The formation of preference in risky choice

A key question in decision-making is how people integrate amounts and probabilities to form preferences between risky alternatives. Here we rely on the general principle of integration-to-boundary to develop several biologically plausible process models of risky-choice, which account for both choices and response-times. These models allowed us to contrast two influential competing theories: i) within-alternative evaluations, based on multiplicative interaction between amounts and probabilities, ii) within-attribute comparisons across alternatives. To constrain the preference formation process, we monitored eye-fixations during decisions between pairs of simple lotteries, designed to systematically span the decision-space. The behavioral results indicate that the participants' eye-scanning patterns were associated with risk-preferences and expected-value maximization. Crucially, model comparisons showed that within-alternative process models decisively outperformed within-attribute ones, in accounting for choices and response-times. These findings elucidate the psychological processes underlying preference formation when making risky-choices, and suggest that compensatory, within-alternative integration is an adaptive mechanism employed in human decision-making.

[1]  Neil Stewart EPS Prize Lecture: Decision by sampling: The role of the decision environment in risky choice , 2009, Quarterly journal of experimental psychology.

[2]  Alexandre Pouget,et al.  Optimal policy for value-based decision-making , 2016, Nature Communications.

[3]  M. Birnbaum,et al.  New Paradoxes of Risky Decision Making , 2022 .

[4]  Marius Usher,et al.  Attentional Selection Mediates Framing and Risk-Bias Effects , 2018, Psychological science.

[5]  R. Luce,et al.  Individual Choice Behavior: A Theoretical Analysis. , 1960 .

[6]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[7]  A. Glöckner,et al.  What is adaptive about adaptive decision making? A parallel constraint satisfaction account , 2014, Cognition.

[8]  Brandon M. Turner,et al.  Some task demands induce collapsing bounds: Evidence from a behavioral analysis , 2018, Psychonomic Bulletin & Review.

[9]  P. Glimcher,et al.  Neuroeconomics: The Consilience of Brain and Decision , 2004, Science.

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

[11]  Gordon D. A. Brown,et al.  Decision by sampling , 2006, Cognitive Psychology.

[12]  Sheryl B. Ball,et al.  It’s not what you see but how you see it: Using eye-tracking to study the risky decision-making process. , 2016 .

[13]  Andreas Glöckner,et al.  Cognitive models of risky choice: Parameter stability and predictive accuracy of prospect theory , 2012, Cognition.

[14]  D. Kumaran,et al.  The Neurobiology of Reference-Dependent Value Computation , 2009, NeuroImage.

[15]  R. Poldrack,et al.  Prospect Theory and the Brain , 2009 .

[16]  A. Tversky Intransitivity of preferences. , 1969 .

[17]  S. S. Stevens On the psychophysical law. , 1957, Psychological review.

[18]  J. Rieskamp The probabilistic nature of preferential choice. , 2008, Journal of experimental psychology. Learning, memory, and cognition.

[19]  Pietro Perona,et al.  The Attentional Drift Diffusion Model of Simple Perceptual Decision-Making , 2017, Front. Neurosci..

[20]  A. Glöckner,et al.  Multiple-reason decision making based on automatic processing. , 2008, Journal of experimental psychology. Learning, memory, and cognition.

[21]  Andreas Glöckner,et al.  Decisions beyond boundaries: when more information is processed faster than less. , 2012, Acta psychologica.

[22]  M. Usher,et al.  Fast and effective: Intuitive processes in complex decisions , 2018, Psychonomic Bulletin & Review.

[23]  John W. Payne,et al.  Task complexity and contingent processing in decision making: An information search and protocol analysis☆ , 1976 .

[24]  Marius Usher,et al.  Disentangling decision models: from independence to competition. , 2013, Psychological review.

[25]  Christof Koch,et al.  The Drift Diffusion Model Can Account for the Accuracy and Reaction Time of Value-Based Choices Under High and Low Time Pressure , 2010, Judgment and Decision Making.

[26]  Wim Fias,et al.  Interacting neighbors: A connectionist model of retrieval in single-digit multiplication , 2005, Memory & cognition.

[27]  A. Rangel,et al.  Multialternative drift-diffusion model predicts the relationship between visual fixations and choice in value-based decisions , 2011, Proceedings of the National Academy of Sciences.

[28]  B. Dosher,et al.  Strategies for multiattribute binary choice. , 1983, Journal of experimental psychology. Learning, memory, and cognition.

[29]  D H Brainard,et al.  The Psychophysics Toolbox. , 1997, Spatial vision.

[30]  Joseph W. Kable,et al.  Preference Reversals in Decision Making Under Risk are Accompanied by Changes in Attention to Different Attributes , 2012, Front. Neurosci..

[31]  I. Krajbich,et al.  Attention and Choice Across Domains , 2018, Journal of experimental psychology. General.

[32]  S. Shimojo,et al.  Gaze bias both reflects and influences preference , 2003, Nature Neuroscience.

[33]  James L. McClelland,et al.  Loss aversion and inhibition in dynamical models of multialternative choice. , 2004, Psychological review.

[34]  Roger Ratcliff,et al.  The Diffusion Decision Model: Theory and Data for Two-Choice Decision Tasks , 2008, Neural Computation.

[35]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[36]  Nick Chater,et al.  Economic irrationality is optimal during noisy decision making , 2016, Proceedings of the National Academy of Sciences.

[37]  F. Hermens,et al.  Eye Movements in Risky Choice , 2015, Journal of behavioral decision making.

[38]  Peter N. C. Mohr,et al.  Gaze bias differences capture individual choice behaviour , 2019, Nature Human Behaviour.

[39]  Gerd Gigerenzer,et al.  Risky choice with heuristics: reply to Birnbaum (2008), Johnson, Schulte-Mecklenbeck, and Willemsen (2008), and Rieger and Wang (2008). , 2008, Psychological review.

[40]  Joseph G. Johnson,et al.  A computational model of the attention process in risky choice. , 2016 .

[41]  R. Hertwig,et al.  The priority heuristic: making choices without trade-offs. , 2006, Psychological review.

[42]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[43]  Andreas Glöckner,et al.  An eye‐tracking study on information processing in risky decisions: Evidence for compensatory strategies based on automatic processes , 2011 .

[44]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[45]  Mark C. W. van Rossum,et al.  Accurate multiplication with noisy spiking neurons , 2011, Journal of neural engineering.

[46]  Jacob L. Orquin,et al.  Attention and choice: a review on eye movements in decision making. , 2013, Acta psychologica.

[47]  Richard Gonzalez,et al.  On the Shape of the Probability Weighting Function , 1999, Cognitive Psychology.

[48]  Postscript: Rejoinder to Brandstatter, Gigerenzer, and Hertwig (2006) , 2008 .

[49]  M. Woolrich,et al.  Mechanisms underlying cortical activity during value-guided choice , 2011, Nature Neuroscience.

[50]  Scott D. Brown,et al.  Revisiting the Evidence for Collapsing Boundaries and Urgency Signals in Perceptual Decision-Making , 2015, The Journal of Neuroscience.

[51]  Geoffrey Fisher An attentional drift diffusion model over binary-attribute choice , 2017, Cognition.

[52]  James L. McClelland,et al.  The time course of perceptual choice: the leaky, competing accumulator model. , 2001, Psychological review.

[53]  J. Townsend,et al.  Decision field theory: a dynamic-cognitive approach to decision making in an uncertain environment. , 1993, Psychological review.

[54]  James L. McClelland,et al.  Distributed memory and the representation of general and specific information. , 1985, Journal of experimental psychology. General.

[55]  W. Thorngate Efficient decision heuristics. , 1980 .

[56]  Ariel Rubinstein,et al.  Tracking Decision Makers under Uncertainty , 2011 .

[57]  R. Hertwig,et al.  Prospect Theory Reflects Selective Allocation of Attention , 2018, Journal of experimental psychology. General.

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

[59]  Scott D. Brown,et al.  Diffusion Decision Model: Current Issues and History , 2016, Trends in Cognitive Sciences.

[60]  Eric J. Johnson,et al.  Adaptive Strategy Selection in Decision Making. , 1988 .

[61]  D. Ariely,et al.  In Search of Homo Economicus: Cognitive Noise and the Role of Emotion in Preference Consistency , 2009 .

[62]  Andreas Glöckner,et al.  The Dynamics of Decision Making in Risky Choice: An Eye-Tracking Analysis , 2012, Front. Psychology.

[63]  Nick Chater,et al.  Salience driven value integration explains decision biases and preference reversal , 2012, Proceedings of the National Academy of Sciences.

[64]  Ian Krajbich,et al.  Visual fixations and the computation and comparison of value in simple choice , 2010, Nature Neuroscience.

[65]  Brian P. Dyre,et al.  Bias in proportion judgments: the cyclical power model. , 2000, Psychological review.

[66]  Neil Stewart,et al.  A decision-by-sampling account of decision under risk , 2008 .

[67]  M. Usher,et al.  Integration to boundary in decisions between numerical sequences , 2019, Cognition.

[68]  Colin Camerer,et al.  The Attentional Drift-Diffusion Model Extends to Simple Purchasing Decisions , 2012, Front. Psychology.

[69]  C. H. Coombs,et al.  Mathematical psychology : an elementary introduction , 1970 .

[70]  E. Spelke,et al.  Language and Conceptual Development series Core systems of number , 2004 .

[71]  Eric J. Johnson,et al.  Search predicts and changes patience in intertemporal choice , 2017, Proceedings of the National Academy of Sciences.

[72]  C. Koch,et al.  Simultaneous modeling of visual saliency and value computation improves predictions of economic choice , 2013, Proceedings of the National Academy of Sciences.

[73]  Timothy L. Mullett,et al.  Implications of Visual Attention Phenomena for Models of Preferential Choice , 2016, Decision.

[74]  Jerome R. Busemeyer,et al.  Psychological models of deferred decision making , 1988 .

[75]  Patryk A. Laurent,et al.  Value-driven attentional capture , 2011, Proceedings of the National Academy of Sciences.

[76]  D. McFadden Econometric Models of Probabilistic Choice , 1981 .

[77]  C. Koch,et al.  Relative visual saliency differences induce sizable bias in consumer choice , 2012 .

[78]  E. Brandstätter,et al.  Attention in risky choice. , 2014, Acta psychologica.

[79]  K.-Y. Choi,et al.  Spin–orbit coupled molecular quantum magnetism realized in inorganic solid , 2016, Nature Communications.