Nested Sets and Natural Frequencies

Abstract

Is the nested sets approach to improving accuracy on Bayesian word problems simply a way of prompting a natural frequencies solution, as its critics claim? Conversely, is it in fact, as its advocates claim, a more fundamental explanation of why the natural frequency approach itself works? Following recent calls, we use a process-focused approach to contribute to answering these long-debated questions. We also argue for a third, pragmatic way of looking at these two approaches and argue that they reveal different truths about human Bayesian reasoning. Using a think aloud methodology we show that while the nested sets approach does appear in part to work via the mechanisms theorised by advocates (by encouraging a nested sets representation), it also encourages conversion of the problem to frequencies, as its critics claim. The ramifications of these findings, as well as ways to further enhance the nested sets approach and train individuals to deal with standard probability problems are discussed.