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On the Use of Rational Choice Theory in Evolutionary Biology

Samir Okasha, University of Bristol

Introduction

The aim of this paper is to offer some philosophical reflections on the use of rational choice

theory within evolutionary biology. Since the 1960s, concepts and models from rational

choice theory have often utilized by biologists, usually with some modifications, to shed light

on evolutionary phenomena. This is particularly true in behavioural ecology – the science that

studies animal behaviour from a Darwinian perspective. For example, Bayesian decision

theory has been used to study foraging behaviour in animals (e.g. Houston and McNamara

1999); non-cooperative game theory has been used to study the evolution of strategic

behaviour, a development that gave rise to evolutionary game theory (see Maynard Smith

1982, Hammerstein 2012 ); and bargaining theory has been used to study the division of

reproduction within animal societies (Johnstone and Cant 2009, Roughgarden 2010). More

recently, there have been attempts to use ideas from social choice theory to shed light on

biological scenarios involving individuals with divergent interests living in groups (Okasha

2009, 2012; Conradt and List 2009; Bossert, Qi and Weymark 2013).

From one perspective, the fruitful transfer of ideas from rational choice theory to

evolutionary biology is surprising, given that non-human animals have rather limited powers

of rational deliberation. What explains it? The answer, I conjecture, stems from the fact the

concept of utility in rational choice theory plays a rather similar role to the concept of fitness

in evolutionary theory. Just as rational choice theorists typically assume that agents make

choices that maximize their utility, so evolutionary biologists assume, and in some cases can

show, that animals will makes choices that maximize their Darwinian fitness (roughly,

expected number of offspring) or some proxy for it. Thus the utility-maximizing paradigm of

the rational choice theorist corresponds closely to the fitness-maximizing paradigm of the

evolutionary biologist. At this abstract level, it is thus easy to see why rational choice models

should have biological applications.

A related phenomenon is the widespread use of teleological language to describe both

the process of Darwinian evolution and its products. Though the process that Darwin

described – descent with modification – is of course purely naturalistic, biologists have often

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characterized it in quasi-teleological terms, e.g. as a ‘hill climbing’ process in which natural

selection drives populations up peaks in an ‘adaptive landscape’, thus effecting

‘improvements’. (Though this is controversial – see below). Still more commonly, the

products of the evolutionary process – the highly-adapted organisms that we see today – are

described in intentional or teleological terms. Thus the behaviour of even the simplest

organisms is often treated as purposive, in that it has the ‘aim’ of increasing the organism’s

fitness; and we find frequent talk of the ‘interests’ and ‘strategies’ of an organism or gene, of

‘conflicts of interests’ between organisms and genes, of ‘selfish’ and ‘altruistic’ behaviours.

Language of this sort, which pervades the professional and the popular biological literature, is

the informal counterpart to the explicit use of rational choice models to study animal

behaviour.

The transfer of ideas from rational choice theory in evolutionary biology raises a

number of interesting questions, both philosophical and technical, which have been the focus

of my research for the last six years or so. Here I offer an overview of some of this research,

with a focus on broad conceptual issues. Further details may be found in my previously

published papers, listed in the References section, some of which I draw on below.

The structure of this paper is as follows. Section 1 distinguishes two different ways in

which rational choice concepts have been applied to evolution, and discusses their relation.

Section 2 examines the long-standing opposition among some evolutionary theorists to the

notion of optimization, and explores the consequences for the evolution / rational choice

connection. Section 3 explores the parallel between utility and fitness, with a focus on

measurement-theoretic issues. Section 4 asks whether in applying rational choice theory to

biology, we should think of genes, individuals, groups, or some other units as the agents

doing the maximizing. Section 5 focuses on social behaviour, outlines Hamilton’s inclusive

fitness concept, and describes a recent attempt to integrate the concept into decision theory.

Section 6 discusses two scenarios in which it has been suggested that evolution will give rise

to non-rational behaviour. Section 7 concludes.

1. Evolution and the Rational Choice Metaphor: Product versus Process

The notion of optimization (or maximization) is central to rational choice theory. An agent

whose choice behaviour meets certain highly intuitive rationality constraints, notably

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transitivity, may be represented as maximizing a utility function, or solving an optimization

problem. This simple idea lies at the heart of much of economic theory. The notion of

maximizing is also central to evolutionary biology, where ‘fitness’ is the quantity usually said

to be maximized. Thus it is natural to expect a connection between rational choice theory and

evolutionary theory, and the literature is replete with suggestions that there is such a

connection.

In fact, there are two quite different ways in which rational choice ideas can be

applied to evolution, depending on whether we focus on the process of evolution or its

product. Taken the former way, the idea is that natural selection may be viewed as a process

in which ‘mother nature’ chooses between alternative phenotypes, or traits, depending on

their biological fitness in the relevant environment. So the agent that does the choosing is

mother nature (i.e. a personification of natural selection); and the objects that she chooses

between are alternative genotypes or phenotypes (or in some versions of the metaphor,

alternative distributions of phenotypes in a population). Since mother nature’s choices will

presumably satisfy transitivity, they can be regarded as rational. Thus it seems that the

concept of rational choice may be applied, metaphorically, to any process of natural selection.

The metaphor helps articulate the intuition, popular among some biologists, that the

Darwinian process, though causal, is nonetheless still teleological in a sense.

Taken the second way, the idea is that the choice behaviour of evolved organisms

may be viewed through the lens of rational choice theory. The putative justification for this is

that since organisms have evolved by natural selection, their behaviour, including their choice

behaviour, is presumably adaptive, or “ecologically rational”, and should therefore satisfy

standard rational choice principles. Thus faced with a choice between alternative actions, an

evolved organism is expected to choose the fitness-maximizing one, and will thus exhibit

complete and transitive choice behaviour. Note that talk of an organism ‘choosing’, in this

context, is understood in an ‘as if’ sense: organisms are assumed to exhibit behavioural

plasticity, not to be capable of conscious deliberation. In this sense, organisms as simple as

bacteria can be regarded as making choices. The point of using rational choice theory is then

to help explicate, in a precise way, the assumption that an organism’s behaviour should be

adaptive.

These two ways of applying rational choice concepts to evolutionary biology are not

exclusive, for they have different foci. The former concerns the evolutionary process; the

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suggestion is that this process may usefully be viewed as one in which some variants are

chosen, or preferred, over others, by a rational agent trying to achieve a goal. The second

concerns the behaviours that are produced by that process; the suggestion is that these

behaviours may usefully be viewed as if the organism performing them were a rational agent

trying to achieve a goal. In both cases, the ‘goal’ is supposed to be maximization of fitness,

though what exactly this means needs to be spelled out.

Interestingly, the notion of optimization has a rather chequered history within

evolutionary biology. Some biologists routinely assume that organisms will behave as if

maximizing their fitness, or some proxy for it (e.g. probability of survival); this is a standard

assumption in behavioural ecology and also in life-history theory, and models based on that

assumption enjoy considerable empirical success (cf. Krebs and Davies 1997, Stearns 1992).

However in other quarters the idea that natural selection optimizes is regarded as

demonstrably untrue, apart from in the simplest cases; since the 1960s this has been the

conventional view in mathematical population genetics, and has been reinforced by recent

developments in adaptive dynamics and evolutionary game theory (e.g. Ewens 2004, Rice

2005, Metz, Mylius and Diekmann 2008).

This apparent inconsistency is partly due to the fact that the two camps are focusing

on somewhat different issues, as Grafen (2006) has insightfully pointed out (though this is

not the whole story). In terms of our distinction above, the opponents of optimization are

generally focusing on the evolutionary process itself, while the proponents are generally

focusing on the behaviour of evolved organisms. In the light of this, it is worth probing more

deeply the validity of the rational choice analogy as applied to evolutionary biology. To do

this we focus briefly on the status of optimization ideas in biology, as applied to both the

process and the products of Darwinian evolution, examining the objections to them; and we

trace the implications for the rational choice analogy.

2. Optimization and its discontents

2.1 The process version

The optimizing view of the process of evolution by natural selection, and the problems it

faces, can be appreciated by recalling the ‘adaptive landscape’ metaphor of evolution.

Introduced by the American geneticist Sewall Wright (1932), the adaptive landscape pictures

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evolution as a hill-climbing process in which natural selection pushes populations up ‘peaks’

in the landscape. The landscape (in one of its versions) is a based on a function from the

genetic composition of a population, represented by a vector of allele frequencies, to the

population’s mean fitness w . Peaks in the landscape correspond to populations with (locally)

maximal mean fitness. A simple adaptive landscape in three dimensions, involving just two

genes, is depicted below; note that any real case will be highly multi-dimensional.

Figure 1: The Adaptive Landscape

Wright argued that natural selection would tend to push a population up the steepest

peak in the adaptive landscape, by changing a population’s genetic composition so as to

increase its mean fitness; thus mean fitness was akin to a ‘potential function’ in physics. This

idea, and the adaptive landscape metaphor itself, became central to the thinking of many

evolutionary biologists in the 20th

century. However in fact, it is only true in special cases

that selection tends to increase w , a fact known since the 1960s (cf. Edwards 1995, Ewens

2004). If we consider selection at a single genetic locus, with fixed genotype fitnesses, then it

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is true that w must always increase; but the argument cannot be generalized to more

complicated genetic architectures (e.g. two-locus cases), nor to cases where genotype

fitnesses vary over generations. Thus the ‘hill-climbing’ view of evolution is only defensible

in special cases.

This conclusion is reinforced by recent work on adaptive dynamics – a version of

evolutionary game theory that explicitly incorporates feedback between an evolving trait and

the ecological environment. This literature emphasizes that the fitness of a particular trait, or

genetic variant, is environment-relative, and that the relevant ‘environment’ typically

includes the frequency of the trait in the population, and the population density. (This is true

of many behavioural traits and most life-history traits.) In these circumstances, it is intuitively

clear that mean fitness need not be maximized. In fact, a stronger conclusion emerges,

namely that the evolutionary process, even when driven exclusively by selection, does not

necessarily maximize any quantity at all (so does not “obey an optimization principle”, as it is

often put). One way to see this is to note that the dynamics may be cyclical, never settling

down to an equilibrium (cf. Metz, Mylius and Diekmann 2008).

Despite all this, the idea that Darwinian evolution is an optimizing process still has

wide currency in biology, and is sometimes treated as trivially true. What explains this? The

answer, I think, is that a weaker claim is often intended, to the effect that at any given point in

time, selection will favour fitter over less fit variants, and will thus tend to modify a

population’s composition in the direction of higher fitness if the environment remains

constant. This weaker claim is indeed true, and follows from R.A. Fisher’s famous

‘fundamental theorem of natural selection’ (on the ‘modern interpretation’ of the theorem;

see Edwards 1994, Okasha 2009). Fisher claimed that this theorem revealed the tendency of

natural selection to “improve” organisms, an assertion with clear teleological overtones.

What renders this compatible with the fact that w does not always increase (a point that

Fisher had himself emphasized against Wright) is the fact that the ‘environment’ typically

changes over generations; so the ‘improving tendency’ need not actually be realized, and in a

population of constant size, it cannot be.

Where does this leave the rational choice metaphor as applied to the evolutionary

process? The answer, I think, is that the metaphor is partially tenable. At any point in time,

mother nature chooses between variant phenotypes according to their ‘fitness’ in the

environment at the time, and so is akin to a rational agent maximizing a utility function. But

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mother nature has schizophrenic tastes: her utility function is continually changing, and so the

long-term evolutionary dynamics of the population cannot be predicted from her utility

function at any one point in time, except in those special cases where an optimization

principle, such as maximum w , does apply.

2.2 The product version

The optimizing view in its product version holds that since organisms are highly evolved,

their current behaviour should be adaptive, or ‘well designed’, hence at least locally optimal.

This viewpoint is partly motivated by theoretical arguments, and partly by the empirical

observation that much animal behaviour does in fact appear adaptive, and purposive.

Advocates of this viewpoint, who include many behavioural biologists, typically argue that

evolved behaviour has the function, or purpose, of maximizing the organism’s fitness. If this

is true, an evolved organism’s observed choices should presumably conform to the canons of

rational choice theory.

The status of this optimization assumption is a moot issue. Clearly the assumption is

predicated on a Darwinian or ‘adaptationist’ view of biology, which emphasizes the power of

natural selection to shape phenotypes, including behaviours, to meet environmental demands.

However general objections to adaptationism are not my focus here. For even granting the

validity of adaptationism, it is still unclear whether we should expect evolved behaviour to be

fitness-maximizing, or optimal. The issue is complicated for at least two reasons.

Firstly, though it is often asserted that fitness-maximizing behaviour is the inevitable

or at least the likely outcome of natural selection (e.g. Maynard Smith 1978), a general

demonstration of this proposition has not been provided in evolutionary theory. Recent work

by Alan Grafen has attempted to fill this lacuna, but it is only partly successful. In particular,

Grafen’s results do not apply to game-theoretic scenarios in which fitnesses are frequency-

dependent; and in fact, in such scenarios it is well-known that the evolutionary dynamics can

drive a population to a so-called ‘branching point’ at which evolved behaviours are not even

locally optimal, for they are at a minimum of the individual fitness function (cf. Abrams,

Matsuda & Harada 1993). Moreover, even in the absence of frequency-dependence, genetic

constraints mean that sub-optimal phenotypes can exist in a population at equilibrium, since

the optimal phenotype cannot breed true; Grafen’s results do nothing to escape this well-

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known problem. So the theoretical justification for assuming that evolution will lead to

fitness-maximizing behaviour is at best imperfect.

A second issue concerns what ‘fitness’ means and what the ‘organisms’ (or

‘individuals’) are whose behaviour is supposed to maximize it. In the simplest case, an

‘organism’ refers to a multi-celled metazoan, e.g. a human, and ‘fitness’ may be defined as

the expected number of offspring produced over a lifetime. But complications abound. This

definition of fitness is known to be inapplicable in more complex cases, e.g. when there are

social interactions involved, or in stochastic environments involving aggregate risk. More

complicated fitness measures, e.g. ‘inclusive fitness’, then become needed; see sections 4 and

5 below. Moreover in some cases biologists apply the fitness concept to groups rather than to

individuals, or to the genes within individuals; this conceptual shift is needed to

accommodate a variety of empirical phenomena within the fitness-maximizing paradigm. So

we cannot simply take the concepts of individual, or organism, for granted; indeed these are

disputed concepts in biology. Nor can we take for granted that we know how to define the

‘fitness function’, if any, that natural selection will lead them to maximize.

This last point is relevant because workers in a numbers of fields have argued, and in

some cases produced models to show, that Darwinian evolution can in fact give rise to

irrational choice behaviour. Thus Sober (1998) and Skyrms (1995) both argued that in

certain cases, evolution and rational choice ‘part ways’, in that weakly or even strictly

dominated behaviours can be favoured by natural selection. Similarly, Robson (1996) argues

that in the face of environmental uncertainty, behaviours that violate expected utility

maximization may be selectively advantageous. And Houston, McNamara and Steer (2007)

devise models to show that irrational behaviour, e.g. intransitive preferences, can evolve in

certain circumstances. However as we will see later, these arguments for the ‘evolution of

irrationality’ typically make specific assumptions about who the maximizing agent is (e.g.

individual), what their utility function is (e.g. number of offspring), and what the state-space

of the decision problem is. By suitably altering these assumptions, the irrationality can often

be made to go away.

Where does this leave us as regards the validity of employing rational choice theory to

understand organismic behaviour? As I see it, the position is this. In so far as evolved

behaviour is locally optimal, hence fitness-maximizing, then it is valid to think of the

organism, in its behavioural choices, as akin to a rational agent seeking to maximize a utility

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function. However the justification for this optimality assumption must ultimately be

empirical, not theoretical. Moreover we cannot assume a priori that we know which

biological entity (gene, individual, group etc.) is playing the role of the rational agent, nor

that we know what the agent’s utility function is; both of these are up for grabs. Despite these

caveats, the rational agent model remains a valuable way to think about evolved behaviour, in

my view.

3. The utility / fitness connection: foundational issues.

The observation that utility and fitness play similar roles in rational choice theory and

evolutionary theory respectively is by no means new. However the utility / fitness connection

has rarely been studied in detail. A natural starting point is to consider measurement-theoretic

issues. In the case of utility, we customarily distinguish between ordinal, cardinal, ratio and

absolute scales for measuring utility, depending on the class of transformations to which we

think we can subject the utility function without losing information. What about biological

fitness? What is the appropriate measurement scale for fitness?

In evolutionary theory, fitness is often defined on an absolute scale, e.g. as expected

number of offspring, or probability of survival, or intrinsic growth rate, or gametic

contribution to the next generation. These quantities are all absolutely measurable, in that the

actual numbers are meaningful. However it does not follow that for the purposes of

evolutionary analysis, all of this information is necessary. In fact, it many cases what matters

is how many offspring an organism or genotype leaves relative to others in the population;

this determines whether it will be favoured by natural selection or not, and is often sufficient

to determine the evolutionary dynamics.

In some evolutionary analyses, a purely ordinal fitness concept is sufficient. For

example, if competing strains of bacteria are growing in a nutrient broth, then under well-

known conditions the strain with the highest intrinsic growth rate will be the only one found

at equilibrium. So to predict the equilibrium state, we need only be able to order the strains

by growth rate; the actual growth rates do not matter. But in other cases ordinality is not

enough. For example, in a one-locus two-allele population genetics model we know that the

population will converge to a polymorphic equilibrium if the heterozygote is fitter than the

two homozygotes, (i.e. wAa > waa and wAa > wAA); but to determine the actual equilibrium

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composition of the population we need to know the fitness differences between the three

genotypes, which requires cardinal measurability. And to determine the rate at which the

population approaches equilibrium, we need to know the ratios of the genotype fitnesses to

one another, which requires ratio-scaled measurability.

To focus the issue more generally, consider the Price equation, a standard formalism

for expressing the evolutionary change in a trait (or gene) over one generation in a

population:

∆ z = [Cov (wi, zi) + Exp (wiδi)] / w

where zi is the trait value (or gene frequency) of individual i, wi is the fitness of individual i,

z the mean trait value in the population, ∆ z the one generational change, δi the deviation in

trait value between individual i and its offspring; and Cov and Exp are the covariance and

expectation operators respectively (in the sense of population averages). (To apply the Price

equation to a discrete trait or gene, simply let zi be an indicator function for the presence of

the trait in individual i.) It is easily seen that the class of transformations to which the fitness

function w may be subject, while leaving ∆ z unchanged, involves multiplication by a

positive constant, implying that fitness is ratio-scale measurable. Note, though, that if we are

only interested in the sign of ∆ z (i.e. in whether a gene or trait will be favoured by selection

or not), then cardinal measurability is enough; since adding a constant to the fitness function

leaves the sign of ∆ z unchanged.

There are other contexts in which cardinality will also suffice. For example in ‘one

population’ evolutionary game theory, in which organisms are drawn at random from an

infinite population to play a symmetric game, the standard continuous-time replicator

dynamics are unaffected by addition of a constant to each payoff, and multiplication of each

payoff by a positive constant only changes the velocity with which the population moves

through the state space, not the orbits (cf. Weibull 1995 p.73-4). (Though other dynamics can

be affected, and in two population models the situation is different.) So for the purposes of

answering the questions that evolutionary game theory usually asks, fitnesses need only be

cardinally measurable. But in general, it cannot be assumed that adding a constant to the

fitness function makes no difference, as the zero point of fitness is meaningful. This is

particular clear in evolutionary ecology, where the fitness concept is used to study changes in

a population’s density as well as its genetic composition.

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Besides measurability, rational choice theorists often ask whether utility is

interpersonally comparable, i.e. whether utility differences and /or levels can be meaningfully

compared across individuals. What about fitness? It might be thought that fitness is obviously

interpersonally comparable: surely the whole point of the fitness concept is to permit

comparison between the individuals in a population? However this reply is not to the point.

For in typical applications of the rational choice metaphor in biology, either there is only one

individual (“mother nature”), or there are many individuals but they all have the same utility

function, i.e. the analysis focuses on the behaviour of a ‘typical’ organism in the population.

This is true even in a game-theoretic context, so long as the organisms are playing a

symmetric game. So the fact that a population contains many organisms, whose fitnesses may

be compared, does not constitute an analogue of interpersonal comparability, so long as there

is a single fitness function. Different organisms exhibit different behaviours, hence have

different fitnesses; but this is simply the analogue of a rational agent receiving different

utility from different outcomes, which involves only intrapersonal comparison.

However some biological scenarios do involve multiple individuals with different

fitness functions. For example, in a symbiotic interaction, the individuals come from different

species (e.g. plants and fungi); the evolutionary analysis must then study both populations at

once. There are then two fitness functions, one for each population, from which the co-

evolutionary dynamics can be deduced. Or within a single population, there may be different

‘roles’, e.g. owner versus intruder, or predator versus prey, where a different fitness function

is associated with each role. (Such examples have often been studied using asymmetric game

theory.) More generally, biological scenarios that involve conflict of interest, e.g. between

queen and workers in an insect colony, or between nuclear and mitochondrial genes, or

between males and females, require us to consider multiple fitness functions. It is common to

use rational choice-theoretic concepts to describe such cases, e.g. by regarding the competing

genes or individuals as agents ‘trying’ to achieve incompatible goals.

In such ‘multiple individual’ cases, the analogue of the interpersonal comparability of

utility question does arise. What is the answer? Since biological fitness is in principle

absolutely measurable, it must therefore be fully comparable. However again, the real

question is whether all of this information is needed for evolutionary analysis. In the simplest

genetical models of co-evolution, which track genetic change in two separate populations of

interacting organisms, ratio-scale measurability is necessary, but different ratio-scales can be

used for the two populations. (This can be seen by applying the Price equation to two

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separate populations.) Thus in these cases, fitness satisfies what social choice theorists call

“ratio-scale measurability without interpersonal comparability” (cf. Hammond 2005).

The situation is slightly different in two-population evolutionary game theory, which

is often used to model asymmetric interactions. In that case, whether affine transformation of

one player’s payoffs, independently of the other players, has an effect on the solution orbits

depends on both the evolutionary dynamics that are assumed, and on whether the

transformation involves adding a constant or multiplying by a positive constant; see Weibull

(1995 p.174) for useful discussion.

The overall moral, then, is that the appropriate measurability and comparability

assumptions for biological fitness depend on what questions are being asked, and what

modelling assumptions are made. In principle, biological fitness is absolutely measurable and

hence fully interpersonally comparable, but for many purposes not all of this information is

needed; weaker assumptions would suffice. The situation is interestingly different from in

rational choice theory, where different measurability and comparability assumptions about

utility are also used in different contexts (e.g. ordinal non-comparability in consumer theory,

but cardinal unit comparability in discussions of utilitarianism). In this case, the different

possible assumptions require justification, in that it is an open question whether they make

sense metaphysically. In the biological case, by contrast, the issue is not whether a given

measurability / comparability assumption is metaphysically permissible, but whether it is

sufficient to allow the evolutionary analysis to be done.

Besides measurability and comparability, a related foundational issue concerns the

‘revealed preference’ construal of utility maximization. In orthodox rational choice theory,

utility maximization is usually given a strictly ‘as if’ construal. So to say that an agent

maximizes their utility, or expected utility, is not to speculate about their psychological

makeup, but simply to say that their preferences (or choice behaviour) conform to certain

axioms. This behaviourist understanding of utility is a key element in ‘revealed preference

theory’, and routinely taught in microeconomics courses, though it has not gone unchallenged

(cf. List and Dietrich’s contribution to this conference.)

What about biological fitness? Should fitness-maximization in biology also be

understood on the ‘revealed preference’ model? In one respect the answer is clearly yes.

Biologists who study organismic behaviour using the fitness-maximizing paradigm are

obviously not suggesting that organisms are consciously trying to maximize their fitness (or

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any other quantity); rather the suggestion is that natural selection leads them to behave as if

they were doing this. So the maximization is strictly in ‘as if’ sense, just like in utility theory.

But there is also a disanalogy. On the revealed preference view, preference is

conceptually prior to utility. Thus rational choice theorists begin their analysis of individual

behaviour by focusing on an agent’s binary preferences (or their hypothetical choice

behaviour) over a set of alternatives. The agent’s real-valued utility function is then

introduced as a representation of this preference relation. But in biology it is the other way

around. Talk of an organism’s ‘preferences’ and ‘interests’ is commonplace in biology, but

these notions are always derivative from the organism’s fitness function. To say that an

organism prefers outcome A to B, for example, means that the organisms receive a higher

fitness in A than B. So in this respect, the situation is the opposite from revealed preference

theory.

To illustrate this last point, consider the well-known conflict of interest that arises

between nuclear and mitochondrial genes in flowering plants over the sex-ratio of their host

plant. Mitochondrial genes are only transmitted in ovules, not pollen, so prefer that their plant

have an all-female brood. Nuclear genes generally prefer a fifty-fifty sex ratio (presuming

outbreeding and random mating). So the genes have opposing interests, and conflict is likely:

the mitochondrial genes will try to bias the sex ratio towards females, while the nuclear genes

will try to prevent this, leading to what is known as ‘intra-genomic conflict’. The key point is

this. Talk of the genes’ interests, preferences and aims is perfectly legitimate here, but it

derives from the underlying fitness functions. Suppose that in alternative A, the host plant’s

sex ratio is 3:1 in favour of females, while in alternative B it is 1:1; the total gametic output is

the same in both alternatives. Then, a mitochondrial gene has higher fitness in alternative A

than B, so ‘prefers’ A to B, so will ‘try’ to bring about A rather than B; while the reverse is

true for a nuclear gene. Thus the preference relations derive from the real-valued fitness

functions, not vice-versa.

Despite this difference, it could well be interesting to take a ‘preference first’

approach in evolutionary biology. For one aspect of the rationale for this approach in rational

choice theory is that preferences and choices are observable, while real-valued utility

functions are not. (This much is fairly uncontroversial.) This obviously applies to animal as

much as to human behaviour. So despite the conceptual priority of the real-valued fitness

function over the evolutionary ‘preferences’ that it induces, it could nonetheless be

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interesting to see if the former can be deduced from the latter. This is discussed further, with

a concrete example, in section 5 below.

4: Who is the rational agent, and what is their utility function?

In rational choice theory, the agent whose behaviour is studied is typically the individual.

There are attempts to treat supra-individual entities, e.g. groups or committees, as rational

agents in their own right (e.g. List and Pettit 2011); and the preference aggregation problem

in social choice theory is sometimes viewed as an attempt to say when ‘society as a whole’

may be regarded as having a rational preference; but in general rational choice theory is

committed to methodological individualism. This makes sense, since it is individuals who

have beliefs, preferences and make choices, in the first instance at least.

In evolutionary biology matters are rather different. Suppose we are persuaded of the

usefulness of applying the rational choice metaphor in an evolutionary context (in its

‘product’ version). Which biological entity should we treat as akin to a utility-maximizing

rational agent? ‘The individual organism’ is the natural answer, and indeed the standard one

in the literature. But there are two related complications. Firstly, it is often unclear what the

‘individual organism’ actually is; in plants, fungi and marine invertebrates, for example, we

find entities whose status as individuals, as opposed to colonies, is controversial. For

example, some biologists would regard a large aspen grove as a single biological with non-

contiguous parts (the trees); while others regard the trees themselves as the individuals.

Secondly, even when it is clear what the individual is, evolutionary theorists recognise that

sub- or supra-individual entities, e.g. genes and groups, can be ‘units of selection’, i.e. subject

to natural selection and thus something that can potentially be treated as a fitness-maximizing

entity.

It is this second problem that we will focus on here. The problem is intimately related

to the familiar ‘levels of selection’ question in evolutionary biology, which asks what the

entities are that natural selection chooses between (cf. Okasha 2006). Candidate answers

include genes, chromosomes, cells, individual organisms, groups and even species. This

question arises from two factors. The first is that the Darwinian process can be characterized

in purely abstract terms, as a process of differential survival and replication, in a way that

leaves open what the entities actually are whose survival and replication is at issue. The

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second is that empirically, organisms display certain traits, including behaviours, that do not

benefit them directly. Such traits do not appear designed to maximize the individual

organism’s fitness, so presumably have not evolved by a process of individual-level selection.

One example of such a trait is altruism, in which an organism performs an action

which benefits others at a personal cost. For example, in social insect colonies, workers

devote their whole lives to assisting the reproductive efforts of the queen, by tending the

larvae, foraging for food and defending the colony. Such workers typically leave no offspring

of their own (and are sometimes physiologically sterile), so have a personal fitness of zero.

One possible evolutionary explanation for the worker behaviour, first broached by Darwin

himself, is that the colony as a whole benefits; so the trait could have evolved by colony-level

selection. Alternatively it may be that the workers are looking after their indirect genetic

interests by helping relatives; see below.

Another example of a trait that is not individually beneficial is cytoplasmic male

sterility in hermaphroditic plants; this is related to the nuclear-mitochondrial conflict

mentioned above. Such plants typically need to make pollen and ova, in order to self.

However, sometimes they cease investing in pollen production completely, producing only

ovules. This ‘male sterility’ trait is detrimental for the fitness of the individual plant, yet is

quite common. The evolutionary explanation is that the genes responsible for the trait are

found in the mitochondria, which are only transmitted in females and thus have no interest in

their host plant producing pollen. The plant ends up with a sub-optimal trait – a lack of pollen

– but the mitochondrial genes reap a benefit.

4.1 Two ways of salvaging the rational choice metaphor

How do these complications affect the use of the rational choice metaphor in biology? At first

blush, they might seem to undermine it. If an organism exhibits traits that do not enhance its

fitness, surely it cannot be treated as akin to a utility-maximizing rational agent? But this is

too quick. What follows is a weaker conclusion, namely that the organism cannot be treated

as a utility-maximizer whose utility function is equal to its personal fitness function. This

leaves open the possibility that by appropriate choice of utility function, the rational choice

analogy can be restored, i.e. the organism may be maximizing some quantity other than its

own fitness. A second possibility is that the rational agent analogy does apply, but that the

playing the role of the rational agent, so doing the maximizing, is not the individual organism

but some other entity.

16

Interestingly, these two possibilities correspond to the two main ways that

evolutionary theorists have tried to account for the prevalence of traits that do not enhance

individual fitness. The first way is by invoking the inclusive fitness concept of Hamilton

(1964). Hamilton’s key contribution was to realise that in social situations, in which

organisms interact with genetic relatives, the classical measure of fitness – expected number

of offspring – is no longer the relevant quantity. An organism that behaves altruistically, by

sacrificing some of its personal fitness in order to help others, may be favoured by natural

selection, so long as the ‘others’ are relatives, rather than random members of the population.

The reason is that relatives share genes, so there is a certain probability that the recipient of

the altruistic act will itself be an altruist. Depending on the magnitude of the cost c incurred

by the altruist, the benefit b conferred on the recipient, and the coefficient of relationship r

between them, it is possible that the altruistic trait will spread by selection. (The coefficient

of relationship measures the genetic distance between altruist and recipient; it equals 1 for

clones, ½ for full-sibs and children, ¼ for grandchildren, 1/8 for cousins etc.).

This insight was captured in Hamilton’s famous rule (rb > c) for when a gene coding

for altruism will be favoured by natural selection; and in the idea that inclusive fitness, rather

than classical (or personal) fitness, is the quantity that organisms’ social behaviour should

appear designed to maximize. An organism’s inclusive fitness is defined as its personal

reproductive output, plus the weighted sum of the portion of each of its relatives’

reproductive output for which it is causally responsible; where the weights are the

coefficients of relatedness. Though it is the former idea – Hamilton’s rule – that enjoys pride

of place in most of the biological literature on social behaviour, it is the latter idea – inclusive

fitness maximization – that is more relevant for the rational agent view of evolved behaviour.

This latter idea, which is a kind of biological analogue of the ‘other regarding preferences’

posited by behavioural economists, suggests that the rational agent metaphor can be applied

to social behaviour, and to traits such as altruism, so long as the agent’s utility function is

taken to be inclusive fitness (cf. Grafen 2006, West and Gardner 2013, Queller 2011). This

idea is discussed further in section 5.

The second way that biologists have reconciled individually disadvantageous traits

with Darwinism is by arguing that the relevant biological unit, whose fitness is being

maximized, need not be the individual organism. Thus proponents of group selection, also

known as ‘multi-level selection’, argue that natural selection often acts at the group level,

favouring some groups over others, with the result that individuals will display traits that are

17

group-beneficial. An extreme version of this idea holds that certain biological collectives, e.g.

honey bee colonies, constitute ‘superorganisms’, in which the parts work largely for the good

of the whole, helping to maximize the group’s fitness. The remarkable complexity and

functional integration that such colonies exhibit lends credence to this view (cf. Holldobler

and Wilson 2009). Though widely dismissed in the 1960s, an attenuated version of the

superorganism idea has recently enjoyed a revival in evolutionary biology, in part because of

the realization that a multi-celled organism – the traditional ‘individual’ – is itself a highly

adapted, complex group of cells, and a eukaryotic cell is itself a group of smaller biological

units (cf. Maynard Smith and Szathmary 1995, Michod 1999). Since cells and multi-celled

organisms do clearly exist, the idea that evolution sometimes works for group advantage

cannot be dismissed.

The appeal to group advantage can be seen as an alternative way of trying to preserve

the rational agent model from the challenge posed by social behaviour. Whereas the inclusive

fitness approach retains the individual as the rational agent but posits a modified utility

function, the group selection approach treats the group rather than the individual as the

analogue of the rational agent, seeking to maximize a ‘group utility function’. Two

interesting questions them arise. Firstly, what is this group utility function? Second, what is

the relation between the ‘inclusive fitness’ and the ‘group advantage’ ways of trying to

accommodate social behaviour? I look at them briefly in turn.

In most though not all group selection models in biology, group fitness is defined as

average or total fitness of the individuals in the group; it is differential group fitness, so

defined, that drives the evolution of group-beneficial traits. (Many of these models are based

on a hierarchical expansion of the Price equation above, which involves partitioning the

covariance term into within and between group components; see Okasha 2006 for details.)

This suggests that the group utility function can be identified with average or total individual

fitness.1 If group fitness is defined this way, it follows that there is an interesting link between

the group fitness notion in biology and the utilitarian definition of ‘social utility’ in social

choice theory. In Okasha (2009) I exploited this analogy, by arguing that standard

axiomatizations of utilitarianism from social choice theory could be a given a biological

interpretation; this in turn allows us to characterize those situations in which group fitness

1 This is the choice of ‘group objective function’ used by Gardner and Grafen (2009) in their

study of the maximizing agent analogy as applied to groups.

18

cannot be defined as average or total individual fitness. My analysis was critiqued and

developed further by Bossert, Qi and Weymark (2013).

What about the relation between the inclusive fitness and group advantage

approaches? Biologists used to regard them as incompatible. Indeed, Hamilton’s work owed

much of its appeal to its ability to explain the evolution of pro-social traits from a strictly

individualistic perspective, without an appeal to group advantage (which for many biologists

remains a problematic notion.) This is the view expressed clearly in Dawkins (1976), for

example. However recently, many social evolutionists have converged on this idea that

inclusive fitness and group or multi-level selection models are ultimately equivalent, i.e. that

the choice is one of modelling preference, not empirical fact (e.g. Marshall 2011). This

equivalence thesis is supported by formal analyses showing that the correct condition for the

evolution of a pro-social behaviour can be expressed both ways. This is a surprising result, as

it suggests that it is partly a conventional matter whether the rational agent should be

identified with the individual or group. The matter is examined further in Okasha

(forthcoming).

4.2 The gene as rational agent

Certain traits that bring no advantage to the individual, such as the example of cytoplasmic

male sterility above, are not group advantageous either. To understand such traits, biologists

often adopt the ‘gene’s eye view’, and regard the trait as an adaptation designed to benefit the

gene that causes the trait, rather than the organism that expresses it. Usually, the interests of

any gene and its host organism co-incide; however in some cases a gene can profit at the

organism’s expense, by reducing the organism’s total fitness but accruing a larger share for

itself. This stems from the fact that, in sexually reproducing organisms, not all the genes in an

organism are transmitted intact to the next generation. Thus mitochondrial genes are only

transmitted in female gametes; while the nuclear genes are broken up by meiosis, so any

gamete only contain half of the complement of nuclear genes found in the host organism. As

a result, traits which are sub-optimal at the organism level can sometimes spread by natural

selection.

Such traits can be understood using the rational agent metaphor, so long as we take

the ‘agent’ to be the gene rather than the organism. The gene behaves as if it is trying to

maximize a utility function – which in this case, must be defined as the number of copies of

the gene transmitted in its host organism’s gametes. The gene ‘chooses’ the strategy that

19

maximizes this number; a side-effect of this is that the organism’s total gametic output may

be reduced, in which case there is a gene / organism conflict. So in this case, preserving the

rational agent view of evolution (in its ‘product’ version) requires descending to the level of

the gene, rather than ascending to the level of the group.

The idea of the gene as rational agent, ‘choosing’ between strategies so as to

maximize its representation in the next generation, may seem reminiscent of Richard

Dawkins’ ‘selfish gene’ concept. But there is in fact a crucial difference. Dawkins (1976)

applied his selfish gene analysis to all genes that evolve by natural selection, including those

that code for traits that benefit their host organism. His point was that all such genes are

‘trying’ to profit at the expense of their alleles in the population. However, our focus above

has been on genes that spread at the expense of their host organism. Such genes, which are

relatively rare, are sometimes called ‘ultra-selfish genes’, or ‘outlaw’ genes. Their

evolutionary dynamics can only be understood be focusing on gene-level, rather than

organism-level, advantage. It is only when studying genes of this sort, or their phenotypic

effects, that we are forced to treat the gene as the rational agent.

It is interesting to consider why it is usually possible to treat the whole organism as

the rational agent, i.e. why we only need descend to the level of the gene in special cases. The

reason is that organisms contain mechanisms designed to align the interests of their

constituent genes, i.e. to eliminate intra-individual conflict by ensuring that no ‘ultra-selfish’

genes can arise. Chief among these is fair meiosis (or Mendelian segregation), which ensures

that each nuclear gene has an equal chance of being passed to a gamete. When these

mechanisms do their job, they ensure that the only way a gene can benefit itself is by playing

a strategy (i.e. coding for a trait) which also benefits the host organism. It is then possible to

treat the whole organism as the adapted unit, since the interests of all of its constituent genes

become identical. Similarly, many apparent superorganisms, e.g. eusocial insect colonies,

contain mechanisms which serve to align the interests of the insects in the colony, i.e.

policing of selfish workers who try to lay their own eggs, rather than tending for the queen. If

the policing mechanism works well, then any worker can only further its own interests by

working for good of the whole colony. The general moral here, now widely accepted in

biology, is that for an entity to function as adapted unit, some mechanism is needed to align

the evolutionary interests of its constituents.

20

This moral is easily, and usefully, understood using the apparatus of rational choice

theory. In effect, conflicts of interest between genes and their host organisms (or organisms

and their host groups) arise when the preference orderings of the different genes, over the set

of alternative ‘outcomes’ that they can bring about, do not all coincide. Thus gene A would

prefer that the organism left 10 gametes, 80% of which contain A, than 15 gametes, 50% of

which contain A; however the organism itself, and all the other genes at unlinked loci, have

the reverse preference. Conflict-reducing mechanisms, such as fair meiosis and policing,

work by restricting the set of feasible outcomes; on the restricted set, interests are aligned.

Thus with Mendelian segregation in place, a gene cannot influence the proportion of the

organism’s gametes in which it is found, but only the total number of them; and it will prefer

that this number be as great as possible. Similarly, if a worker cannot lay eggs of its own, its

choices are restricted to actions that affect the queen’s reproductive output; it will prefer to

maximize this output. Thus we see how a simple rational choice analysis, drawing only the

concepts of preference ordering and feasible set, sheds light on the biology.

To sum up, organisms exhibit many traits that do not benefit them

individually. These are of two broad sorts: those that benefit relatives or fellow group

members, such as altruistic behaviours, and those that arise from ‘ultra-selfish genes’. Both

pose a prima facie challenge to the ‘rational agent’ view of evolution, but it can be overcome.

The former can be brought within the rational agent framework either by taking groups as the

agents or by letting the utility function be inclusive fitness; formally at least, these are

equivalent. The latter can be accommodated by taking genes, rather than their host organisms,

as the maximizing agents. In general, the organism can only be treated as the rational agent if

mechanisms are in place to unify the interests of its constituent genes.

5. Inclusive fitness maximization and rationality

Let us return briefly to the concept of inclusive fitness. As noted above, part of the appeal of

Hamilton’s inclusive fitness concept is that it promises to reconcile organisms’ social

behaviour, including altruistic acts, with the idea of individual maximization. This aspect of

Hamilton’s theory is emphasized by recent authors including Grafen (2006), West and

Gardner (2013) and Queller (2011). In effect, the idea is that an organism will choose

between different possible social actions by working out the inclusive fitness consequences of

each, then choosing the action with the highest inclusive fitness. Thus the key Darwinian idea

21

that evolved behaviour should appear ‘purposive’ can be retained, by taking the ultimate

purpose to be maximization of inclusive fitness.

This way of describing Hamilton’s theory suggests a natural connection with rational

decision theory, with inclusive fitness playing the role of the utility function. This connection

has been noted previously, but has rarely been developed in a systematic manner. One reason

for this is that biologists who have noted this connection, e.g. Grafen (2006), Queller (2011),

have not usually appreciated the ‘as if’ interpretation of utility maximization that is

customary in decision theory (i.e. the revealed preference approach). Thus although they

emphasize the connection between inclusive fitness and rational decision, they have not

sought to relate it explicitly to preferences or to patterns of choice behaviour.

In recent work, joint with John Weymark and Walter Bossert, we attempted to fill this

lacuna, by seeking to deduce the principle of inclusive fitness maximization from a more

primitive basis (Okasha, Weymark and Bossert 2014). To do this, we employed the

conventional decision-theoretic methodology of starting with an organism’s choice

behaviour, summarized in the form of a binary preference relation between actions; we then

sought axioms on this preference relation which are necessary and sufficient for the organism

to always choose between actions in accordance with inclusive fitness maximization. We

succeeded in axiomatically characterizing both inclusive fitness maximization itself, and a

variant that we dubbed ‘quasi-inclusive fitness maximization’ for use in situations when an

organism has incomplete information about degrees of relatedness.

A brief sketch of our model is this. We consider a set of individuals I = (1,...,n).

Individual 1 is the focal individual whose actions we are interested in; the other n-1 comprise

all the other individuals who might be affected by the focal individual’s action. There is a

fixed relatedness vector r = (r1,...,rn), where ri denotes the coefficient of relatedness between

the focal organism and individual i. Thus r1 = 1, and the higher the value of i, the closer the

genetic relation between the focal and the ith

individual. At a given point in time, the focal

individual can perform a number of different actions, each of which potentially affects the

personal fitness (expected no. of offspring) of each individual in the set I. We simply identify

an action with a payoff vector a = (a1,...an) Rn, where ai is the incremental personal fitness

gain or loss that individual i suffers as a result of action a. The set of all possible actions is

Rn; however only some of these may be feasible.

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The focal individual’s choice behaviour is described by a binary preference relation

≿r on the set of feasible actions. The relation ≿r indicates, for any two actions in the feasible

set, which the focal individual would (weakly) prefer, given the relatedness vector r. The

inclusive fitness of a feasible action a is defined as i

riai ; that is, it is a weighted sum over

individuals of the action’s payoff to each individual, with weights given by the relatedness

profile. If the focal individual is an inclusive fitness maximizer, then its preference relation ≿r

is represented by the inclusive fitness function; this means that for any pair of feasible actions

a and b, a ≿r b if and only if i

riai i

ribi . If the organism is a quasi-inclusive fitness

maximizer, it evaluates actions using a weighted sum of the payoffs, but where the weights

are not the true relatendness coefficients but rather any monotonic transformation of them.

Quasi-inclusive fitness maximization can be thought of as an ‘attempt’ to maximize inclusive

fitness for an organism that lacks knowledge about exact degrees of relatedness, but does

know who it is more related to than who.

There is an interesting formal link between inclusive fitness maximization and a

‘weighted utilitarian’ social objective function in social choice theory (see d’Aspremont 1985

or Bossert and Weymark 2004). The latter evaluates a social action by a weighted sum of the

utilities that the action has for each member of society. (In single-person decision theory, the

same functional form could also represent the preferences of someone who takes some

account of the interests of others.) This suggests that an interesting axiomatic characterization

of inclusive fitness maximization might be found by employing axioms analogous to those

used to characterize the weighted utilitarian rule in social choice theory.

In Okasha, Weymark and Bossert (2013) we pursed this line of thought, and found

axioms on ≿r that are necessary and sufficient for the focal individual to be an inclusive

fitness maximizer, and a quasi-inclusive fitness maximizer. The former result is simpler,

using just three axioms that we call Ordering, Focal Individual Monotonicity and Haldane.

Ordering is just the familiar requirement that ≿r be reflexive and transitive; Focal Individual

Montonicity says that if the focal individual can increase its own payoff while leaving

unchanged the payoff of all others, it will strictly prefer to do so. Haldane says that the focal

individual will be prepared to sacrifice x units of its own payoff, if by doing do it can boost

the payoff to the ith

individual by x/ri. (Recall that ri is the relatedness of the focal individual

23

to the ith

individual.) This axiom derives its name from the biologist J.B.S. Haldane’s famous

quip that he would jump into a river to save two brothers or eight cousins. So long as the

focal individual obeys these three simple axioms, this guarantees that it is an inclusive fitness

maximizer.

Our characterization of quasi-inclusive fitness maximization is more complicated, but

has one key advantage. Instead of the Haldane axiom, which is informationally quite

demanding in that it requires that the focal individual ‘know’ its degree of relatedness to

every other individual, this characterization uses an axiom called Nepotism, which says just

that the focal individual would prefer to help more closely than less closely related

individuals. This is a reasonable idealization of the actual powers of kin discrimination of

many social animals.

The significance of these results is three-fold. Firstly, they suggest a possible means

by which natural selection could ‘fine tune’ choice behaviour so as to maximize inclusive

fitness. Secondly, they suggest a way of empirically testing the hypothesis that animals

maximize their inclusive fitness (or something close), by observations of their binary choices.

If it could be shown empirically that an animal’s choices fail to satisfy any of our axioms, we

could immediately infer that they are not an inclusive fitness maximizer. Thirdly, they help

forge a link, both formal and conceptual, between the biologists’ concept of inclusive fitness

maximization and rational choice theory. The chief novelty here is not the suggestion that

inclusive fitness plays the role of the utility function, which has been made before, but rather

the use of a revealed preference approach and the axiomatic method.

6. Challenges to the rational choice analogy

I turn briefly to two interesting challenges to the use of the rational choice analogy to

understand evolved behaviour. Unlike the general objections to optimization discussed in

section 2, these challenges are specific: they describe particular scenarios when the

expectation that natural selection will give to rational behaviour is allegedly violated.

Interestingly, though the challenges involve quite different considerations, a general moral

emerges.

24

6.1 Sober and Skyrms on the correlated prisoner’s dilemma

The first example is an argument made by both Sober (1998) and Skyrms (1995)

(independently, and in slightly different ways). Consider a simple prisoner’s dilemma game,

below. In a rational choice setting, in which the payoffs denote utilities, it is widely agreed

that in the one-shot game the rational agent should play D (defect), as it strongly dominates C

(cooperate). Thus the expected utility of D must exceed that of C. This is so even if the agent

believes that its opponent is likely to play the same strategy that it plays, presuming the truth

of ‘causal decision theory’ (Lewis 1981), as the two players are causally isolated.

Player 2

C D

C (6, 6) (0, 10)

Player 1

D (10, 0) (2, 2)

Figure 2: Prisoner’s Dilemma

Suppose we now transpose to an evolutionary setting. We consider a large population

of organisms engaged in a one-shot pair-wise interaction; an organism’s type (C or D) is

hard-wired genetically, and the payoffs now represent increments of Darwinian (personal)

fitness. Which type has the higher fitness? As Skyrms observes, this depends on the pairing

assumption that we make. Under random pairing, in which the probability of having a C

partner is same for both types, it is obvious that type D must be fitter. The expression for the

fitnesses of the two types are then:

WC = 6. P(C) + 0.P(D)

WD = 10.P(C) + 2.P(D)

Where P(C) and P(D) denote the probabilities of being paired with a co-operator and a

defector respectively; these probabilities are given by the overall frequency of each type in

the population. As Skyrms notes, these expressions for expected fitness are identical to the

corresponding expressions for the expected utility in the rational choice context, calculated

using standard (Savage-style) decision theory. Under random pairing, the type with the

25

highest expected fitness chooses the action that confers the highest expected utility, so

evolutionarily optimal behaviour is identical to rational behaviour.

Skyrms argues that matters are different if there is correlated pairing. We must then

calculate the expected fitness of each type using the conditional probabilities of having a

partner of a given type, which may differ for co-operators and defectors. The resulting

expressions are:

WC = 6. P(C/C) + 0.P(D/C)

WD = 10.P(C/D) + 2.P(D/D)

where P(X/Y) denotes the probability of having a partner of type X, given that one is of type

Y oneself. It is easy to see that if the correlation is strong enough, i.e. the conditional

probability of having a C partner is sufficiently greater for C types than D types, then the C

type may be fitter overall. This is an instance of the familiar statistical phenomenon known as

‘Simpson’s paradox’.

As Skyrms insightfully notes, the expressions for the expected fitness in the case of

correlated pairing correspond to Richard Jeffrey’s recommendation for how to calculate

expected utility in individual decision theory, known as ‘evidential decision theory’ (Jeffrey

1990). The problem, however, is that Jeffrey’s theory is widely agreed to be flawed as a

model of rational decision: it enjoins the agent to co-operate in the one-shot Prisoner’s

dilemma if the agent is sufficiently confident that its opponent will play the same strategy as

it, i.e. to deliberate ignore the difference between causation and correlation! Skyrms assumes,

surely correctly, that this is irrational. So he concludes that with correlated pairing, “rational

choice theory completely parts ways with evolutionary theory. Strategies that are ruled out by

every theory of rational choice can flourish under favourable conditions of correlation” (1995

p.106).

Sober (1998) develops the same point slightly differently, in the context of discussing

what he calls the “heuristic of personification” in evolutionary biology. This heuristic is the

idea that “if natural selection controls which of traits T, A1,…,An evolves in a given

population, then T will evolve, rather than the alternatives, if and only if a rational agent who

wanted to maximize fitness would choose T over A1,…,An.” (1998 p.409). Sober maintains

that this heuristic is usually unproblematic but fails in certain contexts, one of which is the

one-shot Prisoner’s dilemma. The rational agent will never play co-operate, since it is strictly

26

dominated, Sober reasons; however it is possible that natural selection will favour co-operate

over defect if the requisite correlation exists, i.e. if the probability of having a cooperative

partner is sufficiently greater for co-operators than for defectors. Thus the heuristic of

personification fails: the rational strategy and the evolutionarily optimal strategy do not co-

incide.

These arguments are intriguing, but there is an obvious response, developed in detail

by J. Martens (forthcoming). In applying the rational choice model to evolution, there is no

particular reason to equate the rational agent’s utility function with the personal fitness

function (or some affine transformation thereof.) Martens observes that if we take the agent’s

utility function to be its inclusive fitness, then the divergence between rationality and

evolution that Skyrms and Sober call attention to immediately disappears. This can be seen

by simply transforming the above payoff matrix by adding to each player’s payoff in each

cell the quantity ‘r times my partner’s personal payoff’; where ‘r’ is defined as a difference in

conditional probabilities [P(C/C) – P(D/C)] (which is a suitable generalization of Hamilton’s

original definition of ‘r’ for phenotypic rather than for genetic evolutionary models).2 Then,

the condition for the rational agent to prefer strategy C coincides exactly with the condition

for evolution to favour that strategy.

The immediate significance of Martens’ point is that Sober and Skyrms were too

quick to argue that evolution and rational choice ‘part ways’, in this example. For there is no

particular reason to equate utility with personal fitness, even if it is a convenient starting

assumption. So Sober and Skyrms’ policy of transposing a payoff matrix from a rational

choice to an evolutionary context, by re-interpreting the payoffs as ‘personal fitness’ instead

of ‘utility’, is not the only way to proceed. Given that, in social contexts, personal fitness is

not the quantity that evolution will lead to individuals to maximize, it makes more sense to

use inclusive fitness as the payoff. Alternatively, we could simply adopt a revealed

preference approach, and define rationality as consistency of choice, rather than as

maximization of expected utility for a specific choice of utility function. Had Skyrms and

2 Note that this definition of ‘r’ is well-motivated, for it is a special case of a definition widely used in the

biology literature, namely the linear regression of partner genotypic value on actor genotypic value. (If we take

this ‘value’ to be 1 for C and 0 for D, then this linear regression simply is the difference in conditional

probabilities given in the text.) This statistical definition of ‘r’ generalizes the original genealogical definition of

Hamilton’s 1964 papers.

27

Sober proceeded this way, their ‘parting of ways’ argument would not have got off the

ground.

In a way, what we have here is an evolutionary analogue of a moral familiar from

behavioural economics; namely that certain patterns of choice behaviour that may appear

anomalous, e.g. ‘altruistic punishment’, can be easily rationalized by positing other-regarding

preferences. Such behaviours only threaten the utility-maximization paradigm if we insist that

an agent’s utility function depends only on their own (material) payoff; and there is no good

reason for that assumption. The situation is similar for the Skyrms / Sober claim that the

evolutionarily optimal and the rational strategies fail to co-incide in the one-shot prisoner’s

dilemma with correlated pairing: this is true only if the rational agent is assumed to care only

about their own (personal) fitness.

6.2 Robson and McNamara on risk preferences

A quite different reason for thinking that natural selection may give rise to irrational

behaviour emerges from the analysis of optimal choice in the face of risk / uncertainty. The

problem of how a rational agent should choose between risky options (lotteries) has a long

history, of course; the standard answer is given by expected utility (EU) theory, first made

explicit by von Neumann and Morgenstern (1944). Though numerous alternatives to EU

theory have been developed in the last thirty years, primarily because systematic violations of

EU have been repeatedly discovered, EU remains the normative standard for how an ideally

rational agent should make risky choices.

Interestingly, the problem of optimal choice in the face of risk also arises in

evolutionary biology (cf. Okasha 2011). A typical problem in this area is as follows. An

animal can forage either in a resource-rich area where there is a high risk of predation, or a

resource-poor area where there is a lower risk. More resources mean greater survival and thus

more offspring and higher Darwinian fitness. Which strategy should an animal choose? This

question has attracted a large literature, empirical and theoretical, in behavioural ecology,

much of it based on statistical decision theory.

This prompts the question: what is the relation between rational choice and

evolutionarily optimal choice under uncertainty? Specifically, will natural selection lead

organisms to exhibit choices that satisfy expected utility maximization? Many authors have

assumed that the answer to this question must be ‘yes’; in part, I suspect, because ‘expected

28

number of offspring’ is a commonly-used measure of biological fitness in non-social

situations. Thus it is natural to assume that, when faced with a choice between two lotteries,

(e.g. ‘½ chance of 10 offspring, ½ chance of none’ and ‘4 offspring for certain’), natural

selection will lead an organism to prefer the option with the higher expected number of

offspring. On average, organisms with such a preference will leave more offspring than ones

with any other.

However, matters are not quite so simple. It is well-known in evolutionary theory that

the average performance of a behaviour or strategy does not always determine its

evolutionary fate: variability in performance is often relevant too. Thus J. Gillespie (1977)

showed, for example, that in the face of certain forms of stochasticity in payoff, the fittest

genotype will in fact be the one that (approximately) maximizes:

Exp (no. of offspring) – f [Var(no. of offspring)].

where ‘Exp’ and ‘Var’ denote expectation and variance respectively and ‘f’ is an increasing

function. (Which function depends on the exact pattern of stochasticity.) Gillespie’s formula

is strikingly reminiscent of M. Allais’s famous critique of EU theory; Allais maintained, to

the consternation of orthodox EU theorists, that a rational agent would discount the expected

utility of an action by some positive function of the variance in utility (Allais 1953). This

suggestive link between Gillespie’s evolutionary analysis and Allais’s rational choice

analysis is examined further in Okasha (2011).

The question of evolutionarily optimal preferences was studied by A. Robson (1996)

and J. McNamara (1995) who arrived (independently) at similar answers. Both conclude that

evolution will only favour organisms that maximize expected reproductive output if the risk

they face is ‘idiosyncratic’ rather than ‘aggregate’. Idiosyncratic risk means that each

organism in the population faces an independent lottery over the possible outcomes. This is

plausible in certain cases: the chance that an organism is a victim of predation while foraging

is likely to be independent across organisms. However some risks are aggregate. If there is a

5% chance of a very harsh winter in a given year, in which food will be critically scarce, then

all organisms face a 5% chance of starving. The risk is perfectly correlated across organisms.

Purely aggregate and purely idiosyncratic risk are opposite ends of a spectrum; real cases will

often lie somewhere in between.

29

The significance of the aggregate/idiosyncratic distinction arises because what matters

in evolution is how well one does relative to the population. An organism that leaves x

offspring in a state of the world where the population leaves many offspring, may contribute

a smaller fraction of the population, so be less ‘fit’ in the relevant sense, than an organism

leaving y < x offspring in a state where the population leaves few offspring. With

idiosyncratic risk, then if the population is large enough, the number of offspring produced

will be (effectively) constant across states of the world, by the law of large numbers, and thus

the strategy with the highest expected number of offspring will be fittest. But where risk is

aggregate, this is not so. In that case, McNamara (1995) shows that the optimal strategy

requires that an organism calculate ‘expected’ no. of offspring using a distorted probability

distribution p*(s) over the states of the world, that places less weight on states where the

population as a whole does well, and more on states where it does badly, compared to the true

distribution p(s).

McNamara and Robson both conclude that with aggregate risk, evolution will favour

irrational behaviour. Indeed Robson (1996) argues that evolution will favour individuals

whose choice behaviour violates stochastic dominance, and are not even ‘probabilistically

sophisticated’; since an individual’s evaluation of a lottery (over possible nos. of offspring)

will not even be a function of the marginal probabilities that it faces. Thus consider two

lotteries, A and B. In A, with probability ½ every organism in the population leaves 9

offspring, and with probability ½ everyone leaves 1. In B, each organism either leaves 8.5

offspring or 1 with equal probability, but with independence across organisms. From a single

organisms perspective, A may seem better than B, since A stochastically dominates B (and

yields a higher expected number of offspring). But it follows from the Robson / McNamara

analysis that lottery B is evolutionarily preferable. Natural selection should lead organisms to

prefer B to A, in apparent violation of basic canons of rationality. So again, natural selection

and rational choice appear to ‘part ways’.

An interesting response to this argument comes from Grafen (1999) and Curry (2001),

who argue (in effect) that it rests on a restrictive assumption, namely that an individual’s

utility function must depend only on its own reproductive output. Modulo this assumption, it

follows from Robson’s and McNamara’s analysis that no utility function exists such than an

EU maximizer will be led to make evolutionarily optimal choices. But if we relax that

assumption, then EU maximization can in fact be recovered, simply by letting the

individual’s utility function, in a given state of the world, to be its reproductive output

30

divided by the population average. The expected value of this quantity, over states of the

world, is the criterion that matters for evolution. An organism with preferences that maximize

this quantity – expected relative fitness – will be favoured by natural selection.

It may seem odd that the same evolutionary model can imply that EU maximization is

satisfied and that it is violated. How can this be? In fact, there is no contradiction here. When

Robson argues that EU maximization is violated and Curry argues that it can be rescued, they

are (in effect) using different state spaces to set up the decision problem. They are both using

the traditional von Neumann / Morgenstern set-up, of a finite set of prizes (outcomes) and a

set of lotteries on those prizes over which the agent has a preference ordering. Robson is

assuming that the basic prizes, from which the lotteries are constructed, specify how many

offspring an individual leaves. Curry is assuming that the basic prizes specify how many

offspring an individual has relative to the population average. On the first state space,

evolutionary optimality requires violation of EU maximization, but on the second it does not.

In effect, this means that are dealing with a biological analogue of the well-known

moral that apparent irrationalities of choice can often be removed by enlarging the state

space. This general moral is familiar from discussions of the status of the von Neumann /

Morgenstern independence axiom, or the Savage sure-thing principle, in decision theory. It is

well-know that apparent empirical violations of these axioms can often be ‘explained away’

by positing an enlarged state space. It is intriguing to find an analogue of this issue arising in

evolutionary biology; see Okasha (2011, 2013) for further discussion.

To conclude the section, we have looked briefly at two arguments which suggest that

evolution and rational choice may ‘part ways’, in the sense that what is evolutionarily optimal

may not always correspond to what is rational. Both can in principle be defused by suitable

choice of utility function and/or suitable choice of state space. (The same defusing strategy

can be applied to a recent attempt, by Houston, McNamara and Steer 2007, to show how

evolution may lead to intransitive preferences, as its authors point out.) It is tempting to

suggest that this will always be possible, i.e. that any putative ‘parting of ways’ may be

eliminated by similar means. However this needs to be judged on a case-by-case basis; there

is no a priori reason to think it is true.

31

7. Conclusion

The thematic and formal connections between rational choice theory and evolutionary

biology, and the fruitful transfer of ideas from one field to another, have often been noted but

rarely been explored in detail. In this article I have tried to outline some of the key issues,

philosophical and technical, raised by the connections between the two fields, drawing on my

previous work.

Some of the main morals to emerge are as follows: (i) there is an important distinction

between using a rational choice analogy to understand the process and the product of

evolution; (ii) the traditional objections to optimization in biology complicate but do not

undermine the rational choice analogy; (iii) there are close parallels, but also differences,

between the utility maximizing paradigm of rational choice theory and the fitness-

maximizing paradigm of evolutionary biology; (iv) some biological phenomena require us to

think of the gene, rather than the individual, as the maximizing agent; (v) altruistic

behaviours can be accommodated either by thinking of the group as the rational agent, or by

taking the individual to be maximizing its inclusive, rather than personal, fitness; (vi) it is

possible to formulate inclusive fitness maximization using a ‘revealed preference’ approach,

by deducing it from axioms on choice behaviour; (vii) apparent cases in which evolution and

rational choice ‘part ways’ can often be defused by suitable choice of utility function and/or

by changing the state space of the decision problem.

32

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