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Economic Man
—or Straw Man?
A Commentary
on Henrich et al
Ken Binmore
Economics Department
University College London
Gower Street
London WC1E 6BT, UK
Page 2
Economic Man—or Straw Man?
A Commentary on Henrich et al
by Ken Binmore
1 Ignoratio Elenchi
This commentary on the paper “Economic Man” in Cross-Cultural Perspective
[20] is fiercely critical, but the criticism is not directed at the anthropological field
work reported in the paper, which seems to me entirely admirable.
The criticism is directed at the editorial rhetoric that accompanies the scientific
reports of the experiments carried out in the fifteen small-scale societies studied.
The rhetoric is markedly more subdued than in the book Foundations of Human
Sociality [19] from which the current paper is extracted. (See Samuelson [27] for
a review.) However, the claim remains that “economic man” is an experimental
failure, and that we must seek an alternative paradigm.
This paper argues that the editors’ enthusiasm for this perennially popular claim
has led them into two mistakes. Philosophers call the first mistake the ignoratio
elenchi—the refuting of propositions that your opponent does not maintain. In
particular, it is not axiomatic in orthodox economic theory that human beings are
selfish. Even if such a proposition were axiomatic, the backward induction principle
the authors use when analyzing the Ultimatum Game would not follow.
The second mistake is that of neglecting to report data that does not support
their claims about “economic man”. In particular, although it is not axiomatic in
mainstream economics that human beings maximize their own income, there is a
huge experimental literature whose results are consistent with the hypothesis that
most people behave in this way after gaining sufficient experience of most tasks
they are set in the laboratory.
As a result of these mistakes, the editors contrive to treat conclusions of their
study that are broadly supportive of the game-theoretic approach to social norms
as though they were inconsistent with the principles on which game theory is based.
2 De Gustibus Non Est Disputandum
It is not true that “texbook predictions” based on Homo economicus incorporate
a “selfishness axiom”. The orthodox position amongst economists is embodied in
Paul Samuelson’s theory of revealed preference, which makes a virtue of refusing to
make any a priori hypotheses at all about what goes on inside people’s heads.
2
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The orthodox theory only requires that people behave consistently. It is then
shown that they will then necessarily behave as though they are maximizing some-
thing. Economists call this something utility, but they emphatically do not argue
that people have little utility generators in their heads. Still less do they argue that
people come equipped with mental cash registers that respond only to dollars.
Far from making it axiomatic that human beings maximize money, the orthodoxy
is that the nature of a person’s utility function must be determined empirically by
observing his or her choice behavior in some situations. If the person behaves
consistently, the utility function then serves as a tool in predicting how the person
will choose in other situations.
3 Empirical Data on Selfish Behavior
We have seen that Henrich et al [20] are mistaken in suggesting that it is axiomatic
in mainstream economics that people behave selfishly. Orthodox economic theory
leaves the question of how selfish real people actually are to be decided by empirical
means. However, Henrich et al are right that mainstream economists do commonly
think that we must expect to see a lot of selfishness from experienced subjects
in laboratory experiments. If they want to challenge this consensus, they need to
address the empirical evidence that mainstream economists offer in its support.
Henrich et al [20] tell us that “hundreds of experiments” show that subjects will
“sacrifice their own gains to change the distribution of material outcomes among
others”. We are not told that for every experiment whose results the authors
choose to interpret in this way, there are large numbers of other experiments in
which orthodox game theory predicts the outcome reasonably well on the naive
assumption that subjects who are sufficiently experienced behave as though simply
seeking to maximize their average payoff in money.
In neglecting to draw attention to this empirical fact, Henrich et al might feel
that they are entitled to ignore the experimental work of mainstream experimental
economists—like Vernon Smith and Charles Plott—on the grounds that market
institutions tend to make people behave selfishly. But even if experiments about
markets are omitted, there remains a huge literature in which subjects are reported
as learning to play like income maximizers in games that are not structured like
markets. This fact is now so trite that it is hard to get a paper published if its only
finding is that the subjects’ behavior eventually converges on a Nash equilibrium
in yet another game with money payoffs. One might conceivably argue that the
authors are entitled to regard such work—including my own—as dubious, because
it is carried out by economists who are supposedly biased in favor of a “selfishness
axiom” (Binmore [8, 9]). But I do not see how it is possible to justify passing over
the empirical evidence in the case of one of the games in their own experimental
repetoire.
The Prisoners’ Dilemma is the most famous example of a Public Goods game.
The essence of such games is that each player can privately make a contribution to
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a notional public good. The sum of contributions is then increased by a substantial
amount and the result redistributed to all the players. In such games, it is optimal
for a selfish player to “free ride” by contributing nothing, thereby pocketing his share
of the benefit provided by the contributions of the other players without making any
contribution himself.
We are told that students in such Public Goods games contribute a mean amount
of between 40% and 60% of the total possible, but that this “fairly robust” conclu-
sion is “sensitive to the costs of cooperation and repeated play”. But we are not
told how sensitive. In fact, the results are very sensitive indeed to repeated play. If
their remarks are intended to apply to all the games in their experimental repetoire,
then Henrich et al [20] stand the truth on its head when they claim that:
Initial skepticism about such experimental evidence has waned as subsequent studies
involving high stakes and ample opportunity for learning has repeatedly failed to modify
these fundamental conclusions.
This claim that learning can be disregarded is all the more remarkable in that some of
the authors—notably Camerer (author number four) [12, p.265]—have themselves
published experimental papers which confirm that it can often matter very much
indeed. In the case of Public Goods games, the standard result is exemplified by
the first ten trials of an experiment of Fehr (author number five) and Gachter [14]
illustrated in Figure 3.2 of Henrich at al [19].
Camerer explicitly endorses this result as standard in his recent Behavioral Game
Theory [12, p.46]. As he says, the huge number of experimental studies available
in 1995 was surveyed both by John Ledyard [22] and by David Sally [24], the former
for Roth and Kagel’s authoritative Handbook of Experimental Economics. After
playing repeatedly (against a new opponent each time), the much replicated result
is that about 90% of subjects end up free riding. One can disrupt the march towards
free riding in various ways, but when active intervention ceases, the march resumes.
I emphasize these conclusions because the orthodox view among mainstream
economists and game theorists who take an interest in experimental results is not
that the learning that might take place during repeated play in the laboratory is a
secondary phenomenon to which conclusions may or may not be sensitive. On the
contrary, the fact that laboratory subjects commonly adapt their behavior to the
game they are playing as they gain experience is entirely central to our position.
There is therefore no point in our critics endlessly refuting the proposition that
inexperienced or underpaid subjects in novel situations do not play as game theory
predicts. Everybody accepts that this is true most of the time.
Before leaving this subject, let me observe that nobody maintains that all sub-
jects learn to behave like selfish optimizers in all environments. The 10% or so
of subjects who choose to continue cooperating in Public Goods games in spite of
their experience are a small group, but nobody denies their existence. As for an
environment in which subjects do not seem to adapt their behavior as they gain
experience, we have the Ultimatum Game, discussed below in Section 6.
Nor does mainstream empirical work support the conclusion that most expe-
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rienced people have no other-regarding or social component at all in the utility
functions that describe their final choices. It only supports the conclusion that for
most adequately incentified people in most economic environments in developed
societies, the data can be explained without assuming that such an other-regarding
component is large. However, one would not expect the same conclusion in societies
where kinship is a major social factor.
Nor do mainstream economic theorists hold that the small deviations from selfish
optimization that may well occur in situations in which the hypothesis of income
maximization predicts the data well are necessarily unimportant in other situations.
On the contrary, one of the advantages of a game-theoretic approach is that it is
capable of predicting that such small deviations are likely to have large effects in
certain sensitive games—like the finitely repeated Prisoners’ Dilemma mentioned in
Section 4, or the Public Goods Game with Punishment that is the subject of the
second ten trials in Figure 3.2 of Henrich et al [20].
4 Social Norms as Equilibria in Games
Up to now, this commentary has focused on what orthodox economic theory does
not maintain, but one may reasonably ask what positive insights orthodox economic
theorists think they may be able to contribute to anthropological studies of small-
scale traditional societies.
Our view is that the simplest game that can reasonably model life in such a
community is an indefinitely repeated game in which the players always remain
the same. There is a simple theorem called the folk theorem that applies to those
indefinitely repeated games in which the players have no secrets from each other and
care a lot about their own future welfare.
1
The folk theorem says that such repeated
games always have a large number of Nash equilibria—which is the concept that
game theorists use to predict the behavior of experienced players. The theorem says
that any outcome on which the players might want to contract in the presence of an
external agency ready and willing to enforce contracts is available as an equilibrium
outcome if the players are sufficiently forward-looking.
The significance of this result is that Nash equilibrium outcomes do not need
external enforcement to be viable. They are self-enforcing, since nobody can gain
by deviating from a Nash equilibrium unless someone else deviates first.
Axelrod’s [2] widely cited Evolution of Cooperation is misleading on the subject
of repeated games, not least because his emphasis on the tit-for-tat strategy dis-
tracts attention from the important fact that there are always many Nash equilibria
that support efficent cooperation among the players. Like the tit-for-tat strategy,
all such equilibrium strategies require behavior that would normally be described as
1
The theorem is called the folk theorem, because nobody knew to whom it should be attributed
when it was discovered simultaneously by a number of game theorists in the early 1950s. Aspects
of the folk theorem have been repeatedly rediscovered, notably by Boyd (author number two) and
Richerson [11] in 1992, Axelrod [2] in 1984, and Trivers [30] in 1971.
5
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embodying a strong respect for both reciprocity and reputation—even though no
concern for such emergent phenomena need be built into the utility functions as-
signed to the players. Experimental findings that reciprocity and reputation matter
in some social interactions therefore come as no surprise to orthodox game theorists.
The biologist Robert Trivers [30] says that strategies which support full coopera-
tion in repeated games exhibit reciprocal altruism. He cares about this phenomenon
because Nash equilibria do not only describe the outcome of rational play; under
appropriate conditions, they also describe the end-product of evolutionary processes.
It is therefore of some importance that the only one of Axelrod’s conclusions that
seems to be genuinely robust is his claim that we should normally expect the kind
of evolutionary computer simulations that he pioneered to lead to efficient (fully
cooperative) Nash equilibria (Binmore [4, p.313]).
A social norm can be seen as a device for solving the equilibrium selection
problem that the folk theorem says is built into a society’s indefinitely repeated
“game of life”. We then obtain a putative explanation for the cultural evolution of
different social norms in different societies. The folk theorem therefore provides a
theoretical backdrop for the ideas on cultural evolution pioneered by Boyd (author
number two) and Richerson [10, 11].
The important point is that only the Nash equilibria of a society’s game of life
can be evolutionarily stable, but nothing says that evolution must select the same
equilibrium in different societies. (See Samuelson [26] and Young [31].) Just as the
French use the Nash equilibrium for the Driving Game in which everyone drives on
the right and the English use the Nash equilibrium in which everyone drives on the
left, so we must expect different social norms that select different equilibria to have
evolved in different societies.
The social norms that interest me most are those that we normally describe in
terms of fairness or justice (Binmore [3, 4]). My recent Natural Justice [5] offers
an algebra-free version of my theory of fairness that draws on both psycholological
and anthropological thinking. In passing, I try to explain that the reason neo-
conservative economists see no role for fairness in their models of the world is that
their absurdly over-simplified models only have one equilibrium, and so there is
no equilibrium selection problem for fairness to solve. I do not like the policies
advocated by such economists any more than the authors of the paper we are
discussing, but the answer is not to throw the baby out with the bathwater by
seeking to discredit the basic methodology of economics using whatever rhetoric
seems currently persuasive, but to direct the attention of neo-conservatives toward
economic models that are genuinely descriptive.
Game theorists think the folk theorem is particularly relevant to the social
norms (or social contracts) of small-scale societies, because—unlike our own large
societies—the no-secrets proviso of the folk theorem has a good chance of being
reasonably descriptive. It is no problem that kinship is likely to be an important
explanatory variable in such societies, because we can simply write this fact into a
player’s utility function using an appropriate version of Hamilton’s rule before ap-
pealing to the folk theorem. (Remember that the idea that our theories necessarily
6
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depend on a “selfishness axiom” is a canard.)
If this attempt to apply game theory in an anthropological context has some
descriptive validity, what should we expect to happen when we ask inexperienced
subjects from small-scale societies to participate in a novel laboratory game de-
signed to provide information on how people respond to situations involving social
phenomena like fairness, trust, or reciprocity? The answer that seems obvious to
me is that we should expect them to behave as they would behave in real life if
they were offered similar cues to those offered in the laboratory. That is to say, we
should use whichever equilibrium their own society operates in its repeated game of
life to predict their intitial behavior, rather than one of the equilibria of the one-shot
game they are required to play in the laboratory.
And this seems to be broadly what happens. As Henrich et al [20] say: “Ex-
perimental play often reflects patterns of interaction found in everyday life.” The
anthropologist, Jean Ensminger (author number ten), is more explicit when com-
menting on why the Orma contributed generously in her Public Goods Game:
When this game was first described to my research assistants, they immediately iden-
tified it as the ‘harambee’ game, a Swahili word for the institution of village-level
contributions for public goods projects such as building a school. ...I suggest that
the Orma were more willing to trust their fellow villagers not to free ride in the Public
Goods Game because they associated it with a learned and predictable institution.
While the game had no punishment for free-riding associated with it, the analogous
institution with which they are familiar does. A social norm had been established over
the years with strict enforcement that mandates what to do in an exactly analogous
situation. It is possible that this institution ‘cued’ a particular behavior in this game
(Henrich at al [19, p.376]).
The enforcement here is enforcement by the players themselves as envisaged in
the folk theorem, and not external enforcement by the government. (National or
cross-regional attempts at harambee collections are predictably corrupt.)
If Ensminger is right, then it would be a huge mistake to try to explain the be-
havior of the Orma in the Public Goods Game on the hypothesis that their behavior
was adapted to the game they played in her makeshift laboratory. In particular, in-
venting other-regarding utility functions whose maximization would lead to generous
contribution in the Public Good Game would be pointless. Ensminger is suggesting
that the subjects’ behavior is adapted to the Public Goods game embedded in the
repeated game that they play every day of their lives, for which the folk theorem
provides an explanation that does not require us to invent anything at all.
Of course, if the subjects play a laboratory game repeatedly (against a new op-
ponent each time), then mainstream economic theory predicts that their behavior
would eventually diverge from the equilibrium of the repeated game they are accus-
tomed to play in real life to some equilibrium of the one-shot game they are actually
playing in the laboratory.
2
As observed in Section 2, contrary to the impression given
2
There is a risk of confusion when the repeated play of a one-shot game is under discussion.
The assumption is then that players never expect to interact with their current opponents again.
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by Henrich et al [20], such adaptation to the strategic realities of the actual game
being played is uncontroversially the norm in most economic experiments carried
out with western undergraduates.
To what extent does such trial-and-error learning occur in the societies studied
in “Economic Man” in Cross-Cultural Perspective? I do not know the answer
because no data on this subject is reported, either in the paper or in the book from
which it was extracted. My guess is that in most—perhaps all—of the experiments
the subjects never played the same game twice, as is clearly the case in Ensminger’s
account of her experiment. If so, then these experiments did not offer “ample time
for learning”. They offered no opportunity for learning at all.
The results of the experiments are therefore incomparable with the mainstream
experimental-economics literature in which income-maximizing behavior is com-
monly reported only after the subjects have had the opportunity to learn about
each other and the game they are playing. But the rhetoric adopted by Henrich et
al [20] obscures this point by pretending that no account need be taken of learning
when discussing the data on inexperienced subjects to which they choose to restrict
their attention.
However, far from their findings flying in the face of orthodox wisdom, they
seem rather to constitute an endorsement of the game-theoretic approach. Game
theorists are not in the least surprised to find that the data supports the view that:
As a consequence of these adaptive learning processes, societies with different historical
trajectories are likely to arrive at different social equilibria.
Henrich et al [20]
But game theorists go further by predicting that when the game of life being played
by a society changes, then its social norms will also eventually change by ceasing to
coordinate behavior on an equilibrium of the old game and coordinating behavior
instead on an equilibrium of the new game. When the anthropological authors of
“Economic Man” in Cross-Cultural Perspective write on their own behalf, they
seem to agree. For example, Michael Alvard (author number eight) tells us that:
As the results in this volume show, people do not universally play fair. The question
is no longer why people seem to have a preference for fairness. The question is now:
do people behave more or less fairly in adaptive ways?
Henrich et al [19, p.433]
We differ only in never having thought that the way to model fairness is to write a
taste for fairness into the utility functions of the players.
3
It is interesting that the change in the economic means of production recently
forced on the Ache of Paraguay provides a natural experiment on this issue. Our
Unlike the repeated games to which the folk theorem applies, selfish optimizers will then have no
reason to take account of either reciprocity or reputation.
3
Ernst Fehr (author number five) has been prominent in offering experimental evidence to the
contrary, but we do not accept that his claims are supported by the data. Shaked [29] provides
documentation in the case of Fehr and Schmidt’s [15] theory of inequity aversion. Fehr and
Schmidt’s [16] reply to Shaked’s intemporate note makes it clear that they are indeed guilty of
what seem to me the more telling of Shaked’s accusations of unscientific practice.
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prediction would be that the Ache would begin by trying to operate on the basis of
the same social contract that they operated as hunter-gatherers—which might be
idealistically described by saying that each contributes according to his ability and
receives according to his need. But the result of applying such a social contract is
not likely to be an equilibrium of their new farming game, because one would expect
the old social norms to be destabilized by the emergence of free riders. Cultural
evolution should then be expected eventually to generate new social norms that do
succeed in coordinating the players’ behavior on an equilibrium of the new game.
Judging from experience elsewhere, these new social norms would incorporate a
stronger sense of private property and less social sharing.
It is hard to estimate the extent to which Ache social norms are adapting to their
new game of life from Hill (author number twelve) and Gurven’s (author number
fourteen) [19, p.338] account, but mainstream economists would be surprised if the
Ache do not eventually adapt to their new environment in much the same way as
western undergraduates adapt to the one-shot Prisoners’ Dilemma.
5 Backward Induction
This section returns to the theme that the economic man of “Economic Man”
in Cross-Cultural Perspective is made of straw. The authors proceed as though
their “selfishness axiom” predicts that only subgame-perfect Nash equilibria will
be observed. That is to say, that players will solve games by backward induction,
as described for the Ultimatum Game in their paper. The same line is taken on
“income maximizing” in Henrich et al [19].
It is hard to believe that the economists on the panel of authors do not know
that this claim is at best controversial. To defend backward induction, one needs
not only that it is common knowledge among the players that they are all utility
maximizers, but that they disregard any evidence to the contrary that they might
receive when playing the game.
To see how unreasonably strong such assumptions are, consider the game ob-
tained by repeating the Prisoners’ Dilemma 100 times. The only subgame-perfect
equilibrium of this (finitely repeated) game requires that both players always plan to
defect at every repetition. But this is not what is observed in the laboratory. Most
experienced subjects cooperate until the closing stages of the game, at which point
they try to take advantage of their opponent by being the first to defect (Selten
et al [28]). However, nobody thinks that such results refute an income-maximizing
hypothesis, because of the famous gang-of-four paper, which shows that behavior
like that observed in the laboratory would be optimal in the presence of a tiny
fraction of “irrational” players who always play the tit-for-tat strategy. (See Kreps,
Milgrom, Roberts and Wilson [21].)
The gang-of-four idea can be generalized to a wide variety of games, so that
even if you held the unorthodox view that income maximization alone necessarily
requires the play of a subgame-perfect equilibrium, you would have to concede that
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the introduction of small perturbations to the game under study can force you to
change your prediction to some other Nash equilibrium of the original game. (See
Fudenberg, Kreps and Levine [17].) Moreover, evolutionary modeling shows that it
is very easy indeed for an adaptive process to converge on Nash equilibria that are
not subgame-perfect, or which are weakly dominated. (See Samuelson [25].)
Game theorists were admittedly sold on the idea of subgame-perfect equilibrium
some twenty years or so ago, but theoretical results like those mentioned above have
led to the idea falling into disfavor. The modern view is that no Nash equilibria can
safely be eliminated by appealing to “rationality refinements” that go beyond the
assumption that both players know the other is a maximizer of utility. This theo-
retical rejection of backward induction is supported by a large body of experimental
papers, the most convincing of which is that of Camerer et al [13]. Backward
induction does not even work in two-stage Ultimatum Games, when one is allowed
to attribute to the players the kind of inequity-averse social preferences favored by
Fehr and Schmidt (Binmore et al [7]).
There remain economic theorists like Aumann [1] who defend backward induction
as rational play in very idealized circumstances, but nobody, including Aumann
and his followers, believes in using subgame-perfection for predictive purposes in
laboratory experiments.
The seemingly interminable multiplication of cases in which backward induction
fails to predict human behavior in the laboratory is therefore pointless. The claim
that income maximization entails backward induction is not so much a straw man
as a dead horse. I do not know of any economist using income maximization for
predictive purposes in their experiments who feels at all threatened when shown yet
another example in which backward induction fails. They all know that you need a
lot more than straight utility maximization to justify backward induction.
6 Ultimatum Game
All these issues come to a head in any discussion of the Ultimatum Game, which is
the game on which the authors of “Economic Man” in Cross-Cultural Perspective
concentrate. I hope to explain here why it would be hard to find a game to study
in the laboratory less well suited to refuting orthodox economic theory if that were
your aim.
In the Ultimatum Game, a sum of money can be divided between Alice and Bob
if they can agree on a division. The rules are that Alice proposes a division and that
Bob is then restricted to accepting or refusing. The game was originally proposed
by Reinhard Selten—the inventor of subgame-perfect equilibrium—to his student
Werner Guth as an example in which subgame-perfection would be unlikely to work
in the laboratory. Guth [18] and his coworkers confirmed Selten’s intuition, and
thereby created a small experimental industry in which their results are endlessly
replicated.
If the subgame-perfect equilibrium (in which Bob acquiesces when Alice demands
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almost all the money) were the only Nash equilibrium of the game, then the fact
that Alice’s modal offer in the laboratory is a fifty:fifty split would be a serious
challenge to game theory, since this conclusion is indeed robust when the amount
of money is made large or repeated play (against a new opponent each time) is
allowed.
However, the Ultimatum Game actually has many Nash equilibria. In fact, any
split of the money whatsoever is a Nash equilibrium outcome on the income maxi-
mizing hypothesis. Not only does the Ultimatum Game have many Nash equilibria,
but computer simulations show that plausible models of adaptive learning can easily
converge on one of the infinite number of Nash equilibria that are not subgame-
perfect (Binmore, Gale and Samuelson [6]).
The same computer simulations show that one must expect any convergence
that takes place to be very slow. (See also Roth and Erev [23].) Figure 1 shows one
of the very large number of computer simulations reported by Binmore et al [6].
The original sum of money is $40 and the simulation begins with Alice offering
Bob about $33, leaving $7 for herself. One has to imagine that the operant social
norm in the society from which Alice and Bob are drawn selects this Nash equilibrium
outcome from all those available when ultimatum situations arise in their repeated
game of life. However, this split (like any other split) is also a Nash equilibrium
outcome in the one-shot Ultimatum Game.
The figure shows our (perturbed replicator) dynamic leading the system away
from the vicinity of this (7, 33) equilibrium. The system eventually ends up at
a (30, 10) equilibrium. This final equilibrium is not subgame-perfect (where the
split would be (40, 0)), but this fact is not the point of drawing attention to the
simulation. What is important here is that it takes some 60,000 periods before
our simulated adaptive process moves the system any significant distance from the
vicinity of the original (7, 33) equilibrium. This enormous number of periods has to
be compared with the 10 or so commonly considered “ample” for adaptive learning
to take place in the laboratory.
More generally, if a society’s social norms lead inexperienced players to start
playing close to a Nash equilibrium of a one-shot laboratory game, then, if there
is any movement away from the original Nash equililibrium at all due to adaptive
learning, we must expect such movement to be very slow at the outset. As a
consequence, the much replicated results in the Ultimatum Game represent no
threat to the income-maximizing hypothesis.
To threaten the income-maximizing hypothesis, one needs to use a game that
does not share the pathologies of the Ultimatum Game described above. Such a
game would not confuse the issue by having a huge number of Nash equilibria. Nor
would simple models of adaptive learning converge only with glacial slowness. The
Prisoners’ Dilemma meets both criteria without difficulty—but we have seen that
90% of subjects eventually end up acting as though they were maximizing their
income in the one-shot Prisoners’ Dilemma.
11
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Figure 1
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7 Conclusion
Economic theory is a popular target for those who would like to live in a fairer
world, but we need not believe the claims made by irresponsible neo-conservative
economists when they claim that equity is incompatible with efficiency. We certainly
do not need to attack the principles of orthodox economic theory in order to show
that they are wrong. It is even less necessary to follow the authors of the rhetoric
in “Economic Man” in Cross-Cultural Perspective and Foundations of Human
Sociality by misrepresenting what these principles are.
It is an enormous pity that the gathering of the kind of quantitative anthropo-
logical data reported in these works should have been left until many traditional
societies are on their last legs, and others have vanished altogether. It would be an
even greater pity if the small amount of data available were to be discredited by the
way it is presented.
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[4] K. Binmore. Just Playing: Game Theory and the Social Contract II. MIT
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[5] K. Binmore. Natural Justice. Oxford University Press, New York, 2005.
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