Predominant perspectives in privacy behavior research describe human decision making as boundedly rational, cognitively biased, and driven by heuristics. This description stands in contrast to Bayesian decision theory, which de-scribes decision making as mathematically rational utility maximization. Recently, research has proposed rational process modeling as a way of considering justified criticisms of Bayesian models with regards to psychological plausibil-ity. In rational process modeling, locally irrational behavior emerges from an approximation of Bayesian inference focused on the attribution of cognitive resources. In two online surveys, we have applied a rational process model to predict the choice behavior of 103 and 113 participants. They saw 3 (study 1) and 2 (study 2) app store offerings of fictional smartphone apps related to travel or messaging and decided whether to use them. Stated preferences for features of these apps were gathered and sampled from until triggering a probabilistic stopping rule. Then, they were integrated via Bayes’ rule and used to predict service adop-tion. Depending on the number of samples, the model would show behavior ranging from extreme probability matching to near-deterministic utility maximization. We compared the model prediction of observed participant behavior to three alternative models by using Bayes Fac-tors: a deterministic Bayesian model, the take-the-best heuristic, and a probabilistic variant of said heuristic. We found that the data give the most support to the proposed rational process model, although all models tended to over-estimate service adoption. We connect our results to previ-ous work in cognitive science and online privacy research and outline approaches derived from the model to encour-age privacy-preserving user behavior through interventions.