Nested Sets and Natural Frequencies
- Stephen Dewitt, University College London, London, United Kingdom
- Anne Hsu, Queen Mary University, London, United Kingdom
- David Lagnado, Department of Experimental Psychology, University College London, London, United Kingdom
- Saoirse Connor Desai, Department of Psychology, City, University of London, London, United Kingdom
- Norman Fenton, Queen Mary University of London, London, United Kingdom
AbstractIs 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.
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