Influential economic approaches as random utility models or quantal-response equilibria assume a monotonic relation between error rates and choice difficulty or "strength of preference", in line with widespread evidence from discrimination tasks in psychology and neuroscience. However, while the latter define difficulty through objective dimensions (weight, length, etc), for economic decisions under risk the appropriate dimension remains unclear, with candidates including payoff-irrelevant numerical magnitudes. The very existence of the effects remains largely untested, because fitting models which assume such relations to data simply produces spurious findings. We provide a systematic empirical validation relying on two parsimonious experimental designs. Strength-of-preference effects are explained by expected values if objectively-correct answers exist, and by cardinal differences in independently-estimated utilities for preferential choices. Numerical magnitudes produce additional but minor effects. Finally, response times are inversely related to strength of preference, confirming that the observed relations are not "as if" explanations.