Heuristics as Bayesian inference under extreme priors

Abstract

Simple heuristics are often regarded as tractable decision strategies because they ignore a great deal of information in the input data. One puzzle is why heuristics can outperform full-information models, such as linear regression, which make full use of the available information. These "less-is-more'' effects, in which a relatively simpler model outperforms a more complex model, are prevalent throughout cognitive science, and are frequently argued to demonstrate an inherent advantage of simplifying computation or ignoring information. In contrast, we show at the computational level (where algorithmic restrictions are set aside) that it is never optimal to discard information. Through a formal Bayesian analysis, we prove that popular heuristics, such as tallying and Take-the Best, are formally equivalent to Bayesian inference under the limit of infinitely strong priors. Varying the strength of the prior yields a continuum of Bayesian models with the heuristics at one end and ordinary regression at the other. Critically, intermediate models perform better across all our simulations, suggesting that down-weighting information with the appropriate prior is preferable to entirely ignoring it. Rather than because of their simplicity, our analyses suggest heuristics perform well because they implement strong priors that approximate the actual structure of the environment. We end by considering how new heuristics could be derived by infinitely strengthening the priors of other Bayesian models. These formal results have implications for work in psychology, machine learning and economics.

Active learning reveals underlying decision strategies

“…The dissociation between people's active learning strategies and their choice strategies at test (Table 1) suggests that people may be more sensitive to differential weighting of information than is evident from the more common procedure of passive model fitting to participants' binary choices. This finding is in line with the possibility that heuristics may provide a good general characterization of data but that other accounts that are sensitive to additional information sources may perform even better (Parpart, Jones, & Love, 2017). Here, active learning provided a novel means to reveal the nuances of how people make decisions.…”

Rational arbitration between statistics and rules in human sequence processing

“…We also tried to rescue the normative single-system model that monitors transition probabilities of different orders using a prior distribution biased towards extreme values of 0 or 1 specifically for higher-order transition probabilities ( H’ rule ) 47 , so as to capture the fact that deterministic rules afford more certain predictions than statistical biases. However, this version further aggravated the problem of excessive false alarms even for very weak biases of prior distributions (see Supplementary Note 2 ) and it could not mimic the observed abrupt detection of deterministic rules.…”

Fast or frugal, but not both: Decision heuristics under time pressure.

“…The set of candidate solution procedures could extend beyond heuristic procedures to include gist representations ( Peters et al, 2009 ; Reyna, 2008 ) and parallel constraint satisfaction approaches ( Glöckner & Betsch, 2008 ). Alternatively, there is also recent work suggesting that heuristics can be viewed as a special case of Bayesian inference ( Parpart, Jones & Love , under revision).…”

“…When compared with algorithms that are more computationally intensive such as linear regression, TAL and TTB have various algorithmic aspects in common. Their most salient similarity is that they both disregard covariance structure among cues ( Parpart, Jones & Love , under revision). Both heuristics also disregard relative cue weight magnitudes.…”