ratify
From LSJ
ὁδὸς ἄνω κάτω μία καὶ ὡυτή → the road up and the road down is one and the same, the upward path and the downward path are the same
P. and V. κυροῦν, ἐπικυροῦν, ἐμπεδοῦν (Plato also Ar.), V. ἐχέγγυον ποιεῖν.
ratify with a nod: P. and V. ἐπινεύειν.
ratify by voting: P. ἐπιχειροτονεῖν.