Explaining success in Bayesian reasoning with the adaptive toolbox and expertise.

Research on Bayesian reasoning has been shaped by two productive traditions: ecological rationality, which explains why natural frequencies facilitate inference, and nested sets accounts, which show how transparent set relations support analytic reasoning. Together, these approaches have generated a rich empirical literature on representational facilitation. Yet a broader pattern has emerged: Bayesian reasoning accuracy improves with training and visualisation, varies systematically with numeracy and domain knowledge, and can be high among mathematically trained reasoners even in probability formats. These findings suggest that Bayesian competence is not reducible to a privileged input format but reflects the acquisition and deployment of multiple inferential tools. Building on prior integrative contributions, we propose that Gigerenzer's adaptive toolbox, combined with principles from expertise research, provides a productive theoretical framework and research agenda. From this perspective, natural frequencies and nested set representations function as scaffolds that make particular tools easier for novices to access, rather than as the sole route to success. An expertise-based interpretation helps explain how inferential tools are learned, automatised, and selected through experience, why tool use varies across individuals and tasks, and how accurate Bayesian reasoning can be achieved across representational formats. We further argue that expert-novice comparisons and process-tracing methods provide a powerful approach to identifying the tools that support probabilistic inference and to guiding the design of more generalisable training interventions. This framework links representational facilitation to learning and strategy selection, shifting the focus of Bayesian reasoning research from which formats work best to how people become capable of Bayesian reasoning at all.