# “Take the Middle” – Averaging Prior and Evidence as Effective Heuristic in Bayesian Reasoning

- Katharina Loibl, University of Education Freiburg, Freiburg, Germany
- Timo Leuders, University of Education Freiburg, Freiburg, Germany

**Abstract**When humans revise their assumptions based on evidence, they process information on the (un)certainties of the situation. This process can be modeled by a (mathematically optimal) Bayesian reasoning strategy. Humans typically deviate from this norm and apply heuristic strategies, often by only partially processing the available information (e.g., neglecting base rates). From a perspective of ecological rationality, such heuristics possibly constitute viable cognitive strategies in certain situations. We investigate the adequacy of a cognitively plausible heuristic strategy, which amounts to approximately averaging the probability information on prior hypotheses and evidence.
We compare this strategy to optimal Bayesian reasoning and to information-neglecting strategies by exploring the situational parameter space (number of hypotheses, prior and likelihood values). Finally, we frame this in the context of teachers’ diagnostic judgments on students’ potential misconceptions (priors) based on students’ solutions (evidence) and interpret the resulting accuracy of decisions within the ecology of informal student assessment.