Examining the relationship between environmental distributions and belief

In a complex and volatile environment, agents must learn to capitalize on regularities in their surroundings to be able to infer unknown quantities and generalize past knowledge. However, what properties are learned when adapting to environmental regularities is still unclear. One possibility is that only a few representative examples are stored in memory (Mozer, Pashler, & Homaei, 2008). Alternatively, one could infer rough summaries of the distribution of instances, such as the expected value over all instances and their variability (Tran, Vul, & Pashler, 2017). Finally, agents might acquire full distributional knowledge about environmental regularities, for instance, that instances are distributed according to a powerlaw distribution (Griffiths & Tenenbaum, 2006). These accounts differ in complexity and, as a result, in their ability to capture complex environmental distributions. Intuitively, an agent should strive to match the environmental statistics as closely as possible, with an ideal observer considering the exact environmental statistics as prior information when performing inferences. However, this intuitive notion has been challenged based on theoretical arguments and simulations, arguing that reproducing the environmental frequencies exactly is not robust to possible environmental changes and amounts to overfitting. Instead of veridical environmental frequencies, ideal observers should favor more entropic prior beliefs (Feldman, 2013). Here, we test this argument empirically by contrasting people's beliefs about everyday statistics with their corresponding environmental frequencies. By adopting a novel elicitation technique, random generation as belief elicitation (León-Villagra et al., 2022), we gain access to people's belief distributions for a set of eight domains with different distributional properties. Participants (N=120) produced random draws from everyday quantities (e.g., cake baking times, movie lengths, life expectancies), uttering each item aloud. We transcribed the sequences of utterances, obtaining a trace of "random" draws. Then, we compared the distributions resulting from these draws and the entropy of these distributions to the corresponding environmental distributions and their entropy. We found a significant effect of the domain on the participants' belief entropy, with six out of eight domains resulting in participants exhibiting higher entropy than the environmental data. Our results provide initial evidence for Feldman's theoretical argument for agents' learning beliefs that are more entropic than their encountered environmental frequencies.