We present a statistical investigation into the magnetosonic Mach number dependence of the efficiency of reconnection at the Earth's dayside magnetopause. We use the transpolar voltage V PC, derived from radar observations of the ionospheric electric field, as a proxy for the dayside reconnection voltage. Our results show that the IMF clock angle dependence of V PC is closely approximated by the function f($\theta$) = sin2($\theta$/2), which we use in the derivation of a solar wind transfer function E* = E SW f($\theta$), wherein E SW is the solar wind electric field. We find that V PC is strongly related to E*, increasing almost linearly with small E* but saturating as E* becomes high. We also find that E* is strongly dependent on the magnetosonic Mach number, M MS, decreasing to near-zero values as M MS approaches 12, due principally to decreasing values of the IMF strength. V PC, on the other hand, is only weakly related to M MS and, for lower, more usual values of E*, actually shows a modest increase with increasing M MS. This result has implications for the solar wind-magnetosphere interaction at the outer planets where the Mach number is typically much higher than it is at 1 AU. Examples of SuperDARN convection maps from two high Mach number intervals are also presented, illustrating the existence of fairly typical reconnection driven flows. We thus find no evidence for a significant reduction in the magnetopause reconnection rate associated with high magnetosonic Mach numbers.