The subtleties of error management

Evolution and Human Behavior 31 (2010) 309–319

Short Communication

The subtleties of error managementRyan McKaya,b,c,⁎, Charles Effersona,b

aInstitute for Empirical Research in Economics, University of ZürichbLaboratory for Social and Neural Systems, University of Zürich

cCentre for Anthropology and Mind, University of Oxford

Initial receipt 14 October 2009; final revision received 24 April 2010

Abstract

Error management theory is a theory of considerable scope and emerging influence. The theory claims that cognitive biases do notnecessarily reflect flaws in evolutionary design, but that they may be best conceived as design features. Unfortunately, existing accounts arevague with respect to the key concept of bias. The result is that it is unclear that the cognitive biases that the theory seeks to defend are notsimply a form of behavioral bias, in which case the theory reduces to a version of expected utility theory. We propose some clarifications andrefinements of error management theory by emphasizing important distinctions between different forms of behavioral and cognitive bias. Wealso highlight a key assumption, that the capacity for Bayesian beliefs is subject to constraints. This assumption is necessary for what we seeas error management theory's genuinely novel claim: that behavioral tendencies to avoid costly errors can rest on systematic departures fromBayesian beliefs and that the latter can be adaptive insofar as they generate the former.© 2010 Elsevier Inc. All rights reserved.

Keywords: Error management theory; Cognitive biases; Behavioral biases; Expected utility theory

1. Introduction

An influential theory in the recent evolutionary psychol-ogy literature is error management theory (Haselton, 2007;Haselton et al., 2009; Haselton & Buss, 2000, 2003;Haselton & Nettle, 2006). Proponents of error managementtheory argue that biologically evolved systems of decisionand judgment reveal a general engineering principle.Namely, when one type of error is consistently more costlythan others, behavior that suppresses the rate at whichindividuals commit the more costly error will be favored.This principle is true even though the total number of errorsmay be higher than they are in the case where individualscommit all types of error at the same rate. To illustrate thegeneral engineering principle, consider the winnower, a farmimplement designed to separate grains of wheat from chaff.The winnower works by using a blower to blow away theless dense and unwanted chaff, while the heavier wheat fallsout the bottom. A winnower can be viewed as making two

⁎ Corresponding author. Centre for Anthropology and Mind, Universityof Oxford, Oxford OX2 6PE, United Kingdom.

E-mail address: [email protected] (R. McKay).

1090-5138/$ – see front matter © 2010 Elsevier Inc. All rights reserved.doi:10.1016/j.evolhumbehav.2010.04.005

types of error — it can blow away wheat and it can fail toblow away chaff. If the former type of error is more costly,the operator can set the blower speed so that the winnowerblows away wheat less often than it fails to blow away chaff,and this is optimal even though a higher speed would reducethe overall error rate. In essence, the operator's task is not tominimize errors, but rather to minimize costs.

Error management theory has been used to explaindiverse phenomena, including but not limited to phenomenaassociated with auditory perception, human courtship, foodpreferences and interracial aggression. The error manage-ment perspective, moreover, appears to be a fertile source ofnovel empirical predictions. Our intention is to propose someclarifications and refinements of the theory. Although we areimpressed by its simplicity, scope, and power, we argue thatexisting accounts are vague with respect to a key concept: thenotion of a bias. Error management theory is explicity atheory of cognitive bias. According to the theory, cognitivebiases do not necessarily reflect flaws in evolutionary designbut may be best conceived as design features. Our concern isthat the theory does not adequately distinguish betweencognitive biases and behavioral biases. Below we discussdifferent conceptions of bias in an effort to clarify thesubtleties associated with this important issue.

mailto:[email protected]

http://dx.doi.org/10.1016/j.evolhumbehav.2010.04.005

310 R. McKay, C. Efferson / Evolution and Human Behavior 31 (2010) 309–319

2. Behavioral biases

We begin by describing two types of behavioral bias.These biases are behavioral in the sense that identifying themdoes not require access to the internal (e.g., cognitive) statesof the agent. The first conception is trivial and simplycaptures the notion of a statistical tendency or inclination.Put abstractly, given N possible behaviors, a trivialbehavioral bias exists when the probability distributionover these N behaviors is not uniform. For example, if, in agiven period of time, an individual can engage in one of twopossible behaviors, say choosing heads or tails, a trivialbehavioral bias exists if over many periods the individualchooses heads more often than tails or vice versa. To use asecond example that has become a staple of the errormanagement literature, a male in a singles bar has twooptions with respect to the females he encounters. He canapproach them or not. If over time he approaches femalesmore often than not, or vice versa, he once again shows atrivial behavioral bias.

Our second conception of a behavioral bias is moreinteresting and incorporates the notion of an error. In order tomotivate the idea, imagine that the world can take one of Npossible states, and agents can exhibit one of N possiblebehaviors. States of the world are independently determinedeach period, and a one-to-one mapping between states of theworld and optimal behaviors characterizes payoffs. Specif-ically, if the world is in state x, the optimal behavior is b. Forany b′≠b, b′ is a suboptimal behavior given state x, and wewill call it an “error” because it results in a lower payoff thanb. Altogether, N(N−1) types of error are possible. On ourdefinition, behavior exhibits an interesting bias if over asufficiently large number of periods the empirical distribu-tion over these N(N−1) possible errors is not approximatelyuniform. If someone calls “heads”when the coin is tails moreoften than she calls “tails” when the coin is heads, or viceversa, she displays an interesting behavioral bias. A man in abar can approach women who are not attracted to him,yielding slaps in the face, and he can fail to approach womenwho are attracted to him, yielding missed opportunities. Ifslaps in the face outnumber missed opportunities, or viceversa, he displays an interesting behavioral bias.

Notably, behavior that is trivially biased may not beinterestingly biased, nor is behavior that is trivially unbiasednecessarily interestingly unbiased. Consider a man whoapproaches 50% of the women he encounters and hangs backshyly the rest of the time. His behavior is unbiased by ourfirst, trivial, definition. Nonetheless, if the man in question isGeorge Clooney, then his behavior may be extremely biasedby our second, interesting, definition. Missed opportunitiesmay vastly outnumber slaps in the face. Indeed, behavior caneven be trivially biased in one direction and interestinglybiased in the other direction. If George Clooney is anincorrigible womanizer, he may approach women at a highrate but, given his charms, still have more missedopportunities than slaps in the face.

3. Cognitive biases

We now consider two conceptions of cognitive bias. Aswith our first conception of behavioral bias, our firstconception of cognitive bias is trivial. Given N possiblestates of the world, a trivial cognitive bias exists when anindividual's subjective probability distribution over these Nstates is not uniform. Our roving male in the singles bar has atrivial cognitive bias if he believes that a certain female ismore likely to accept his advances than to reject them or viceversa. The reason this conception of a cognitive bias is sotrivial is that the biased belief in question may be justified bythe evidence. In particular, justified beliefs based on reliableinformation about the state of the environment will be non-uniform, and thus they will count as trivially biased.Debonair characters fully cognizant of their charms willcount as cognitively biased on this trivial conception, as willunattractive men with no illusions about their limited appealto females. Notably, however, extremely small departuresfrom uniform beliefs can in principle generate extremebehavioral biases of both types, trivial and interesting.

Our second conception of cognitive bias ismore interestingthan the first. In the everyday sense of the word, a “bias” refersto a particular tendency or inclination, but especially one thatmerits reproach in some way. Our definition of an interestingcognitive bias captures this idea insofar as it involvesviolations of a rational standard. By our definition, interest-ing cognitive biases obtain when beliefs depart systematicallyfrom those of an agent with Bayesian beliefs. Such acognitively biased individual does not have beliefs that aretheoretically optimal given the available information. More-over, the individual's beliefs depart from the theoreticaloptimum in a systematic, rather than random, fashion.

4. The minimum necessary belief

To clarify the relationship between interesting behavioralbiases and the cost asymmetries so widely discussed in errormanagement theory, we develop a simple binary modelsimilar to that found in Haselton and Nettle (2006). Thedecision maker faces one of two possible situations. We referto these situations as “states” of the decision maker'senvironment. The decision maker can make one of twochoices. One choice is best in one environmental state, whilethe other choice is best in the other environmental state.Accordingly, the decision maker can be wrong in twopossible ways. The costs of these two types of error are notequal, and this is why the decision maker's problem involvesa cost asymmetry. Aside from this cost asymmetry, the otherrelevant part of the problem is the decisionmaker's subjectivebeliefs about which environmental state actually obtains.

4.1. The intuition

To capture the intuition behind the model, consider Mr.Clooney again. When Mr. Clooney encounters a woman, hefaces one of two environmental states. Either the woman will

able 1he payoff matrix for the basic binary model

X=0 X=1

=0 b −d=1 −c a

y assumption, a, b, c, dN0, and a+dNb+c.

311R. McKay, C. Efferson / Evolution and Human Behavior 31 (2010) 309–319

be receptive to any advances from Mr. Clooney, or she willnot. If receptive, the error Mr. Clooney can make is hangingback and missing a fitness-enhancing opportunity. If notreceptive, the error Mr. Clooney can make is approaching heranyway and receiving a slap in the face. A lost matingopportunity costs more than a slap in the face. Importantly,Mr. Clooney's objective is emphatically not to minimize theprobability of an error but, rather, to minimize the expectederror cost. That means he should make choices in a way thatlead him to miss an opportunity less often than they lead himto receive a slap in the face. Equivalently, the belief Mr.Clooney requires that the woman will be receptive before heapproaches her is weaker than the belief he requires that shewill slap him in the face before he hangs back. For example,maybe the cost asymmetry is such that Mr. Clooney willapproach a woman if he thinks she will be receptive withprobability 0.25 and unreceptive with probability 0.75. If thecost asymmetry is even stronger, he requires an even weakerbelief that the woman will be receptive before approachingher. As the following model shows, this reduction in therequired belief responds very dramatically to increases in thecost asymmetry. None of this, however, requires Mr.Clooney to have an interesting cognitive bias. Imagine anextreme case in which Mr. Clooney only requires the beliefthat a woman will be receptive with probability 0.01. If 2%of the women in the world are receptive to Mr. Clooney'sadvances, and he knows this fact with perfect accuracy, hewill approach every woman he meets and receive slaps in theface 98% of the time. His behavior may appear exotic andeven astonishing, but we do not need an interesting cognitivebias to explain it. He's doing exactly what a payoffmaximizer with Bayesian beliefs would do.

4.2. The model

Let the environment take one of two states, where X ∈{0, 1} specifies the state according to P(X =1)=p. For eitherenvironmental state, the decision maker makes a choice, C∈{0, 1}. Table 1 shows how payoffs depend on the realizedstate of the environment and the decision maker's behavior.

The function π:{0, 1}→R assigns an expected payoff(e.g., expected fitness) to each behavior. The expectedpayoff of choosing C=0 is

p 0ð Þ = 1 − pð Þb − pd; ð1Þ

and the expected payoff of C=1 is

p 1ð Þ = − 1 − pð Þc + pa: ð2Þ

Now assume the decision maker does not necessarilychoose the behavior that maximizes the expected payoff.She does, however, choose the behavior that maximizesexpected payoffs with a probability that increases as thedifference in expected payoffs associated with the twopossible behaviors increases. This captures the idea thatchoices may be noisy but still sensitive to expected

TT

CC

B

payoffs. If, for example, the expected payoffs associatedwith the two choices are similar, behavior will be morelike flipping a coin than when the expected payoffs arevery far apart. One can implement this idea in variousways (Camerer, 2003), and the choice is not critical forour purposes. We choose the logit transformation.Specifically, for some λ ∈ R+,

P C = 1ð Þ = exp λp 1ð Þf gexp λp 0ð Þf g + exp λp 1ð Þf g ð3Þ

=1

1 + exp λ p 0ð Þ − p 1ð Þ½ �f g ð4Þ

=1

1 + exp λ b + cð Þ 1 − pð Þ − p a + db + c

� �� : ð5Þ

The quantities λ(b+c), p, and (a+d)/(b+c) are all non-dimensional (unit free), and this shows us that three non-dimensional parameter combinations control choice proba-bilities. The parameter combination λ(b+c) is simply ameasure of how sensitively choice probabilities respond todifferences in the values of π(0) and π(1).

When λ(b+c) is small, decision making is very noisy.When large, the decision maker almost always makes thechoice that maximizes the expected payoff. More impor-tantly, depending on the state of the environment and therealized payoff matrix, the cost of an error is either b+c ora+d. To see this, assume that the environment is in thezero state, and so X=0. If the decision maker makes anerror (i.e., C=1), she pays c and loses the b she wouldhave gotten had she not made an error. This yields a totalcost of b+c. Similar reasoning shows that the cost of anerror when X=1 is a+d. Eq. (5) indicates that (a+d)/(b+c) is the relevant measure of cost asymmetry in thebinary settings that figure so prominently in errormanagement theory. Because this asymmetry will appearrepeatedly, we will call it z. By assumption (see Table 1),zN1, which simply means we are restricting attention forthe moment to cases involving a real asymmetry.

One approach to showing how cost asymmetries lead tointerestingly biased behavior is to identify the minimumbeliefs an agent must have before choosing the behavior thatavoids the more costly error with a probability greater thansome specified threshold. Call this threshold CT. To focus onthe case in which even a weak belief that X=1 leads to astrong tendency to choose C=1, assume that CTN1/2 and


that λ>0. In other words, because avoiding the more costlyerror requires the decision maker to choose behavior 1, weare asking how high p needs to be before she choosesbehavior 1 with a probability that exceeds CT. In this case,the decision maker exhibits a trivial behavioral bias thatfavors C=1. With a bit of algebra, one can show that theindividual chooses such that P(C =1) NCT so long as

p N1

1 + z

� 1 −

1λ b + cð Þ ln

1 − CT

CT

� �: ð6Þ

Call the quantity on the right-hand side of this inequalityg(z). Taking derivatives, the result is

dgdz

=− 1 − 1

λ b + cð Þ ln1 − CTCT

� n o1 + zð Þ2 b 0 ð7Þ

d2gdz2

=2 1 − 1

λ b + cð Þ ln1 − CTCT

� n o1 + zð Þ3 N 0: ð8Þ

This result shows that, if we focus on the case in whichagents show a sufficiently strong behavioral tendency toavoid the costly error [i.e., P (C=1) N CT], then theminimum belief that X=1 required to produce thisbehavioral tendency is a convex decreasing function ofthe cost asymmetry (Fig. 1).

In particular, the minimum belief decreases as theasymmetry increases because the first derivative [Eq. (7)] isnegative when zN1, which is true by assumption. Thedecrease is convex because the second derivative [Eq. (5)] ispositive when zN1. Altogether, this tells us that the belief canbe arbitrarily weak so long as the asymmetry is sufficientlylarge. Moreover, the fact that the minimum necessary beliefdecreases in a convex fashion illustrates the power of costasymmetries. We do not typically need a dramatic costasymmetry to generate a large behavioral tendency because

Fig. 1. The minimum belief that X=1 required to choose C = 1 with aprobability greater than CT = 0.9 shown as a function of z, the costasymmetry. The graph shows this minimum required belief for values ofz from 1 to 20 when λ(b+c)=3.

the biggest marginal effects are associated with smallasymmetries. As shown in Fig. 1, the difference between noasymmetry and a relatively small asymmetry will often behuge, while the difference between the same small asymmetryand a huge asymmetry will often be comparatively small.

5. A profusion of cognitive pathways

To develop the link between cognition and behaviorfurther, we would like to expand the model above. Ourreading of the error management literature suggests to us thatresearchers often take an interesting behavioral bias asevidence for an interesting cognitive bias (see Section 6below). Here we show that inferences about even trivialcognitive biases are underdetermined by evidence of aninteresting behavioral bias.

5.1. The intuition

The basic idea is to decompose cognition into variouspossible mechanisms that could produce behaviors favoredby selection. In particular, we consider a relatively simplecase with three parts. The first part is the decision maker'sbelief that he is making a decision for which costasymmetries obtain. Second, the decision maker thinks theasymmetry, if it obtains, has a specific magnitude. Finally,the decision maker has a belief that, if an asymmetry obtains,the environment is actually in the state in which she canmake the more costly error.

For example, perhaps in certain social settings (on the redcarpet at the Academy Awards, say) Mr. Clooney considersslaps in the face, because of the extreme embarrassmentcaused, just as costly as missed opportunities. In these socialsettings, he does not face a cost asymmetry. In other socialsettings, however, slaps in the face are less costly than missedopportunities, and he does face a cost asymmetry. In any givensocial setting, as a result, Mr. Clooney has some beliefs aboutwhether he faces the former type of social setting or the latter.Mr. Clooney also thinks that a cost asymmetry, if present, hasa particular magnitude. Maybe he thinks that missedopportunities, when in the relevant social settings, are 10times as costly as slaps in the face. Moreover, when in socialsettings of either sort, Mr. Clooney also has some belief that agiven woman will respond positively to his advances. Theseare the three parts of Mr. Clooney's decision making weconsider. The model below addresses the case in which anincrease in the rate at which Mr. Clooney approaches womenis advantageous. In this case, given the three cognitivemechanisms we consider, there are infinitely many ways toaccomplish the required behavioral change. This is an exampleof how inferences about cognition can be radically under-determined when one observes an interesting behavioral bias.

5.2. The model

Specifically, assume the decision maker considers one oftwo possible payoff matrices, one with a cost asymmetry and

Table 2The payoff matrices for the binary model with two alternative payoffstructures

The matrix on the left corresponds to M=0, while the matrix on the rightcorresponds to M=1.


the other without. As detailed in Table 2, the payoff matrixthat denotes the map from the space of choices byenvironments to payoffs takes one of these two forms,M ∈ {0, 1}, where P (M=1)=q.

If matrix 0 holds (i.e., M=0), then no cost asymmetryobtains. If matrix 1 holds (M=1), then we have the same costasymmetry characterized by z that we considered in Section4. With this kind of uncertainty about the actual payoffstructure of the decision-making situation, the expectedpayoff of choosing C=0 is

p 0ð Þ = 1 − pð Þ 1 − qð Þb + qbf g + p 1 − qð Þ − cð Þ − qdf g;ð9Þ

and the expected payoff of C =1 is

p 1ð Þ = 1 − pð Þ 1 − qð Þ − cð Þ − qcf g + p 1 − qð Þb + qaf g:ð10Þ

Analogous to the simpler model above [Eqs. (3–5)],choice probabilities take the form

P C = 1ð Þ = exp λp 1ð Þf gexp λp 0ð Þf g + exp λp 1ð Þf g ð11Þ

=1

1 + exp λ b + cð Þ 1 − 2p + pqð Þ − pq a + db + c

� �� : ð12Þ

Choice probabilities now depend on four non-dimen-sional parameter combinations, λ(b+c), p, q, and (a+d)/(b+c). We would like to focus on three of these (z, p, andq), so we denote P(C=1)=f(z, p, q). Given that zN1 byassumption, one can show that

AfAz

=λ b + cð Þpq exp λ b + cð Þ 1 − 2p + pqð Þ − pq zð Þ½ �f g

1 + exp λ b + cð Þ 1−2p + pqð Þ−pq zð Þ½ �f g½ �2 N 0

ð13Þ

AfAp

=λ b + cð Þ 2 + q z − 1ð Þð Þexp λ b + cð Þ 1 − 2p + pqð Þ − pq zð Þ½ �f g

1 + exp λ b + cð Þ 1−2p + pqð Þ−pq zð Þ½ �f g½ �2 N 0

ð14Þ

AfAq

=λ b + cð Þp z − 1ð Þexp λ b + cð Þ 1 − 2p + pqð Þ − pq zð Þ½ �f g

1 + exp λ b + cð Þ 1−2p + pqð Þ−pq zð Þ½ �f g½ �2 N 0:

ð15Þ

Although Eqs. (13–15) look formidable, all we really careabout is the fact that all three partial derivatives areunambiguously positive. Because these derivatives tell ushow the function changes in response to our three cognitivevariables, the result tells us that we have three separatecognitive mechanisms for increasing the decision maker’stendency to avoid the more costly error. If selection favors abehavioral modification of this sort, then we have a profusionof cognitive pathways. An increase in the perceived payoffasymmetry given that one exists (i.e., z), an increase in thebelief that the environment is in the state where a costly erroris possible (i.e., p), or an increase in the belief that a costasymmetry actually obtains (i.e., q) will all do the trick. Sowill infinitely many combinations of the three. Indeed, wecan even reduce the forces favoring C=1 in one or two of thecognitive dimensions we consider and still get a localincrease in the probability of choosing C=1. This unusualpossibility simply requires that the remaining cognitivedimensions involve countervailing forces that overcompen-sate. Formally, for the probability of C=1 to increase at themargin, all we need is a positive total differential,

df =AfAz

dz +AfAp

dp +AfAq

dq N 0: ð16Þ

As Eq. (16) makes clear, this condition can be satisfied invarious ways, and this remains true even if some cognitivemechanisms, in isolation, are actually increasing theprobability of choosing C=0 and by extension increasingthe decision maker's tendency to make the more costly error.The net result is that, if we only have behavioral datashowing a strong tendency to choose C=1, we have anextremely restricted ability to draw inferences aboutcognitive processes–there are just too many free parameters.A strong behavioral tendency can arise from variouscombinations of at least three different quantities related tocost asymmetries. In essence, inferences about cognition areradically underdetermined. This is a version of the moregeneral point that adaptationist thinking is often more usefulfor making predictions about adaptive phenotypes thanpredictions about the proximate mechanisms by whichselection will fashion such phenotypes.

6. Error management biases

Having sketched several definitions of bias, we nowconsider the claims of error management theory in relation tothis taxonomy. As noted above, error management theoristsargue that cognition is biased, and they seek to recastcognitive biases as evolutionary adaptations to ancestralenvironments. What, however, do they mean by cognitivebiases? Which, if either, of our two conceptions of cognitivebias do they have in mind? Given the trivial nature of the firstconception, one might expect that the second, interestingconception is the only possibility. After all, probably every


cognitive agent that has ever existed has had trivial cognitivebiases. If you consider it relatively unlikely that the worldwill end in the next five minutes, or that a talking horse willbe elected the next Pope, then you are cognitively biased inthe trivial sense. No one has ever complained that humanshave cognitive biases of this sort. Any attempt to defend orreframe cognitive biases, therefore, must presumably refer tocognitive biases of the second, more interesting sort, namelybeliefs that depart systematically from the beliefs ahypothetical Bayesian would have.

The situation, however, is not so clear. In their article,“The Paranoid Optimist: An Integrative Evolutionary Modelof Cognitive Biases,” Haselton and Nettle (2006, p. 48)distinguish between errors of belief and errors of behavior:

In general, there are four possible outcomes consequent on ajudgment or decision. A belief can be adopted when it is infact true (a true positive or TP), or it cannot be adopted andnot be true (a true negative or TN). Then there are twopossible errors. A false positive (FP) error occurs when aperson adopts a belief that is not in fact true, and a falsenegative (FN) occurs when a person fails to adopt a belief thatis true. The same framework applies to actions. An FP occurswhen a person does something, although it does not producethe anticipated benefit, and an FN when a person fails to dosomething that, if done, would have provided a benefit.

Here the authors acknowledge a distinction betweenbelief and behavior. Erroneous beliefs involve a mismatchbetween belief and reality. Perhaps the world is in state x, butthe individual has an unjustifiably strong belief that it is instate x′. Erroneous behavior, instead, occurs when anindividual takes an action that is not optimal given thestate of the world. On the next page of the article, however,Haselton and Nettle (2006, p. 49) explictly conflate beliefand behavior when they say, “By adopting a belief, we meanbehaving or reasoning as if the corresponding propositionwere true.” In our view this conflation creates substantialconfusion. After all, if approaching uninterested females inbars carries no meaningful costs but occasionally largebenefits, selection will favor men who approach womeneven if they only have an exceedingly weak belief that theywill succeed with any given woman. A man may be nearlyconvinced that a particular woman is not interested in him.Nonetheless, if he admits any hope, however slim, he willbehave as if she is interested. He will do so precisely becausethe fitness costs of a missed encounter are so much largerthan the costs of brief embarrassment. Crucially, this bias inbehavior does not require an interesting bias in beliefs.

Given this conflation of belief and behavior, thepossibility arises that the cognitive biases Haselton andNettle (2006) seek to defend are not cognitive biases at all.Indeed, much of what they discuss gives the impression thatthe biases they seek to recast as design features are notinteresting cognitive biases but interesting behavioral biases.Consider, for example, this extract from their paper'sabstract, “EMT [error management theory] predicts that if

judgments are made under uncertainty, and the costs of falsepositive and false negative errors have been asymmetric overevolutionary history, selection should have favored a biastoward making the least costly error.”Haselton and Nettle, ofcourse, are exactly right; selection should favor a bias towardmaking less costly errors. This, however, is an interestingbehavioral bias. Biased behavior simply requires a biaseddecision rule. It does not require a cognitive bias in the senseof beliefs that depart systematically from the theoreticaloptimum given the available evidence. Haselton and Nettle(2006, pp. 48-49) repeatedly mention decision rules,implying that humans have evolved to make decisions in amanner that maximizes reproductive success:

According to EMT, certain decision-making adaptations haveevolved through natural selection to commit predictableerrors. Whenever there exists a recurrent cost asymmetrybetween two types of errors over evolutionary time, selectionwill fashion mechanisms biased toward committing errors thatare less costly in reproductive currency… EMT predicts thathuman psychology contains evolved decision rules biasedtoward committing one type of error over another.

Without doubt, actors showing interesting behavioralbiases will often end up making more errors than actorswho minimize the overall error rate. Again, however, thetask is not to minimize errors but rather to minimize costs.If this is the basic claim of error management theory, it iscertainly persuasive. Nonetheless, the problem is that thesame claim follows in a straightforward way from expectedutility theory (von Neumann & Morgenstern, 1944), andthe idea is central to the game theoretic solution conceptknown as “risk dominance” (Harsanyi & Selten, 1988).From this perspective, error management theory mightseem somewhat derivative.

Fortunately, however, we think that error managementtheory provides a basis for a more novel claim, namely thatinteresting behavioral biases can rest on interesting cognitivebiases, and that the latter can be adaptive insofar as theygenerate the former. More rigor is necessary, however, informulating this claim precisely.

In what follows, we will attempt to bring this claim intosharper focus. Before proceeding, however, we would like totouch on another important point. Haselton and Nettle (2006,p. 49) put forward an unbiased decision rule for “adoptingthe belief S,” where adopting the belief S is apparentlyviewed as a binary outcome equivalent to exhibiting thebehavior S. If s is a state of the world, ¬s is thecomplementary set of states, and e is available evidence,then the decision rule is to adopt or exhibit S when P(e|s)/P(e|¬s)N1. This is indeed an unbiased decision rule forbehavior under our second, interesting definition of abehavioral bias, but only if the prior probabilities of s and¬s are equal (Bar-Hillel, 1980; Kahneman & Tversky, 1973).Although Haselton and Nettle acknowledge this assumption,they do not emphasize the fact that it rarely holds. Applyingsuch a decision rule when the priors are not equal can lead to


serious consequences. Consider a situation in which anairport security guard is trying to decide whether or not tosubject a certain passenger to extra screening measures.Judging by his clothing, the passenger is a Muslim. Thequestion of interest to the security guard is whether thepassenger is also likely to be a terrorist. Let S be the decisionto implement extra screening, and e be the empiricalevidence available to the security guard. Further, let s bethe state in which the passenger is in fact a terrorist and ¬s thestate in which the passenger is not. The security guardestimates that P (e|s)=0.99, i.e., 99% of the world's activeterrorists have clothing that makes them seem Muslim. Theguard also estimates that P (e|¬s)=0.2, which means that20% of the world's peacable citizens have clothing thatmakes them seem Muslim. Because 0.99/0.2N1, the guardsubjects the passenger to additional screening, as indeed hedoes with all passengers who appear to be Muslim.

Whatever limited merits the security guard's decision rulemight have (see Press, 2009), it is clearly biased. The reason,of course, is that the security guard fails to account for thebase rates of terrorism and peacable tendencies in the generalpopulation. Given that the vast majority of Muslims whopass through airport security are not terrorists, the guard'sdecision rule generates a huge number of false positives.

A more general decision rule is

P s jeð ÞP Is jeð Þ =

P e jsð ÞP sð ÞP e jIsð ÞP Isð ÞN 1: ð17Þ

This rule incorporates the prior probabilities of s and ¬s.Because terrorists are vastly outnumbered by non-terrorists,this rule yields a very different decision from the rule above.Even if the security guard assumes that the proportion ofactive terrorists in the world is 0.1, which is surely a radicaloverestimate, then P(s|e)/P(¬s|e)=0.55, and the guard willlet the passenger in question through unmolested. Indeed,she will let all passengers through unmolested. This newrule, of course, is also biased because it only generates falsenegatives. In fact, it is completely worthless as a rule becauseit never discriminates between terrorists and non-terrorists.In terms of the absolute numbers of errors, however, this rulegenerates far fewer than the previous rule.

7. The evolution of interesting cognitive biases

We now return to what we see as the interesting and novelclaim that error management theory makes. We view theclaim as having three parts.

• Interesting behavioral biases require patterns ofbehavior that result in a non-uniform distributionover the possible types of error. Such biases will beadaptive in many situations.

• Beliefs and decision-making rules that yield suchbiases under appropriate conditions will be favoredby selection.

• In general, optimal beliefs will correspond to thebeliefs of a Bayesian because, all else equal, we cannotdo better than Bayesian beliefs in deliberative contexts.Nonetheless, in principle, Bayesian beliefs could beunavailable because, say, they are too expensiveneurologically. If something like this is the case, sys-tematic departures from the beliefs of a Bayesian,which constitute interesting cognitive biases, may beadaptive provided they lead to behaviors that areinterestingly biased in the adaptive direction.

The idea that some constraint may preclude Bayesianbeliefs is crucial, but Haselton and Nettle (2006) do notmention it. For example, they argue (p. 48),

Because men's reproduction is limited primarily by thenumber of sexual partners to whom they gain sexual access, abias that caused men to err on the side of assuming sexualinterest would have resulted in fewer missed sexualopportunities, and hence greater offspring number, thanunbiased sexual inferences. Therefore, natural selectionshould favor sexual overperception in men.

It is true, to give an extreme example, that a man whopursues every woman he meets because he thinks they allwant to sleep with him will have no more missed sexualopportunities than someone with Bayesian beliefs. Indeed,his number of missed opportunities will be zero, and thus, itwill probably be strictly less than the number of missedopportunities for someone with Bayesian beliefs. On theother hand, chasing all those women who in fact are notinterested will probably bring costs in other fitness-relevantdomains. As a result, departures from Bayesian beliefs arenot obviously adaptive. Bayesian beliefs, after all, aredistinguished by the fact that they are theoretically justifiedgiven all the available evidence. What Haselton and Nettleneed is an additional assumption, namely, the assumptionthat some kind of constraint limits the ability of selection toimplement perfectly Bayesian beliefs. To see how systematicdepartures from Bayesian beliefs might be adaptive givensuch a constraint, consider the following.

As Haselton and Nettle point out, when some objectmaking a sound is approaching, and one needs to prepare forthe arrival of the object, estimating an arrival time that issystematically too early is better than a time that issystematically too late (Neuhoff, 2001). What Haseltonand Nettle overlook is that, all else equal, it is better still toestimate an arrival time that is neither systematically tooearly nor too late. Such optimal estimates are Bayesian.Asymmetric costs may affect the optimal point in time fortaking an action relative to the estimated arrival, but this is aseparate issue entirely. Suppose, however, that someunspecified constraint limits our ability to have perfectlyBayesian beliefs. As a result, our subjective distribution ofarrival times is not the same as a Bayesian would have. Twodistributions, of course, can differ in several ways, but forsimplicity, we focus on the case in which two distributions


differ only in terms of their means. In this case,systematically underestimating arrival times should beadvantageous relative to systematic overestimation orunsystematic misestimations. This conclusion follows fromthe relatively weak assumption that being prepared a bit tooearly is usually better than being prepared a bit too late.

We have refined the claims of error management theoryby providing precise definitions of behavioral and cognitivebiases and by highlighting the importance of a keyassumption. Namely, assuming constraints limit our abilityto form Bayesian beliefs, some interesting cognitive biases,which are here defined as systematic departures from thebeliefs of a Bayesian, may be adaptive in many situations.What the theory now needs is an account of why constraintsmight prohibit Bayesian beliefs. One possibility is thatcognition is to a large extent general purpose, andperformance in some domains is negatively correlated withperformance in other domains. Dependent on the relevantcost functions, globally optimal performance in this casemay entail sub-optimal performance in some or all of theindividual domains.

From an evolutionary psychological perspective, how-ever, this idea clashes with an important assumption of thediscipline, namely, the assumption that the human mind isnot a general-purpose cognitive system but rather acollection of functionally specialized modules (Cosmides& Tooby, 1997). Insofar as these modules interact, effects inone module may constrain optimization in other modules.Insofar as these modules operate independently, however,natural selection should be free to optimize in one domainwithout affecting other domains. Evolutionary psycholo-gists are notable for positing a high degree of modularity,which would weaken the constraint argument above. Analternative explanation for constraints, which is perhapsmore consistent with the hypothesized degree of modularityassociated with evolutionary psychology, is that the neuralcircuitry required to implement Bayesian inference in all ormost domains is prohibitively costly. We leave it to othersto evaluate such possibilities.

8. Empirical evidence

The final point we want to make concerns the empiricalevidence for interesting cognitive biases. We have claimedthat, to argue for the adaptive nature of systematic departuresfrom Bayesian inference, one needs to invoke constraints.But why make this argument at all? Why not just assume thatevolved cognitive systems incorporate data in the optimalway by producing theoretically justifiable beliefs consistentwith Bayesian updating? This seems to be the mostparsimonious approach in the absence of contrary evidence.In our view, however, contrary evidence is available, but todate, published error management accounts have not clearlydiscriminated between evidence for interesting cognitivebiases and evidence for mere behavioral biases. We conclude

by considering three different domains of evidence in aneffort to demonstrate the interpretive complexities involved.

8.1. Protective biases in disease defense

In their overview of different biases, Haselton and Nettle(2006; see also Haselton et al., 2009) mention biologicalsystems designed to protect the body from harm, viamechanisms such as allergy and cough. Such defensesystems are often mobilized in the absence of any realthreat. Coughs, for example, probably frequently representfalse positives, and for this reason dampening them withmedication often leads to few negative effects (Nesse, 2001).This phenomenon seems a plausible candidate for aninteresting behavioral bias. Specifically, the more costlyerror, not coughing when a real threat exists, occurs lessfrequently than the less costly error, namely, coughing whenno threat is present. We see no need, however, to invoke aninteresting cognitive bias here. Although interesting cogni-tive biases may reinforce adaptive interesting behavioralbiases in some settings, evidence of an interesting behavioralbias is not evidence for an interesting cognitive bias. We maycough a lot because coughs are cheap and disease isexpensive, but this observation does not require us to posit adistortion in the body’s processing of information.

8.2. Hot hand behavior

The hot hand phenomenon occurs when researchparticipants expect streaks in sequences of hits and misses,the probabilities of which are, in fact, independent. Does thisphenomenon reflect an interesting cognitive bias? Wilke andBarrett (2009) have suggested that the phenomenon reflects apsychological adaptation for successful foraging. Weconsider this hypothesis in some detail here.

To begin, we define two relevant foraging errors: (1)Over-foraging: having discovered a desired resource, anindividual continues to forage when the reality is thatcontinued foraging will prove fruitless; (2) Under-foraging:having discovered a desired resource, the individual ceasesforaging when continued foraging would have (perhapsliterally) yielded further fruits. Now, imagine that ananthropologist visits a particular field location and observesinterestingly biased foraging behavior in that location.Specifically, she notes that foragers there are more likely toover-forage than to under-forage. What might this hypothet-ical researcher conclude? We distinguish two distinctpossibilities, both compatible with the data she has collected.

The first possibility is that the foragers are flawlessBayesians who maximize expected utility under appropriateincentives. These cognitively laudable creatures reliably trackthe relevant environmental contingencies. The bias towardover-foraging that they exhibit may stem from the fact thatthey accurately perceive that their resources of interest arespatially clumped (positively autocorrelated at a given scale).Having discovered some of the resource, they may accuratelyinfer that further foraging at this scale is statistically more


likely to yield fruit than to not yield fruit. Alternatively, oradditionally, the foragers may accurately perceive that thecost of the two foraging errors is asymmetric. If they considerthat the cost of a missed foraging opportunity is greater thanthe cost of fruitless foraging, then they may adjust theirforaging behavior so as to produce the observed non-uniformdistribution over error types (i.e., they will tend to over-foragerather than under-forage).

The second possibility is that the observed interestingbehavioral bias reflects an interesting cognitive bias in theforagers. It may be that some kind of constraint in theevolutionary past (e.g., a historical or ecological constraint)limited selection's ability to implement Bayesian beliefs. Inthis case, systematic departures from Bayesian updating(interesting cognitive biases) may have proven adaptiveinsofar as they generated adaptive tendencies to avoid costlyerrors. The present-day foragers retain this cognitive bias(which may or may not still be adaptive, depending onwhether the relevant environmental contingencies aredifferent to those that obtained in the environment ofevolutionary adaptedness).

One of our main points in this paper is that the evidencethe anthropologist has collected in this hypotheticalexample is consistent with both hypotheses. Having simplyinferred interesting behavioral biases, therefore, researchersshould be very cautious about inferring interestingcognitive biases—especially given that the latter possibilityis somewhat unparsimonious (involving, as it does, theconstraint assumption).

A recent study by Wilke and Barrett (2009), however,represents a much more rigorous and controlled investigationof the issue than that conducted by our hypotheticalanthropologist. Wilke and Barrett designed computer tasksin which participants could forage for different resources.Participants were presented with a sequence of hits (e.g.,fruits) and misses (e.g., no fruits) and were required, aftereach event in the sequence, to predict whether the next eventwould be a hit or a miss. In this paradigm there were tworelevant errors: guessing hit when the subsequent trial was amiss and guessing miss when the subsequent trial was a hit.Crucially, however, the (opportunity) cost of these errorswas perfectly symmetric—participants were paid a standardamount for each correct response (whether true positive ortrue negative) and were not penalized for false alarms ormisses. Observed behavior in this study thus transparentlyrevealed cognition in a way that it did not in the hypotheticalanthropological study above because there is every reason tosuspect that a participant's button press for hit indicated abelief of at least one half that the next trial would be a hit.

Given (1) that responses appeared to indicate anassumption of clumpiness across all resource types, althoughdistributions were in fact equivalent to a series of coin tosses,and (2) that there was no evidence of learning over time(participants were uniformly hot handed over the course ofthe computer task—if anything, hot-handedness increasedas the experiments progressed), the conclusion that partici-

pants showed interesting cognitive biases in this domaindoes not initially seem unwarranted. However, there is animportant caveat here. Assume, for a moment, that theparticipants were in fact flawless Bayesians. In this case, theparticipants would soon correctly infer that the distributionof hits and misses was uniform. Given this knowledge, whatguessing strategy should they have employed? The answer isthat no strategy would have presented itself as preferable toany other. Participants would have fared just as well if theyhad guessed at random, if they had chosen hit on every trial,if they always chose the event that had just occurred, or anyother strategy whatsoever. Our point is that hot handbehavior had absolutely no payoff consequences here. Thefact that participants displayed hot hand tendencies is nottherefore at odds with their having had Bayesian beliefs.Although the fact that they displayed hot hand behavior iscertainly suggestive, we cannot be sure that they had hothand beliefs.

In order to demonstrate an interesting cognitive biasexperimentally, it is necessary to set things up such thatcognitive biases will yield one sort of behavior, and Bayesianbeliefs will yield another. Because all behavior is equallyrational in the situation where participants must, in effect,guess the outcomes of repeatedly flipping a fair coin, theabove experiment does not ultimately accomplish this.Another possible approach would be to artificially constrainthe distribution of hits and misses in the experiment such thatthere is an equal global proportion of each, and to tell theparticipants this in advance. Truly Bayesian participants inthat situation would update the probabilities of hits andmisses after each event, and at each point in time they wouldchoose the option that had occurred least often up to thatpoint. For example, if the participant knows that 50 hits and50 misses will be presented in random order, then hersubjective probability of a hit at the outset will be 50/50. Ifthe first two events turn out to be hits, then her updatedprobability of a hit on the third event will be 48/98, and shewill choose miss. Note that the Bayesian strategy here willnot consist in simply choosing the event that has justoccurred—so evidence of hot hand behavior here would beconvincing evidence of interesting cognitive bias. Suchbehavior would have a detrimental effect on payoffs.

A different, and perhaps even better approach, would beto set things up such that the outcomes in the experiment arenegatively autocorrelated. Wilke and Barrett (2009) foundthat participants displayed hot hand tendencies even forresources (such as bird nests) that are dispersed (rather thanclumped) in the real world. However, these resources werenot negatively autocorrelated in their experiment—as withthe other resources they used, the distribution of bird nesthits and misses was equivalent to that generated by a seriesof coin tosses. One way of producing negatively auto-correlated outcomes would be to use two different coins, onebiased toward heads and the other biased toward tails, and torepeatedly flip these coins in turn. A Bayesian in thatsituation would end up exhibiting reverse hot hand behavior,


so standard hot hand behavior in that situation would, again,be convincing evidence of interesting cognitive bias.

8.3. Sexual overperception by men

Our final example pertains to the domain of sexualinference discussed earlier. One claim is that natural selectionhas favored sexual overperception in men (Haselton & Buss,2000; Haselton & Nettle, 2006). As we have indicated, thisclaim is underdetermined by evidence that men exhibitinteresting behavioral biases in this domain. If wastedopportunities are costlier than rejections, as seems plausible,then expected fitness maximizers with Bayesian beliefs willbehave so as to avoid wasted opportunities, and they will doso without any sort of interesting cognitive bias. Evidence inthe domain of sexual overperception, however, goes beyondsimply demonstrating an interesting behavioral bias. Anumber of studies do, in fact, suggest interesting cognitivebiases. For example, Abbey (1982) had unacquainted menand women interact briefly in pairs. Hidden observers, bothmale and female, observed the interactions and rated thesexual intent of both parties. Male observers perceivedgreater sexual intent in the target women than did femaleobservers. Other studies have documented similar effects,including interesting studies by Haselton (2003) andHaselton and Buss (2000). In these studies, given that menand women have the same data, so to speak, it would appearthat they cannot both be cognitively unbiased (in theinteresting sense).

However, consider one final caveat. It is possible thatpeople are born with evolved domain-specific priors, priorsthat, in effect, encode the evolutionary history of humans. Inprinciple, men and women could be congenitally equippedwith the same prior beliefs about the sexual interest of agiven woman. Men and women, however, are socialized insystematically different ways. As a result, they will havedifferent evidence available to them as they proceed throughlife, and they may enter an experimental scenario withdifferent prior beliefs about female sexual interest—beliefsthat may be justifiable in each case, given the evidence theyhave, respectively, encountered. We make no claims aboutwhether this is true or about what form differentialsocialization would take (see Haselton and Buss, 2000,who consider a related point and offer convincing evidenceagainst it). We simply want to point out that differentposterior beliefs in men and women could, in principle,reflect different prior beliefs that are justified in each case. Ifthe experiment were continued for long enough, with maleand female observers exposed to the same evidence, it ispossible that their respective posteriors would convergethrough time and be empirically indistinguishable.

9. Discussion and conclusion

Error management theory is a theory of emerginginfluence and broad application. The theory claims that

cognitive biases do not necessarily reflect flaws inevolutionary design, but that they may be best conceivedas design features. Unfortunately, existing accounts of thetheory are vague regarding the key concept of bias. Theresult is that it is unclear that the cognitive biases that thetheory seeks to defend are not simply a form of behavioralbias, in which case the theory reduces to a version ofexpected utility theory. We have offered some refinementsand clarifications in an effort to highlight what we see aserror management theory's genuinely novel claim: thatbehavioral tendencies to avoid costly errors can rest onsystematic departures from Bayesian beliefs, and that thelatter can be adaptive insofar as they generate the former.

We have outlined a taxonomy of biases, comprisingtrivial and interesting conceptions of both behavioral biasand cognitive bias. We have shown that inferences aboutcognition are radically underdetermined by evidence ofinteresting behavioral bias. On the one hand, evidence of abehavioral tendency to avoid costly errors is not, in itself,evidence of interesting cognitive bias. Individuals withperfectly Bayesian beliefs will display such tendencies to theextent that they maximize expected utility under appropriateincentives. On the other hand, we have noted that eveninferences about trivial cognitive biases are underdeterminedby evidence of behavioral bias. We have identified threedifferent trivial cognitive biases that might result inbehavioral bias—trivially biased beliefs about states of theworld will do the trick, as will trivially biased beliefs aboutthe existence and/or magnitude of cost asymmetries. Finally,we have highlighted a key assumption, that the capacity forBayesian beliefs is subject to constraints. To date, publishedaccounts of error management theory have not mentionedthis assumption, but the claim that systematic departuresfrom Bayesian beliefs can be adaptive insofar as theygenerate adaptive interesting behavioral biases requires it.

Acknowledgments

The first author was supported by a research fellowship aspart of a large collaborative project coordinated from theCentre for Anthropology and Mind (http://www.cam.ox.ac.uk) at the University of Oxford and funded by the EuropeanCommission's Sixth Framework Programme (”ExplainingReligion”). The second author was supported by the SwissNational Science Foundation, grant No. 105312-114107.Thanks to Daniel Fessler, Nick Chater, David Hugh-Jones,Christian Ruff, and two anonymous reviewers for valuableinput. Special thanks to Martie Haselton and Daniel Nettlefor constructive and generous comments.

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