How can the success of Bayesian models be reconciled with demonstrations of heuristic and biased reasoning? In recent years, Bayesian models of cognition have been used - with considerable success - to explain human reasoning in a variety of inferential tasks (Chater, Tenenbaum, &amp; Yuille, 2006). These models represent a &quot;probabilistic approach&quot; that seeks to derive the optimal solutions to inferential problems, and the success of these models is often interpreted as evidence that intuitive reasoning is fundamentally rational. Other successful research traditions, however, adopt a starkly different view of human rationality. Researchers interested in judgment and decision making, for example, often assume that intuitive inference is heuristic, error-prone, and subject to biases (Kahneman &amp; Tversky, 1982; Gilovich, Griffin, &amp; Kahneman, 2002).
How is it possible that the probabilistic and heuristic-and-biases approaches have both been successful while adopting fundamentally incompatible views of rationality? I suspect that many psychologists have thought about this question, but so far as I can tell, these approaches have only been directly compared on a few inferential tasks, and there are still fewer (published) attempts to derive any general answers to this question.

References

Chater, N., Tenenbaum, J.B., &amp; Yuille, A. (2006) Probabilistic models of cognition: Conceptual foundations. Trends in Cognitive Sciences 10(7): 287-291. [pdf]

Gilovich, T., Griffin, D., &amp; Kahneman, D. (Eds.) (2002) Heuristics and biases: The psychology of intuitive judgement. Cambridge Univ. Press.

Kahneman, D. &amp; Tversky, A. (1982) The psychology of preferences. Scientific American 246(1): 160-173.
Your question is predicated on the assumption that Bayesian modeling has been successful in all domains. I think this is a stance that many (except hardened Bayesians) would disagree with. For instance, consider the classic Tversky &amp; Shafir experiments on the violation of the sure thing principle:

What are popular rationalist responses to Tversky &amp; Shafir?

The above approach can be reconciled with standard rationalism, but you are in fact building theories of heuristics-and-biases to do so; that is how Kahneman &amp; Tversky arrived at their models. Similarly, you can build very awkward Bayesian models for these sort of tasks (other difficult tasks are ones that show an order effect) but it is hard to say how these models are different from heuristics. For a more general treatement:

What tasks does Bayesian decision-making model poorly?

However, in the domain where Bayesian modeling is a good fit, the reason it works well to reconcile with heuristics-and-biases is because it has the perfect mechanism for modeling bias: the initial prior distribution. In fact you can use the prior distribution in the bayesian approach to quantify bias.

To summarize, you can model heuristics-and-biases with the bayesian approach. For bayesians heuristics are how the task is modeled/represented and biases are the intial prior distributions