Counterfactual Reasoning Underlies the Learning of Priors in Decision Making

Summary Accurate decisions require knowledge of prior probabilities (e.g., prevalence or base rate), but it is unclear how prior probabilities are learned in the absence of a teacher. We hypothesized that humans could learn base rates from experience making decisions, even without feedback. Participants made difficult decisions about the direction of dynamic random dot motion. Across blocks of 15–42 trials, the base rate favoring left or right varied. Participants were not informed of the base rate or choice accuracy, yet they gradually biased their choices and thereby increased accuracy and confidence in their decisions. They achieved this by updating knowledge of base rate after each decision, using a counterfactual representation of confidence that simulates a neutral prior. The strategy is consistent with Bayesian updating of belief and suggests that humans represent both true confidence, which incorporates the evolving belief of the prior, and counterfactual confidence, which discounts the prior.

[1]  Joseph W Kable,et al.  Normative evidence accumulation in unpredictable environments , 2015, eLife.

[2]  D. Kahneman Thinking, Fast and Slow , 2011 .

[3]  J. Gold,et al.  Visual Decision-Making in an Uncertain and Dynamic World. , 2017, Annual review of vision science.

[4]  Ariel Zylberberg,et al.  The construction of confidence in a perceptual decision , 2012, Front. Integr. Neurosci..

[5]  A. Pouget,et al.  The Cost of Accumulating Evidence in Perceptual Decision Making , 2012, The Journal of Neuroscience.

[6]  W. Edwards,et al.  Conservatism in a simple probability inference task. , 1966, Journal of experimental psychology.

[7]  D. Wolpert,et al.  Piercing of Consciousness as a Threshold-Crossing Operation , 2017, Current Biology.

[8]  Rajesh P. N. Rao,et al.  How Prior Probability Influences Decision Making: A Unifying Probabilistic Model , 2012, NIPS.

[9]  Robert C. Wilson,et al.  An Approximately Bayesian Delta-Rule Model Explains the Dynamics of Belief Updating in a Changing Environment , 2010, The Journal of Neuroscience.

[10]  Nancy E. Avis,et al.  Base rates can affect individual predictions. , 1980 .

[11]  P. Latham,et al.  References and Notes Supporting Online Material Materials and Methods Figs. S1 to S11 References Movie S1 Optimally Interacting Minds R�ports , 2022 .

[12]  Michael N. Shadlen,et al.  Probabilistic reasoning by neurons , 2007, Nature.

[13]  Lewis R. Goldberg,et al.  Man versus model of man: A rationale, plus some evidence, for a method of improving on clinical inferences. , 1970 .

[14]  Timothy D. Hanks,et al.  Bounded Integration in Parietal Cortex Underlies Decisions Even When Viewing Duration Is Dictated by the Environment , 2008, The Journal of Neuroscience.

[15]  W. Ma Organizing probabilistic models of perception , 2012, Trends in Cognitive Sciences.

[16]  M. Sigman,et al.  The human Turing machine: a neural framework for mental programs , 2011, Trends in Cognitive Sciences.

[17]  Elyse H. Norton,et al.  Suboptimal Criterion Learning in Static and Dynamic Environments , 2017, PLoS Comput. Biol..

[18]  L. Beach,et al.  Man as an Intuitive Statistician , 2022 .

[19]  William K. Estes,et al.  Research and Theory on the Learning of Probabilities , 1972 .

[20]  Wei Ji Ma,et al.  Bayesian inference with probabilistic population codes , 2006, Nature Neuroscience.

[21]  Jeannette A. M. Lorteije,et al.  The Formation of Hierarchical Decisions in the Visual Cortex , 2015, Neuron.

[22]  M. Shadlen,et al.  Response of Neurons in the Lateral Intraparietal Area during a Combined Visual Discrimination Reaction Time Task , 2002, The Journal of Neuroscience.

[23]  J. Gold,et al.  Neural computations that underlie decisions about sensory stimuli , 2001, Trends in Cognitive Sciences.

[24]  Daniel M. Wolpert,et al.  Confidence Is the Bridge between Multi-stage Decisions , 2016, Current Biology.

[25]  Timothy E. J. Behrens,et al.  Perceptual Classification in a Rapidly Changing Environment , 2011, Neuron.

[26]  R. Ratcliff,et al.  Bias in the Brain: A Diffusion Model Analysis of Prior Probability and Potential Payoff , 2012, The Journal of Neuroscience.

[27]  Michael N. Shadlen,et al.  The Speed and Accuracy of a Simple Perceptual Decision: A Mathematical Primer. , 2007 .

[28]  M. Shadlen,et al.  Representation of Confidence Associated with a Decision by Neurons in the Parietal Cortex , 2009, Science.

[29]  J. Gold,et al.  Coupled Decision Processes Update and Maintain Saccadic Priors in a Dynamic Environment , 2017, The Journal of Neuroscience.

[30]  Amnon Rapoport,et al.  Sequential decision-making in a computer-controlled task , 1964 .

[31]  Tobias H. Donner,et al.  Adaptive History Biases Result from Confidence-Weighted Accumulation of past Choices , 2017, The Journal of Neuroscience.

[32]  R H S Carpenter,et al.  Changes in expectation consequent on experience, modeled by a simple, forgetful neural circuit. , 2006, Journal of vision.

[33]  Pierre Simon Laplace Essai philosophique sur les probabilités , 1921 .

[34]  Timothy D. Hanks,et al.  Elapsed Decision Time Affects the Weighting of Prior Probability in a Perceptual Decision Task , 2011, The Journal of Neuroscience.

[35]  M. Shadlen,et al.  The effect of stimulus strength on the speed and accuracy of a perceptual decision. , 2005, Journal of vision.

[36]  Michael N. Shadlen,et al.  Counterfactual reasoning underlies the learning of priors in decision making , 2017 .

[37]  R. H. S. Carpenter,et al.  Neural computation of log likelihood in control of saccadic eye movements , 1995, Nature.

[38]  Braden A. Purcell,et al.  Hierarchical decision processes that operate over distinct timescales underlie choice and changes in strategy , 2016, Proceedings of the National Academy of Sciences.

[39]  Joseph T. McGuire,et al.  Functionally Dissociable Influences on Learning Rate in a Dynamic Environment , 2014, Neuron.

[40]  B. Love,et al.  Social Information Is Integrated into Value and Confidence Judgments According to Its Reliability , 2017, The Journal of Neuroscience.

[41]  J. Bernardo Reference Posterior Distributions for Bayesian Inference , 1979 .

[42]  M. Shadlen,et al.  A Neural Implementation of Wald’s Sequential Probability Ratio Test , 2015, Neuron.

[43]  Christopher R Fetsch,et al.  The influence of evidence volatility on choice, reaction time and confidence in a perceptual decision , 2016, eLife.

[44]  P. Sterzer,et al.  Mesolimbic confidence signals guide perceptual learning in the absence of external feedback , 2016, eLife.

[45]  D. Medin,et al.  Problem structure and the use of base-rate information from experience. , 1988, Journal of experimental psychology. General.

[46]  Seongmin A. Park,et al.  Integration of individual and social information for decision-making in groups of different sizes , 2017, PLoS biology.

[47]  James L. McClelland,et al.  Integration of Sensory and Reward Information during Perceptual Decision-Making in Lateral Intraparietal Cortex (LIP) of the Macaque Monkey , 2010, PloS one.

[48]  Luigi Acerbi,et al.  Practical Bayesian Optimization for Model Fitting with Bayesian Adaptive Direct Search , 2017, NIPS.

[49]  Florent Meyniel,et al.  The Sense of Confidence during Probabilistic Learning: A Normative Account , 2015, PLoS Comput. Biol..

[50]  M. Gluck,et al.  Probabilistic classification learning in amnesia. , 1994, Learning & memory.

[51]  Michael Zehetleitner,et al.  Visibility Is Not Equivalent to Confidence in a Low Contrast Orientation Discrimination Task , 2016, Front. Psychol..

[52]  Z. J. Ulehla,et al.  Optimality of perceptual decision criteria. , 1966, Journal of experimental psychology.

[53]  Timothy E. J. Behrens,et al.  Learning the value of information in an uncertain world , 2007, Nature Neuroscience.

[54]  Jonathan D. Cohen,et al.  Sequential effects: Superstition or rational behavior? , 2008, NIPS.