Bayesian reasoning tasks require processing data in proba-bilistic situations to revise risk estimations. Such tasks are difficult when data is presented in terms of single-event probabilities; the multiplicative combination of priors and likelihoods often is disregarded, resulting in er-roneous strategies such as prior neglect or averaging heu-ristics. Proportions (relative frequencies) are computation-ally equivalent to probabilities. However, proportions are connected to natural mental representations (so-called ra-tio sense). Mental representations of nested proportions (70% of 20%) allow for a mental operation that corre-sponds to a multiplicative combination of percentages. In two studies, we focused on the conceptual understanding underlying Bayesian reasoning by utilizing graphical rep-resentations without numbers (to avoid calculations with percentages). We showed that verbally framing Bayesian tasks in terms of proportions, as opposed to single-event probabilities, increased correct Bayesian judgment, and re-duced averaging heuristics. Thus, we claim, proportions can be regarded as a natural view on normalized Bayesian situations.

When humans revise their assumptions based on evidence, theyprocess information on the (un)certainties of the situation. Thisprocess can be modeled by a (mathematically optimal) Bayes-ian reasoning strategy. Humans typically deviate from thisnorm and apply heuristic strategies, often by only partially pro-cessing the available information (e.g., neglecting base rates).From a perspective of ecological rationality, such heuristicspossibly constitute viable cognitive strategies in certain situa-tions. We investigate the adequacy of a cognitively plausibleheuristic strategy, which amounts to approximately averagingthe probability information on prior hypotheses and evidence.We compare this strategy to optimal Bayesian reasoning and toinformation-neglecting strategies by exploring the situationalparameter space (number of hypotheses, prior and likelihoodvalues). Finally, we frame this in the context of teachers’ diag-nostic judgments on students’ potential misconceptions (pri-ors) based on students’ solutions (evidence) and interpret theresulting accuracy of decisions within the ecology of informalstudent assessment.