Extending a biologically inspired model of choice: multi-alternatives, nonlinearity, and value-based multidimensional choice

doi:10.1017/CBO9780511731525.009

6 - Extending a biologically inspired model of choice: multi-alternatives, nonlinearity, and value-based multidimensional choice

from Part I - Rational and optimal decision making

Published online by Cambridge University Press: 05 November 2011

Jiaxiang Zhang and

Edited by

Tony J. Prescott and

Anil K. Seth: Affiliation:
University of Sussex
Tony J. Prescott: Affiliation:
University of Sheffield
Joanna J. Bryson: Affiliation:
University of Bath

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Summary

The Leaky Competing Accumulator (LCA) is a biologically inspired model of choice. It describes the processes of leaky accumulation and competition observed in neuronal populations during choice tasks and it accounts for reaction time distributions observed in psychophysical experiments. This chapter discusses recent analyses and extensions of the LCA model. First, it reviews the dynamics and it examines the conditions that make the model achieve optimal performance. Second, it shows that nonlinearities of the type present in biological neurons improve performance when the number of choice-alternatives increases. Third, the model is extended to value-based choice, where it is shown that nonlinearities in the value function, explain risk-aversion in risky-choice and preference reversals in choice between alternatives characterised across multiple dimensions.

Introduction

Making choices on the basis of visual perceptions is an ubiquitous and central element of human and animal life, which has been studied extensively in experimental psychology. Within the last half century, mathematical models of choice reaction times have been proposed which assume that, during the choice process, noisy evidence supporting the alternatives is accumulated (Laming, 1968; Ratcliff, 1978; Stone, 1960; Vickers, 1970). Within the last decade, data from neurobiological experiments have shed further light on the neural bases of such choice. For example, it has been reported that while a monkey decides which of two stimuli is presented, certain neuronal populations gradually increase their firing rate, thereby accumulating evidence supporting the alternatives (Gold and Shadlen, 2002; Schall, 2001; Shadlen and Newsome, 2001). Recently, a series of neurocomputational models have offered an explanation of the neural mechanism underlying both, psychological measures like reaction times and neurophysiological data of choice. One such model, is the Leaky Competing Accumulator (LCA; Usher and McClelland, 2001), which is sufficiently simple to allow a detailed mathematical analysis. Furthermore, as we will discuss, this model can, for certain values of its parameters, approximate the same computations carried out by a series of mathematical models of choice (Busemeyer and Townsend, 1993; Ratcliff, 1978; Shadlen and Newsome, 2001; Vickers, 1970; Wang, 2002).

Type: Chapter
Information: Modelling Natural Action Selection , pp. 91 - 119

DOI: https://doi.org/10.1017/CBO9780511731525.009 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2011

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References

Barnard, G 1946 Sequential tests in industrial statisticsJ. Roy. Stat. Soc. Suppl 8 1CrossRef Google Scholar

Bernoulli, D 1738 Exposition of a new theory on the measurement of riskEkonometrica 22 23CrossRef Google Scholar

Bogacz, RBrown, EMoehlis, JHolmes, PCohen, J. D 2006 The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced choice tasksPsychol. Rev 113 700CrossRef Google Scholar PubMed

Bogacz, RGurney, K 2007 The basal ganglia and cortex implement optimal decision making between alternative actionsNeural Comput 19 442CrossRef Google Scholar PubMed

Bogacz, RUsher, MZhang, JMcClelland, J. L 2007 Extending a biologically inspired model of choice: multi-alternatives, nonlinearity and value-based multidimensional choicePhil. Trans. Roy. Soc. B 362 1655CrossRef Google Scholar PubMed

Britten, K. HShadlen, M. NNewsome, W. TMovshon, J. A 1993 Responses of neurons in macaque MT to stochastic motion signalsVis. Neurosci 10 1157CrossRef Google Scholar PubMed

Brown, EGao, JHolmes, P 2005 Simple networks that optimize decisionsInt. J. Bifurcat. Chaos 15 803CrossRef Google Scholar

Brown, EHolmes, P 2001 Modeling a simple choice task: stochastic dynamics of mutually inhibitory neural groupsStoch. Dynam 1 159CrossRef Google Scholar

Busemeyer, J. RTownsend, J. T 1993 Decision field theory: a dynamic-cognitive approach to decision making in uncertain environmentPsychol. Rev 100 432CrossRef Google Scholar PubMed

Busemeyer, J. RTownsend, J. TDiederich, ABarkan, R 2005 Contrast effects or loss aversion? Comment on Usher and McClelland (2004)Psychol. Rev 111 757Google Scholar

Cisek, P 2006 Cortical mechanisms of action selection: the affordance competition hypothesisPhil. Trans. Roy. Soc. B 362 1585CrossRef Google Scholar

Dehaene, S 2003 The neural basis of the Weber–Fechner law: a logarithmic mental number lineTrends Cog. Sci 7 145CrossRef Google Scholar PubMed

Dhar, RNowlis, S. MSherman, S. J 2000 Trying hard or hardly trying: an analysis of context effects in choiceJ. Con. Psych 9 189CrossRef Google Scholar

Dragalin, V. PTertakovsky, A. GVeeravalli, V. V 1999 Multihypothesis sequential probability ratio tests – part I: asymptotic optimalityIEEE Trans. I.T 45 2448Google Scholar

Glimcher, P. W 2004 Decisions, Uncertainty, and the Brain: The Science of NeuroeconomicsCambridge, MAMIT PressGoogle Scholar

Gold, J. IShadlen, M. N 2002 Banburismus and the brain: decoding the relationship between sensory stimuli, decisions, and rewardNeuron 36 299CrossRef Google Scholar PubMed

Hacking, I 1980 Strange expectationsPhil. Sci 47 562CrossRef Google Scholar

Hertwig, RBarron, GWeber, E. UErev, I 2004 Decisions from experience and the effect of rare events in risky choicePsych. Sci 15 534CrossRef Google Scholar PubMed

Houston, A. IMcNamara, JSteer, M 2006 Do we expect natural selection to produce rational behaviourPhil. Trans. Roy. Soc. B 362 1531CrossRef Google Scholar

Kahneman, D 2003 Maps of bounded rationality: psychology for behavioral economicsAm. Econ. Rev 93 1449CrossRef Google Scholar

Kahneman, DTversky, A 2000 Choices, Values and FramesCambridgeCambridge University PressGoogle Scholar

Kveraga, KBoucher, LHughes, H. C 2002 Saccades operate in violation of Hick's lawExp. Brain Res 146 307CrossRef Google Scholar PubMed

Laming, D. R. J 1968 Information Theory of Choice Reaction TimeNew YorkWileyGoogle Scholar

LeBoef, RShafir, E. B 2005 Decision-makingCambridge Handbook of Thinking and ReasoningHolyoak, K. JMorisson, R. GCambridgeCambridge University Press, pp. 243–66Google Scholar

Martin, R 2004 The St. Petersburg ParadoxThe Stanford Encyclopedia of PhilosophyZalta, EStanford, CAThe Metaphysics Research Labhttp://plato.stanford.edu/archives/fall2008/entries/paradox-stpetersburg/Google Scholar

Mazurek, M. ERoitman, J. DDitterich, JShadlen, M. N 2003 A role for neural integrators in perceptual decision makingCereb. Cortex 13 1257CrossRef Google Scholar PubMed

McMillen, THolmes, P 2006 The dynamics of choice among multiple alternativesJ. Math. Psych 50 30CrossRef Google Scholar

Neyman, JPearson, E. S 1933 On the problem of the most efficient tests of statistical hypothesesPhil. Trans. Roy. Soc. A 231 289CrossRef Google Scholar

Platt, M. LGlimcher, P. W 1999 Neural correlates of decision variables in parietal cortexNature 400 233CrossRef Google Scholar PubMed

Ratcliff, R 1978 A theory of memory retrievalPsychol. Rev 83 59CrossRef Google Scholar

Ratcliff, R 1988 Continuous versus discrete information processing: modeling accumulation of partial informationPsychol. Rev 95 238CrossRef Google Scholar PubMed

Roe, R. MBusemeyer, J. RTownsend, J. T 2001 Multialternative decision field theory: a dynamic connectionist model of decision makingPsychol. Rev 108 370CrossRef Google Scholar PubMed

Roitman, J. DShadlen, M. N 2002 Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time taskJ. Neurosci 22 9475CrossRef Google Scholar PubMed

Schall, J. D 2001 Neural basis of deciding, choosing and actingNat. Rev. Neurosci 2 33CrossRef Google Scholar PubMed

Seung, H. S 2003 Amplification, attenuation, and integrationThe Handbook of Brain Theory and Neural NetworksAdbib, M. ACambridge, MAMIT Press,94Google Scholar

Shadlen, M. NNewsome, W. T 1998 The variable discharge of cortical neurons: implications for connectivity, computation, and information codingJ. Neurosci 18 3870CrossRef Google Scholar PubMed

Shadlen, M. NNewsome, W. T 2001 Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkeyJ. Neurophysiol 86 1916CrossRef Google Scholar PubMed

Slovic, P 1995 The construction of preferenceAm. Psychol 50 364CrossRef Google Scholar

Snowden, R. JTreue, SAndersen, R. A 1992 The response of neurons in areas V1 and MT of the alert rhesus monkey to moving random dot patternsExp. Brain Res 88 389CrossRef Google Scholar PubMed

Stone, M 1960 Models for choice reaction timePsychometrika 25 251CrossRef Google Scholar

Sugrue, L. PCorrado, G. SNewsome, W. T 2004 Matching behavior and the representation of value in the parietal cortexScience 304 1782CrossRef Google Scholar PubMed

Sugrue, L. PCorrado, G. SNewsome, W. T 2005 Choosing the greater of two goods: neural currencies for valuation and decision makingNat. Rev. Neurosci 6 363CrossRef Google Scholar PubMed

Teichner, W. HKrebs, M. J 1974 Laws of visual choice reaction timePsychol. Rev 81 75CrossRef Google Scholar PubMed

Tversky, A 1972 Elimination by aspects: a theory of choicePsychol. Rev 79 281CrossRef Google Scholar

Tversky, AKahneman, D 1979 Prospect theory: an analysis of decision under riskEconometrica 47 263Google Scholar

Tversky, AKahneman, D 1991 Loss aversion in riskless choice: a reference-dependent modelQ. J. Economet 106 1039CrossRef Google Scholar

Tversky, ASimonson, I 1993 Context-dependent preferencesManage. Sci 39 1179CrossRef Google Scholar

Usher, MDavelaar, E. J 2002 Neuromodulation of decision and response selectionNeural Networks 15 635CrossRef Google Scholar PubMed

Usher, MMcClelland, J. L 2001 The time course of perceptual choice: the leaky, competing accumulator modelPsychol. Rev 108 550CrossRef Google Scholar PubMed

Usher, MMcClelland, J. L 2004 Loss aversion and inhibition in dynamical models of multialternative choicePsychol. Rev 111 759CrossRef Google Scholar PubMed

Usher, MNiebur, N 1996 Modeling the Temporal Dynamics of IT Neurons in Visual Search: A Mechanism for Top-Down Selective AttentionJ. Cog. Neurosci 8 311CrossRef Google Scholar PubMed

Vickers, D 1970 Evidence for an accumulator model of psychophysical discriminationErgonomics 13 37CrossRef Google Scholar PubMed

Vickers, D 1979 Decision Processes in PerceptionNew YorkAcademic PressGoogle Scholar

Wald, A 1947 Sequential AnalysisNew YorkWileyGoogle Scholar

Wang, X. J 2002 Probabilistic decision making by slow reverberation in cortical circuitsNeuron 36 955CrossRef Google Scholar PubMed

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6 - Extending a biologically inspired model of choice: multi-alternatives, nonlinearity, and value-based multidimensional choice

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