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Searching for the Approximation Method used to Perform rationaL inference by INdividuals and Groups

Periodic Reporting for period 2 - SAMPLING (Searching for the Approximation Method used to Perform rationaL inference by INdividuals and Groups)

Reporting period: 2020-10-01 to 2022-03-31

Over the past two decades, Bayesian models have been used to explain behaviour in domains from intuitive physics and causal learning, to perception, motor control and language. Yet people produce clearly incorrect answers in response to even the simplest questions about probabilities. How can a supposedly Bayesian brain paradoxically reason so poorly with probabilities? Perhaps brains do not represent or calculate probabilities at all and are, indeed, poorly adapted to do so. Instead, they could be approximating Bayesian inference through sampling: drawing samples from a distribution of likely hypotheses over time.

This promising approach has been used in existing work to explain biases in judgment. However, different algorithms have been used to explain different biases, and the existing data does not distinguish between sampling algorithms. The first aim of this project is to identify which sampling algorithm is used by the brain by collecting behavioural data on the sample generation process, and comparing it to a variety of sampling algorithms from computer science and statistics. The second aim is to show how the identified sampling algorithm can systematically generate classic probabilistic reasoning errors in individuals, with the goal of upending the longstanding consensus on these effects. Finally, the third aim is to investigate how the identified sampling algorithm provides a new perspective on group decision making biases and errors in financial decision making, and harness the algorithm to produce novel and effective ways for human and artificial experts to collaborate.
Since the beginning of the project, we have made substantial progress. For the first aim, our work to identify the sampling algorithm has highlighted how the algorithm used by the brain likely has multiple chains and momentum. For the second aim, we have worked on the theoretical framework underlying the project and have explored how sampling can explain individual probabilistic reasoning errors. We have developed a model, the Bayesian sampler, of how people might make estimates from samples, trading off the coherence of probabilistic judgments for improved accuracy, and provides a single framework for explaining phenomena associated with diverse biases and heuristics such as conservatism and the conjunction fallacy. Other successes include showing how a particular form of sampling can explain how non-informative information can bias judgments, known as the dilution effect, and how sampling and representation can interact when categorizing objects. For the third aim, we have work in progress showing that price prediction time series produced by both people and a sampling algorithm match the dynamics of actual market prices.
The Bayesian sampler turns out to provide a rational reinterpretation of “noise” in a state-of-the-art model of probability judgment, making equivalent average predictions for simple events, conjunctions, and disjunctions. The Bayesian sampler does, however, make distinct predictions for conditional probabilities, and we have shown in new experiments that this model better captures these judgments both qualitatively and quantitatively, going beyond the state of the art. This paper, the dilution effect paper, and the categorisation paper were published in top journals in psychology. We are extending this model to make it a unifying framework for explaining a wide range of human estimates, decisions, response times, and confidence judgments. This extended model will also be able to incorporate our advances, using cognitive time series experiments, in understanding which algorithm best describes human mental sampling both individually and in groups.
Sampling from a complex S-shaped distribution