Millimetric droplets may be levitated on the surface of a vibrating fluid bath. Eddi et al. (2008) demonstrated that when a pair of levitating drops of unequal size are placed nearby, they interact through their common wavefield in such a way as to self-propel through a ratcheting mechanism. We present the results of an integrated experimental and theoretical investigation of such ratcheting pairs. Particular attention is given to characterizing the dependence of the ratcheting behavior on the droplet sizes and vibrational acceleration. Our experiments demonstrate that the quantized inter-drop distances of a ratcheting pair depend on the vibrational acceleration, and that as this acceleration is increased progressively, the direction of the ratcheting motion may reverse up to four times. Our simulations highlight the critical role of both the vertical bouncing dynamics of the individual drops and the traveling wave fronts generated during impact on the ratcheting motion, allowing us to rationalize the majority of our experimental findings.