Do humans make good decisions?Christopher Summerfield and Konstantinos Tsetsos

Department of Experimental Psychology, University of Oxford, South Parks Road, OX1 3UD, Oxford, UK

Opinion

Human performance on perceptual classification tasksapproaches that of an ideal observer, but economicdecisions are often inconsistent and intransitive, withpreferences reversing according to the local context. Wediscuss the view that suboptimal choices may resultfrom the efficient coding of decision-relevant informa-tion, a strategy that allows expected inputs to be pro-cessed with higher gain than unexpected inputs.Efficient coding leads to ‘robust’ decisions that departfrom optimality but maximise the information transmit-ted by a limited-capacity system in a rapidly-changingworld. We review recent work showing that when per-ceptual environments are variable or volatile, perceptualdecisions exhibit the same suboptimal context-depen-dence as economic choices, and we propose a generalcomputational framework that accounts for findingsacross the two domains.

Good or bad decisions?Consider a footballer deciding whether to angle a penaltyshot into the left or right corner of the goal, a medicalpractitioner diagnosing a chest pain of mysterious origin,or a politician deliberating over whether or not to take thecountry to war. All of these decisions, however different inscope and seriousness, require information to be collected,evaluated, and combined before commitment is made to acourse of action. To date, however, the biological andcomputational mechanisms by which we make decisionshave been hard to pin down. One major stumbling block isthat it remains unclear whether human choices are opti-mised to account for prior beliefs and uncertainty in theenvironment, or whether humans are fundamentally bi-ased and irrational. In other words, do we make gooddecisions, or not?

Optimal perceptual integrationAlthough behavioural scientists continue to debate whatmight constitute a good decision (Box 1), optimal behaviouris usually limited only by the level of noise (or uncertainty)in the environment. Consider a doctor diagnosing a patientwho is experiencing vice-like chest pains. Optimal binarydecisions are determined by the likelihood ratio, that is,the relative probability of the evidence (chest pains) givenone hypothesis (incipient cardiac arrest) or another (gastricreflux). When decision-relevant information arises from

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� 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tics.2014.11.005

Corresponding author: Summerfield, C. (christopher.summerfield@psy.ox.ac.uk).Keywords: perceptual decision-making; neuroeconomics; optimality; informationintegration; gain control; efficient coding.

multiple sources, evidence must be combined to makethe best decision. For binary choices, decisions are opti-mised by sequential summation of log-likelihood ratio,expressing the relative likelihood that information wasdrawn from one category or the other [1,2]. An observerwho views a sequence of probabilistic cues (‘samples’)before making one of two responses (e.g., the shapes inFigure 1A) will make the best decision by considering allsamples equivalently, that is, in proportion to the evidencethey convey. In other words, the subjective weight of evi-dence (w.o.e.) for each sample will depend linearly on theweight assigned by the experimenter. Well-trained mon-keys and humans seem to weigh information optimally inthis way (Figure 1B) [3,4]. When some cues are moretrustworthy than others, the best decisions are made byadding up information weighted by its reliability. Again,observers seem to do just this – giving less credence tofeatures or modalities that the experimenter has corruptedwith noise, for example, when combining informationfrom across different senses [5–7]. Thus, the footballeralluded to in the opening sentence will most likely strikethe ball with great precision towards a spot that is justout of the goalkeeper’s reach – factoring in uncertaintydue to the weather conditions and his or her own bodilyfatigue.

Irrational economic decisionsBy contrast, humans choosing among economic alterna-tives are often unduly swayed by irrelevant contextualfactors, leading to inconsistent or intransitive decisionsthat fail to maximise potential reward [8]. For example,consumers will bid higher for a house whose initial pricetag has been deliberately inflated, as if their valuation is‘anchored’ by the range of possible market prices [9]. Simi-larly, human participants undervalued risky prospectswhen most offers consisted of low-value gambles but over-valued the same prospects when the majority of offersconsisted of high-value gambles [10]. Anchoring by anirrelevant, low-value third alternative can also disruptchoices between two higher-valued prospects, leading tosystematic reversals of preference [11]. For example, theprobability that a hungry participant will choose a pre-ferred snack item A over another item B (rather than viceversa) is often reduced in the presence of a yet more inferioroption C, in particular when C resembles B in value [12](Figure 1C).

Irrational economic behaviour can arise if the braincomputes and represents stimulus value relative to thecontext provided by other previously [13] or currentlyavailable options [14,15]. Changing the context of a deci-sion by adding other alternatives (even if they are rapidly

Trends in Cognitive Sciences, 2015, Vol. 19, No. 1 27

Box 1. What makes a good decision?

Behavioural scientists have often disagreed about what constitutes

a good decision. For example, in the absence of overt financial

incentives, experimental psychologists usually define good deci-

sions as those that elicit ‘correct’ feedback, given the predetermined

structure of their task. In experiments where stimuli are noisy or

outcomes are uncertain, a theoretical upper limit can be placed on

performance, by estimating how an ‘ideal’ agent would perform –

one who is most likely to be right, given the levels of uncertainty in

the stimulus. However, it is not always clear whether humans have

the same motives, or are imbued with the same preconceptions, as

an ideal observer [50]. For example, humans often make erroneous

assumptions about the nature of the task they are performing. For

example, in a decision-making task, if participants believe that the

values of prospects are changeable when really they are stationary,

then they will learn ‘superstitiously’ from recent outcomes

[51]. Moreover, although many human volunteers are strongly

motivated to maximise feedback, others might instead try to

minimise the time spent performing a boring or disagreeable task.

Behavioural economists argue that good decisions maximise

expected utility over the short or long term [52]. However, behavioural

ecologists emphasise that organisms need to maximise their fitness,

in order to survive and reproduce [53]. Often these definitions align,

but sometimes they diverge. For example, temporal discount

functions that overweigh short-term reward might deter an animal

from an investment strategy that maximises long-term income.

However, if current resources are insufficient to survive over the

near-term, steep temporal discounting may be the best insurance

against an untimely end [54]. The subjective nature of utility has led

theorists to define a series of axioms that are necessary (but not

sufficient) for optimal decisions [55]. These rational axioms guarantee

that an agent’s preferences – as revealed by overt choices – are

internally coherent and consistent with a stable, context-independent

utility function [56]. Because human behaviour is at systematic odds

with rational axioms [14,44], psychologists used non-normative

frameworks to describe human behaviour [49,57]. These approaches,

despite their descriptive adequacy, have failed to explain why choice

processes are irrational. By contrast, the efficient coding hypothesis

and analogous frameworks, which consider the computational costs

the brain faces while making decisions, promise to offer a normatively

motivated account of irrationalities in human choice.

Opinion Trends in Cognitive Sciences 2015, Vol. 19, No. 1

withdrawn, or so inferior as to be irrelevant) can alter theway that choice-relevant options A and B are valued,biasing the choice between them. For example, the patternof data described in Figure 1C can be explained by a simplecomputational model in which the value of each alternativeis normalised by the total value of all those available(Figure 1C). As the value of C grows, distributions repre-senting noisy value estimates of A and B exhibit moreoverlap, increasing the probability that the inferior optionB is mistakenly chosen over A (although in other circum-stances, increasing the value of C may lead B to be selectedless often, and rival models have been proposed to accountfor this alternative finding [16,17]). Indeed, single-cellrecordings from macaques making choices among juiceor food rewards suggest that neural encoding of value inthe parietal and orbitofrontal cortices is scaled by thecontext provided by the range of possible options[18]. When one measures the scaling factor (or ‘gain’) thatquantifies how subjective value (e.g., drops of juice) ismapped onto neuronal activity (e.g., spike rates) in thesebrain regions, it is found to vary according to the range ofvalues on offer. This ensures that average firing ratesremain in a roughly constant range across blocks or eventrials with variable offers [19–21].

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Efficient codingWhy might the brain have evolved to compute value on arelative, rather than an absolute scale? One compellinganswer to this question, first put forward by Horace Barlow[22] and known as the ‘efficient coding hypothesis’, appealsto the limited capacity of neuronal information processingsystems and their consequent need for efficiency [23,24]. Ef-ficient systems are those that minimise the level of redun-dancy in a neural code, for example, by transmitting asignal with a minimal number of spikes. Efficiency ofneural coding is maximised when sensitivity is greatestto those sensory inputs or features that are most diagnosticfor the decision at hand. In some situations, the mostdiagnostic features will be those that are most likely tooccur, given the statistics of the natural environment or thelocal context. For example, an efficient system will becomemost sensitive to high-valued stimuli when they are abun-dant and to low-valued stimuli during times of scarcity[12,18]. Formally, this strategy maximises the informationthat a neuronal system can encode and transmit, therebyoptimising processing demands to match the availableresources [25].

By contrast, encoding absolute input values is an ineffi-cient strategy. For example, if a hypothetical neuron was tolinearly signal the value of goods with widely disparateeconomic worth (for example, a cappuccino and a holiday inHawaii), then only a very limited portion of its dynamicfiring range could be devoted to any given value of thosealternatives. This would make it very hard for the neuronto signal consistently that the cappuccino was preferredover (say) a cup of tea. Normalisation of neural signals (forexample, via lateral inhibition) is one operation that per-mits efficient information coding in sensory systems[26]. For example, the sensitivity of cells in the early visualsystem is adjusted over the diurnal cycle, ensuring thatneurons with limited dynamic range can continue to en-code information even as the strength of ambient illumi-nation varies over many orders of magnitude [27]. Wheninput signals are transformed in this way, choices can varyas a function of context provided by recent stimulation,potentially leading to preference reversals and other devia-tions from optimal behaviour.

The efficient coding hypothesis thus implies that eco-nomic choices are irrational because they are overly sus-ceptible to variation in the local context. By the sametoken, it could be that perceptual classification judgmentstend towards optimal because psychophysical experimentsusually involve repeated choices made in a single, unvary-ing context. This prompts a prediction: that perceptualjudgments made in variable or volatile environments willdeviate from optimal in ways that resemble economicdecision-making.

Robust perceptual decision-makingIn the task described in Figure 2A, humans are asked tocategorise the average colour of eight elements (samples) as‘red’ versus ‘blue’ (or the average shape as ‘square’ versus‘circle’). This paradigm is similar to the ‘weather prediction’task shown in Figure 1A except that the samples arrive all atonce and their predictive value is conveyed by a continu-ously-varying visual feature (e.g., the degree of redness

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Figure 1. Optimal perceptual classification and irrational economic decisions. (A) Schematic depiction of the ‘weather prediction’ task used in [3]. On each trial, four shapes

appeared in succession. Each shape was associated with a given probability of reward (red/blue colour bar), conditioned on an eye movement to one of two targets (red and

blue dots). Reproduced, with permission, from [3]. In [4], a similar task was used but each shape was replaced on the screen by its successor. (B) Subjective weight of

evidence (w.o.e.) associated with each shape for a monkey [3] and the average of 24 humans [4]. Adapted and reproduced, with permission, from [3,4]. In both cases, dots

fall on a straight line, suggesting that each sample is weighed in proportion to its objective probability. (C) In [14], participants choose between a preferred snack (e.g.,

apple) and a dispreferred snack (e.g., orange); their (uncertain) value is represented by red and blue Gaussian distributions. Because neural value signals are normalised by

the total outcome associated with all stimuli, the introduction of a yet more inferior option (e.g., carrot; black Gaussian) brings the value estimates of the preferred and

dispreferred options closer together, increasing the probability that the dispreferred option (orange) will be chosen.

Opinion Trends in Cognitive Sciences 2015, Vol. 19, No. 1

versus blueness; we refer to this as the ‘feature value’). Anideal observer should thus add up equally weighted featurevalues (which are proportional to the log-likelihood ratios)and compare them to an internal category boundary (in thiscase, red versus blue or square versus circle), thereby usingthe same policy as the experimenter to decide which re-sponse is correct.

However, this is not what humans do [28,29]. The relativeweight associated with each feature value can be calculatedby using a logistic regression model to predict choices on thebasis of the feature values present in each array. Theresulting weights form an inverted u-shape over the spaceof possible features (Figure 2B), indicating that humansgive more credence to inlying samples – those that lie close tothe category boundary (e.g., purple) – than to outlyingsamples (e.g., extreme red or blue). Another way of visualis-ing this effect is by plotting these weights multiplied by theircorresponding feature values, thereby revealing the psycho-physical ‘transfer’ function that transduces inputs into re-sponse probabilities. For an ideal observer, this functionwould be linear. Empirically, however, it is sigmoidal

(Figure 2C). One way of understanding this behaviour isthat when feature information is variable or heterogeneous,humans integrate information in a ‘robust’ fashion, dis-counting outlying evidence, much as a statistician mightwish to eliminate aberrant data points from an analysis.Interestingly, the effect remains after extensive trainingwith fully informative feedback, and equivalent effects areobtained when observers average other features over mul-tiple elements, such as shape [28,29].

Efficient perceptual classificationFrom the viewpoint of the researcher, this robust averag-ing behaviour is suboptimal. However, because the distri-bution of features viewed over the course of the experimentis Gaussian, inlying features occur more frequently thanoutlying features. Thus, humans are exhibiting greatestsensitivity to those visual features that are most likely tooccur – an efficient coding strategy. The sigmoidal transferfunction ensures that for inlying features, a small changein feature information leads to a large change in theprobability of one response over another. Interestingly,

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Figure 2. Robust averaging of variable feature information. (A) In [28], participants judged the average colour (shown) or shape of an array of eight items, receiving

feedback after each response. (B) Decision weights (calculated via logistic regression) associated with item ranks (e.g., sorted by most red to most blue) have an inverted-u

profile, indicating that outlying elements (furthest from category boundary) carried less influence in decisions. (C) Decision weights associated with each portion of feature

space, multiplied by that feature value, reveal the subjective weight of evidence (w.o.e.). Note that the shape is different to that in Figure 1B. (D) Decision weights (similar to

B) for two experiments in which participants separately judged whether the array was more blue versus more purple (left curves: negative feature values) or more red

versus more purple (right curves: positive feature values). Features that are outlying with respect to the relevant category boundary are downweighted. Light and dark grey

lines show weights for items drawn for the two respective categories.

Opinion Trends in Cognitive Sciences 2015, Vol. 19, No. 1

this notion that inputs are transformed in this way sug-gests an explanation for classical ‘magnet’ effects thatcharacterise categorical perception, whereby observersare more sensitive to information that lies close to acategory boundary [30], and for natural biases in percep-tion, such as heightened sensitivity to contours falling closeto the cardinal axes of orientation [31]. Note that theseeffects arise because information is sampled or encoded ina biased fashion; it may still be read out via Bayesianprinciples [32].

Efficient coding is an appealing explanation for thedownweighting of outliers during perceptual averaging,but an alternative culprit could be nonlinearities in featurespace, such as hardwired boundaries in human perceptionof red and blue hues. One way to rule out this possibility isto systematically vary the range of features over whichjudgments are made, so that previously inlying elements(e.g., purple during blue/red discrimination) becoming out-lying elements (e.g., during blue/purple or red/purple dis-crimination). Under this manipulation, those features thatfall far from the category boundary are downweighted,irrespective of their physical properties (Figure 2D). Inother words, feature values are evaluated differentlyaccording to the range of information available, as pre-dicted by the efficient coding hypothesis. Computationally,this finding can be explained if the sigmoidal ‘transfer’function linking inputs to outputs migrates across feature

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space in such a way that its inflection point remainsaligned with the modal feature in the visual environment[28].

In the neuroeconomics literature, a key question per-tains to the timescale over which value signals are normal-ised [18,33]. Perceptual classification has typically beenmeasured in stationary environments, but when categorystatistics change rapidly over time, participants departfrom optimality and use instead a memory-based heuristicthat updates category estimates to their last known value,suggesting that rapid updating is at play [34]. However,can we measure the timescale over which adaptive gaincontrol occurs during perceptual decision-making?

Rapidly adapting gain control during decision-makingThe results of one recent study imply that the gain ofprocessing of decision information can adapt very rapidly– even within the timeframe of a single trial [35]. Partici-pants viewed a stream of eight tilted gratings occurring at4 Hz and were asked to judge whether, on average, theorientations fell closer to the cardinal (08 or 908) or diagonal(458 or �458) axes (Figure 3A). Firstly, this allowed theauthors to estimate the impact of each sample position onchoice – for example, to ask whether early samples (pri-macy bias) or late samples (recency bias) were weightedmost heavily [36]. Secondly, the authors calculated how theimpact of each sample varied according to whether it was

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Figure 3. Adaptive gain control during sequential integration. (A) Cardinal–diagonal categorisation task. Participants viewed a sequence of eight tilted gratings occurring

at 4 Hz. Each sample was associated with a decision update (DU) reflecting whether it was tilted at the cardinal axes (DU = �1) or diagonal axes (DU = +1) or in between

(�1 < DU < 1). Participants received positive feedback for correctly classifying the sum of DU as >0 or <0, i.e., for indicating whether the orientations were on average

closer to the cardinal or diagonal axes. In this task, DU is orthogonal to the perceptual input [58]. (B) Blue dots show decision weights (regression coefficients) for each of

the eight samples as a function of sequence position. Participants showed a recency bias. Green dots: modulation of decision weights for each sample by disparity to

previous sample. Dots are negative, indicating that unexpected samples were downweighted. Lines show fits of the adaptive gain model using two separate fitting

procedures. (C) Illustration of the adaptive gain model. Left panel: grey curves show the theoretical transfer function from feature values to the probability of responding

‘diagonal’. As successive samples are presented (light to dark blue dots) drawn from a category distribution (blue Gaussian), the function mapping inputs onto outputs

adjusts towards the mode of the generative distribution. Right panel: two possible positions of the transfer function. Initially, the transfer function is misaligned with the

generative distribution, so that P (diagonal) only changes slightly with two nearby samples (light grey). Later, when the transfer function is aligned with the generative

distribution, a small change in feature value has a large impact on response (dark grey). The gradual alignment of the transfer function with the true distribution also

explains the recency bias displayed by humans (B).

Opinion Trends in Cognitive Sciences 2015, Vol. 19, No. 1

consistent or inconsistent with the average decision infor-mation viewed thus far. According to the efficient codinghypothesis, neural coding should adapt so that expectedinputs – that is, those consistent with the stream average –should carry more impact than inconsistent information.

Human observers exhibited a recency bias, but they alsodisplayed a tendency to weigh consistent samples moreheavily than inconsistent samples (consistency bias) whenchoosing their response (Figure 3B). Perceptual and deci-sion information are orthogonal in this task, so the latter isnot merely a perceptual priming effect. Both the recencyand the consistency bias were explained by a computation-al model in which the sigmoidal transfer function wasgradually adjusted towards the modal feature informationoccurring on that trial – that is, towards ‘cardinal’ whensamples were closer on average to cardinal, and towards‘diagonal’ when evidence favoured diagonal. This had theeffect of bringing the linear portion of the transfer function– where sensitivity is greatest – in line with the mode ofdistribution of samples experienced thus far (Figure 3C).In other words, observers processed information that wasmost likely to occur (conditioned on the sequence of sam-ples in that trial) with higher gain, in keeping with theefficient coding hypothesis. Interestingly, this model alsopredicts that when evidence arrives in sequence, the con-sistency bias replaces an overall downweighting of outliers.This may help explain why previous studies have shownroughly linear decision weights (Figure 1B). A bias towards

consistency in perceptual classification was also demon-strated in a recent study that asked participants to makesuccessive judgments about visual angle [37]. This workbuilds upon earlier demonstrations that the second of twosuccessive judgments about a visual feature is biased bythe first, in a fashion that indicates the most sensitiveencoding of the most informative feature information[38–40].

The heightened gain for consistent (relative to inconsis-tent) information was also reflected in measures of physi-ological and neural activity. Pupil diameter, thought to bea crude proxy for the gain of cortical processing [41],covaried with the available decision information moresharply when samples were consistent than when theywere inconsistent. Similar effects were observed forelectroencephalography (EEG) activity recorded from elec-trodes situated over central and parietal zones, and blood-oxygen-level dependent (BOLD) signals localised to theparietal cortex, dorsomedial prefrontal cortex, and anteriorinsula [35]. A population coding model in which tuningsharpens to expected features provides a more detailedframework for understanding these effects (Box 2).

Priming by varianceAnother recent study provides evidence that perceptualdecisions are influenced by the context furnished by localenvironmental statistics [42]. Observers judged the aver-age feature (colour or shape) in a ring of coloured shapes

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Box 2. Expectation as sharpening

The efficient coding hypothesis states that we become most sensitive

to those features that are most likely to occur in the environment. One

implication of this view is that the receptive fields of neurons tuned to

expected inputs become sharper – better enabling observers to detect

or discriminate these features. The data described in Figure 3B can

also be accounted for with a population coding model in which

incoming feature information excites sensory neurons with bell-

shaped tuning curves (Figure I). These in turn drive ‘integration’

neurons whose activity level depends on their accumulated inputs

[59]. The state of the integration neurons drives the level of local

inhibition, leading to a sharpening of tuning curves at sensory

neurons coding for expected features (see below). For a more detailed

explanation, see [35].

An established theory – known as the feature-similarity gain

hypothesis – states that the gain of neuronal responses depends on

the degree of similarity between an observed feature and an internal

standard to which it is being compared [60]. However, in psychophy-

sical detection tasks, base rates of occurrence of a target feature (e.g.,

a vertical grating) are typically found to bias responses in an additive

fashion rather than increasing sensitivity measured by d’ [61]. Never-

theless, recent evidence using psychophysical reverse correlation has

revealed that observers show heightened sensitivity to expected

features [62]. Moreover, a recent fMRI study has found that although

expected gratings elicit globally reduced BOLD signals, their angle of

orientation can be more accurately decoded from multivoxel patterns

in visual cortex [63].

TRENDS in Cognitive Sciences

Cardinal Diagonal

Expecta�on ofnext sample?

Lateral inhibi�onKey:Forward excita�onBackward excita�on

Sensory neurons

Inhibitory neurons

Integra�on neurons

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Samples

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Figure I. Top panel. Consider a task in which continuously-valued feature information (e.g., tilt: cardinal vs. diagonal; x-axis) is drawn successively from one of two

categories (grey Gaussian distributions). The most likely feature of the forthcoming sample (blue arrow) can be inferred from the history of samples drawn thus far (blue

dots). An efficient system will maximise sensitivity to expected information. Lower panel. Population coding model for expectation as sharpening. The model consists

of input neurons (blue circles) and integration neurons (green circles). The input neurons are inhibited by local interneurons (grey circles). Sensory information (e.g., the

tilt of a grating) is fed forward from input neurons to integration neurons, where it is linearly accumulated. The integration neurons excite the interneurons in proportion

to the current level of integrated evidence. This ensures that the tuning curves of neurons for expected features become sharper.

Opinion Trends in Cognitive Sciences 2015, Vol. 19, No. 1

similar to that shown in Figure 2A, with feature values (e.g.,red versus blue hues) drawn from Gaussian distributionswith differing dispersion. When each target array was im-mediately preceded by a task-irrelevant ‘prime’ array whosefeature variance was also high or low, performancedepended not only on the consistency between the meanfeature information (e.g., were the prime and target onaverage both red?) but also on their variability (e.g., werethe prime and target arrays both highly variable?), withfaster response times for prime–target pairs with consistentlevels of feature variability. This result held even if theprime and target array were drawn from different categories(e.g., red versus blue). One explanation for this curiousfinding is that the space over which inferences about thetarget array are made is shaped by the range of featureinformation available in the prime array – with the slope of

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the sigmoidal transfer function adapting according to thedispersion of feature information in the prime array. Asimilar mechanism has been reported in the visual systemof the fly during adaptation to dynamic motion variability[43].

Value psychophysicsTaken together, these studies imply that unexpected oroutlying inputs are downweighted when observers judgefeature information with respect to a category boundary.However, seemingly contradictory results have beenobtained from a different averaging experiment, in whichobservers view two streams of numbers and are asked topick the stream with the higher tally [44]. When thenumbers were drawn from two streams with differingvariance, observers exhibited a strong bias to choose the

Opinion Trends in Cognitive Sciences 2015, Vol. 19, No. 1

more variable of the two streams – as if they were givingmore credence to outlying samples (e.g., the higher numberin the pair) during integration. So why do observers seemto overweigh inlying relative to outlying elements duringcategorisation, but do the reverse when comparing twostreams of information?

Recall that an efficient neural coding scheme maximisessensitivity to those features that are most informative forthe decision. When the task is to compare two currently-available sources of information, it is the outlying ratherthan the inlying samples that are most diagnostic for choice[45], just as during fine discriminations, where the ‘off-channel’ features (e.g., exaggerated versions of the featuresin each category) carry most information [40,46]. This isparticularly the case in the number comparison experiment,where the absolute average of features fluctuates unpredict-ably from trial to trial and choices must rely on localcomparisons between the two streams. Thus, when compar-ing two streams, the one with the larger mean payoff willmore likely have a larger number on a given pair, and thelatter is highly diagnostic of the former. Interestingly, in thevalue comparison task, the direction of outlier overweight-ing was dependent on the instructions – when observerswere asked which stream they preferred, high values wereoverweighted; when they were asked to choose which streamthey dispreferred, low values were more impactful – eventhough these two framings are logically equivalent. Thisfinding is reminiscent of classic violations of descriptioninvariance in economic judgments tasks, and is consistentwith a qualitative theory known as reason-based decision-making [47], in which advantages loom larger when parti-cipants are asked which of two prospects they would like toaccept, whereas disadvantages drive decisions that areframed as a rejection. Thus, faced with the choice betweenan extravagant holiday (say, to Bali) and a more modest trip(to Bournemouth), people choose to accept Bali (because it isexciting) but will reject Bali (because it is expensive) inalternate framings of the choice [48].

Robust decisions and heuristicsDiscarding outliers in categorisation tasks and overweight-ing winners in comparison tasks are thus both examples of‘robust’ decision-making – involving coding strategies thatfocus processing resources on the most informative features.Interestingly, extreme versions of these policies both reduceto ‘counting’ strategies – for example, an observer mighttally up the number of ‘winners’ in the stream of pairednumbers, or count the number of samples that favour redversus blue. Strategies such as counting that involve reli-ance on propositional rules or approximations, rather thanstatistical inference, are often proposed as alternatives tooptimal behaviour [49]. As such, efficient coding provides aspace of decision policies that lie on a continuum betweenheuristic choices and full statistical optimality.

Concluding remarksIn the end, is the quality of human decision-making good,bad, or indifferent? There is no doubt that in some situa-tions, humans deviate strongly from statistical optimalityin their judgments, and exhibit inconsistent or irrationalpreferences. However, we argue that human choices can be

understood if information is encoded efficiently, with maxi-mal sensitivity to decision-relevant evidence that is likely tooccur. Classic economic biases, including framing and an-choring effects, as well as the range-dependence of neuralvalue encoding, are explained by a model in which the gain ofneural processing adapts to the local environmental context.When sensory input is rendered variable, volatile, or other-wise heterogenous, perceptual classification judgmentscome to exhibit a similar sub-optimal context-dependence,consistent with the notion that efficient coding of informa-tion is a general-purpose constraint on human decision-making. Conversely, optimal behaviour may emerge whenrepeated decisions are made in stationary environments,such as when psychophysical observers repeatedly attemptto detect a visual stimulus embedded in noise. In terms ofthe computational framework outlined above, during thesejudgments the transfer function becomes aligned so that allfeatures fall in the linear portion of the sigmoid, whereinputs are transduced without loss and decisions are opti-mal. Efficient coding is likely to have evolved as the beststrategy in a rapidly-changing, unpredictable world inwhich optimal inference over all possible eventualities iscomputationally intractable.

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