We present a new theory of decision under risk called third-generation prospect theory. A novel feature of our version of prospect theory is that, by allowing reference points to be uncertain, it is able to accommodate the phenomenon of preference reversal. While several previous theories of preference reversal have been proposed, thus far it has resisted explanation via any empirically plausible model of preferences. We investigate whether our explanation is empirically plausible. We find that the standard patterns of preference reversal are predicted for typical parameterisations of prospect theory already established in the empirical literature. Consequently we suggest that our model constitutes a best buy theory: it offers the predictive power of previous variants of prospect theory and adds to that an explanation of preference reversal. The latter comes ‘free of charge’ since it involves no extra parameters and no re-parameterisation.