Choice inconsistency is ubiquitous in economic decision making. Standard random utility models as well as sequential sampling models account for it and predict a relation between inconsistency rates and utility differences (strength-of-preference effects). The latter phenomenon is well-established empirically. However, recent literature argues that inconsistency might be the outcome of a deliberate attempt to implement an explicit preference for randomization. We collected new data in three preregistered experiments and also reanalyzed the previous evidence for this explanation. Our evidence is generally well-explained by strength-of-preference effects. That is, people are less consistent for choices that are closer to indifference. When an option to randomize is made explicit and salient, this option is sometimes chosen. However, in a within-subject design, we statistically reject the hypothesis that explicit mixing in one-shot decisions (revealed preference for randomization) equals choice proportions in repeated decisions (choice inconsistency). The deliberate choice of randomization devices is influenced both by explicit costs (if any) and whether decision makers are close to indifference between the nonrandomized alternatives. The latter effect might create a correlation with choice inconsistency at the aggregate level.