in this, as there is in all the other Tribes, onely one rod, and that for the head of their Tribe, who is Aaron in this Tribe: whereas it might have been expected that there should have been two rods, one for Aaron, and another for his competitours of the same Tribe. But Aarons name was sufficient to determine both the Tribe, and that branch or family of the Tribe, to whom this dignity should be affixed.