Informed by Grether and Plott (1979) and Cox and Grether (1996), we implement various preference elicitation procedures over a parameter grid. First, we find a lower incidence of preference reversals for probability equivalents from the dual-to-selling version of Becker, Degroot, and Marschak (1964; BDM) than for certainty equivalents from traditional BDM—consistent with conjectures regarding response mode. Second, the Blavatskyy (2009, 2012) model of probabilistic choice can explain the incidence of preference reversals when using probability equivalents. Thus, between response mode (outside the Blavatskyy model) and stochastic choice (as per Blavatskyy), preference reversals in the original certainty equivalent case seem to be explained. We also present estimates for risk and stochasticity parameters; the former are not correlated across mechanisms, but the latter are. Finally, relatively more error-laden behavior (based on within-mechanism checks) can be associated with fewer reversals across mechanisms. The data make clear, empirically, the logical proposition that reducing reversals requires only a better “match” with binary choice, not necessarily rational behavior at any deeper level.