The mathematical theory of communication.

Is human cognition best described by optimal models, or by adaptive but suboptimal heuristic strategies? It is frequently hard to identify which theoretical model is normatively best justified. In the context of information search, naoptimal” models.

The tendency to test outcomes that are predicted by our current theory (the confirmation bias) is one of the best-known biases of human decision making. We prove that the confirmation bias is an optimal strategy for testing hypotheses when those hypotheses are deterministic, each making a single prediction about the next event in a sequence. Our proof applies for two normative standards commonly used for evaluating hypothesis testing: maximizing expected information gain and maximizing the probability of falsifying the current hypothesis. (...) This analysis rests on two assumptions: (a) that people predict the next event in a sequence in a way that is consistent with Bayesian inference; and (b) when testing hypotheses, people test the hypothesis to which they assign highest posterior probability. We present four behavioral experiments that support these assumptions, showing that a simple Bayesian model can capture people's predictions about numerical sequences (Experiments 1 and 2), and that we can alter the hypotheses that people choose to test by manipulating the prior probability of those hypotheses (Experiments 3 and 4). (shrink)

In some circumstances, children of 5 produce identical classifications to 10 year olds when asked to sort a collection of objects. This has been interpreted as meaning that the process of constructing classifications is very similar at 5 and 10 years. But this conclusion rests on a comparison of the product of children's sortings, rather than on a study of their activity in producing sortings. The present paper argues that the process of classifying is in fact very different for 5 (...) and 10 year olds: whereas the older children treat the whole classification as a single unit composed of interrelated classes, the younger children proceed as though each class were independent of the others. At around 7 years, there is evidence for a transitional phase, in which children directly work on the relations between classes and so organize their initially “juxtaposed” procedures into more coherent systems. The tendency to work on the relations between elements in the process of classifying is not, however, simply an age‐related phenomenon: evidence for a similar effect can be observed in children throughout the age range of 5 to 10 years, during the course of short experimental sessions. Furthermore, the effect is not merely a response to errors or difficulties: the tendency to work on classifying relations can be seen in 5‐year‐old children in a task in which they are already successful. It seems that children spontaneously discover and use information about their procedures and the relations between them. This process is an end in itself. It occurs whether or not its results yield more successful performance. The approach taken in this paper is not confined to one area of behavior. This analysis of children's classifying fits closely with work in a very different domain, i.e. Karmiloff‐Smith's work on children's language and other representational systems. The analysis has implications for computer models of skill acquisition, as well as for psychological theories of development. (shrink)