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Sociality as a defensive response to the threat of loss
Johnson, Tim,* Myagkov, Mikhail§ & Orbell, John§
*
Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany.
§
Department of Political Science, University of Oregon, Eugene, OR 97403, USA.
As demonstrated by a generation of laboratory research, social exchange as
modelled by the prisoner’s dilemma is risky: Although people often do
cooperate—that is the central finding of such work—it is also clear that they often
defect. The decision to enter a PD game with a stranger (about whom one has no
good basis for predicting behavior) is, therefore, a risky “bet” that he or she will
cooperate. An extension of the standard paradigm has explored a range of
cognitive processes and individual differences bearing on the choice to enter such
games, but such work has not yet addressed the question of how people respond in
general to the risk that necessarily inheres in social relationships. That is what we
address here. From the well-known finding that people are risk averse in the
domain of gains and risk tolerant in the domain of losses, we predict that, with
game incentives constant, people will be more willing to enter social relationships
when game payoffs are framed as losses than when they are framed as gains. The
data strongly support this prediction, suggesting that human sociality may have
evolved more as a defensive response to the possibility of loss than an opportunistic
attempt to capture gain. .
Laboratory research investigating choice behaviour in the prisoner’s dilemma
behavior was originally focused on testing the prediction that rational people will
choose the dominant defect alternative, absent “extra-PD” incentives supporting
cooperation. Findings are, by now, unambiguous and well accepted: People often do
cooperate in such PD games (Camerer & Hogarth, 2003; Caporael, Dawes, Orbell, &
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van de Kragt, 1989; Dawes & Thaler, 1988; Ledyard, 1995), choosing against their
private interest and, thereby, producing greater social welfare.
Nevertheless, universal cooperation is seldom, if ever, observed in such
laboratory work, meaning that individuals confront the prior problem of deciding how
others are likely to decide in a prisoner’s dilemma-type game, thus whether they should,
or should not, enter such a game with “this” or “that” particular individual. This
question has also been addressed by a modified laboratory paradigm giving subjects the
option of playing vs. not playing PD as well as the “within game” choice between
cooperation and defection. The findings are diverse: Researchers have reported
evidence of cognitive processes that, for better or worse, influence this decision (Orbell
& Dawes, 1993) as well as a variety of individual and structural attributes that
encourage people to enter PD games—or discourage them from doing so (Mulford,
Orbell, Shatto, & Stockard, 1998; Schuessler, 1989; Yamagishi, 1988).
Yet neither of these literatures has addressed the manner in which people
respond to the inherent risk of entering particular PD games. In the natural world, of
course, we do the best we can, using whatever information or intuitions we can muster.
Yet this does not answer the fundamental question: If entering social relationships is
an inherently risky business, are we generally risk tolerant or risk averse when
confronting the possibility of social exchange relationships? Both possibilities have
been raised in academic and lay discourse. Risk tolerance has been casually assumed
since Aristotle’s famous comment about humans’ inherently social nature—viz, as
“social animals” perhaps we are predisposed to be relatively risk tolerant or
(equivalently) relatively trusting of potential partners. Risk aversion has been promoted
by much folk wisdom about how we should respond to others such as, most notably,
that one should “never trust strangers.” Once we have gathered appropriate
information about potential partners’ likely behavior, of course, they are no longer
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“strangers” and can be trusted or not as the information dictates. But the implication
here is that the default choice, absent such information, is to not enter such games with
them.
Well-known findings by Kahneman and Tversky (1985; 1982) suggest a more
complex possibility—that we are risk averse when payoffs involve gains but risk
tolerant when they involve losses. In these authors’ laboratory studies, subjects made
hypothetical choices across certain and risky alternatives that were framed, variously, as
involving losses and as involving gains, but with expected values of the risky and
certain alternatives the same across both frames. In one of their studies (Kahneman et
al., 1985), for example, subjects were asked to choose among certain and risky policies
that they would employ as medical personnel responding to a hypothetical health crisis.
The losses frame presented the certain and risky alternatives in terms of “lives lost”
while the gains frame presented them in terms of “lives saved.” The risky prospect was
chosen significantly more in the losses frame than in the gains frame. This finding has
been replicated using various contents, solidifying the general finding of risk tolerance
when facing loss and risk aversion when facing gain.
Figure 1 shows the utility function proposed by Kahneman and Tversky to
capture these findings. With subjective utility on the vertical axis and objective values
(e.g., lives saved or lives lost) on the horizontal, and with the status quo (everyone lives;
zero die) at the intersection, the function in the upper right quadrant indicates—
consistent with standard economic theory—declining marginal utility to gains (lives
saved), while the function in the lower left quadrant indicates steeply declining utility to
losses (lives lost). A unit loss from the status quo, according to this model, hurts
substantially more than a unit gain from the same point feels good, making the risk
more attractive than the certainty in the losses quadrant, and the certainty more
attractive than the loss in the gains quadrant.
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(Figure 1 about here)
Traditional expected utility theory, alternatively, does not distinguish between
losses and gains; instead, the theory assumes that the value of risky outcomes is
weighted by their probability of occurrence.1 The prediction from this model is
indicated by the dotted diagonal; value lost and value gained map in a linear manner
onto utility lost and utility gained. A more developed version of this model, employed
in much economic theorizing, proposes declining utility over payoffs in general. That
is consistent with Kahneman’s and Tversky’s model in the gains quadrant, but does not
address the shape of the utility function in the losses quadrant; by it, people are risk
averse in general.
What, then, of sociality—that is, interacting in exchange relationships with
(risky) others? Perhaps Kahneman’s and Tversky’s finding generalizes to include social
relations; perhaps, that is, the decision between entering vs. not entering risky social
relationships is governed by the same empirical regularity they document. If so, then
we should expect, ceteris paribus, people to be more willing to “take the social risk”
when payoffs are framed in terms of losses than when they are framed in terms of gains.
If, on the contrary, the more standard model applies to social relations, then no
difference between frames should be found. The following experiment was designed to
distinguish among these two hypotheses.
PD games in losses and gains frames
Here we report findings from a laboratory study in which subjects made real—not
hypothetical—choices between entering PD games with other subjects vs. receiving a
1
Or, in the subjective expected utility framework, the subjective probability of the
event’s occurrence.
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fixed payoff from not entering, and in which appreciable values were at stake. Because
a potential partner’s cooperate vs. defect choice could not be specified in advance,
subjects were operating under uncertainty rather than risk (Ellsberg, 1961), meaning
that the probability of the outcomes associated with the risky (PD play) alternative
could not be presented to them a priori in the manner of the Kahneman and Tversky
experiments. In contrast, our approach was to structure both the certain (don’t play) and
the risky (play) payoffs so they were equivalent in the “gains” and “losses” frames,
leaving any estimating of risk to the subjects themselves, should they choose to proceed
in that manner.
Figure 2 shows the choices and associated payoffs that subjects confronted in the
two frames. Critically, in the losses frame, they made their choices with a 10-point
endowment already in hand, meaning that payoffs from the experiment for subjects in
both conditions were equivalent. The two sets of cooperate and defect payoffs, as well
as the two fixed "no play" payoffs, are also incorporated in Figure 1, along with the
function from prospect theory. Note that, in both frames, the game theoretic expectation
of mutual defection makes the "no play" option dominate the "play" option.
(Figure 2 about here)
Assumptions and predictions
We develop the following model to distinguish the different predictions of expected
utility theory and prospect theory in this experiment. Assume that each individual has a
subjective probability Pci that he or she will encounter cooperation in a social
relationship being considered. Assume furthermore that Pci is itself a random variable
drawn from some distribution F ( F is the same for everybody). Individual i’s utility of
entering the PD game in the domain of gains ( UiG ) is as follows:
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UiG = Pci Ui (C) + ( 1- Pci ) Ui (D),
where Ui (C) and Ui (D) are, respectively, the individual’s utilities from encountering a
co-operator and defector. It is obvious that under the model’s parameters that there
exists a probability ( Pi*G ) such that an individual i would enter the game if
Pci >= Pi*G
and do not enter the PD otherwise. Individual i’s utility of playing the PD game in the
domain of losses is
UiL = Pci Ui (C) + ( 1- Pci ) Ui (D),
where Ui (C) and Ui (D) are individual respective utilities of encountering a co-operator
and defector. It is obvious that under parameters of our game there also exists a
probability ( Pi*L ) such that an individual i would enter the game if
Pci >= Pi*L
and not enter the PD game otherwise. If an individual is risk averse in both gains and
losses (viz. no framing effect is present) then
Pi*L = Pi*G
(1)
If an individual is risk averse in gains and risk seeking in losses (a framing effect is
present) then
Pi*L < Pi*G
From the model, therefore: (1) implies that there will be an approximately equal number
of subjects not entering the PD game in both gains and losses, and (2) implies that there
will be more people not playing the game in the domain of gains than in the domain of
losses.
(2)
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Method
Subjects were recruited from an undergraduate Political Science class addressing
substantially game theoretic themes. They played for points toward their final grade,
with the total number of possible points representing 4% of that grade; an alternative
written assignment was offered to any who chose not to participate, although none did.
We employed a between subjects design, with subjects randomly assigned to either a
gains condition or a losses condition. Subjects in the respective conditions met in sets of
between 5 and 20, depending on their availability. Human subjects forms were read and
signed. Participants in both conditions knew that they would receive 1% of their course
grade simply from participating. All subjects completed an initial task lasting about 15
minutes, with those in the losses condition being told that they had earned 10 points
from that task, some or all of which they could lose in the forthcoming decision task.
Instructions then read by the experimenter said that they would be making about six
strictly anonymous decisions paired with another individual. That other individual
could be in a different room of the same experimental session, but could also be drawn
from the whole subject population, making potential partners thereby effectively
“strangers” to each other. Subjects were made aware of this fact. The PD matrix for the
particular condition was then introduced and explained, along with the payoff for not
playing.
Both paired subjects had a veto on PD play; if one chose to play but the other
chose not to play, no game happened (although the cooperate vs. defect choice of the
former was still recorded). Both also knew that the other confronted exactly the same
options. All questions were answered as fully as possible, with the experimenter not
proceeding until he was satisfied that everyone understood what the condition in
question required; subjects were also assured that no deception was involved. Decisions
were made using pencil and paper, in strict privacy, thus with no opportunity for
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signalling among subjects. No feedback was given by the experimenters until, after the
experiment was completed and toward the end of the course, individuals’ payoffs had
been computed.
Findings
Table 1 shows that subjects were more willing to accept the risky PD game, and to
reject the certain “no play” payoff, in the domain of losses than in the domain of gains.
Although payoffs from the game and from the "no play" option were equivalent across
the two conditions, subjects chose the PD game in preference to the certain payoff in
80% of the losses encounters but in only 57% of the gains encounters.
(Table 1 about here)
Consistent with the dominance of defection in the PD, the incidence of
cooperating in joined games was low. The incidence of cooperation, however, was
essentially the same across the two frames (36% in gains, 35% in losses), consistent
with the possibility that intending co-operators and intending defectors responded to the
frame manipulation in the same way. Also consistent with that possibility, Table 2
shows that there is little difference between the number of “play and cooperate” choices
subjects made in the two frames.
(Table 2 about here)
Finally, and allowing for the 10-point starting endowment in the losses condition,
average payoffs for all subjects who joined PD games were 4.57 and 4.52 in the gains
and losses conditions, respectively. The marked bias toward entering PD games in the
domain of losses was, therefore, not justified by any greater returns subjects reaped
from acting on that bias.
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Discussion
We conclude that the decision between entering and not entering risky social
relationships is consistent with Kahneman’s and Tversky’s finding that individuals are
risk tolerant when confronting loss and risk averse when confronting gain. When
incentives are constant, people enter such relationships under both frames, but they are
significantly more willing to do so in response to the threat of loss than in response to
the possibility of gain. In an uncertain world, sociality appears to be more a defensive
response to the possibility of loss than an opportunistic attempt to capture gain.2
Kahneman’s and Tversky’s model (Figure 1) is a description of an empirical
regularity and their “prospect theory” is an extrapolation from that empirical regularity
to the decision processes underlying choice under risk. As we proposed at the outset, it
is quite possible that this regularity is general—that it applies equally to all situations
where humans confront choices between risky and certain prospects, including risky
choices about entering social relationships with other humans.
It is not evolutionarily satisfying, however, to conclude that a human propensity
to enter social relationships in the domain of losses more than in the domain of gains is
simply a function of a domain general response to risk. As Kahneman and Tversky and
others following them have developed their finding, it is “domain general”—that is, it
applies to all circumstances in which people are confronted by choices between risky
and certain prospects. Yet the case against domain general cognitive mechanisms has
2
We point out that our data also show that Kahneman’s and Tversky’s model
applies to at least one case where probabilities are not explicitly given; in fact, those
authors predicted that this would be so in their original paper.
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been well made in general (Leda Cosmides & Tooby, 1994; Pinker, 2002), and strong
empirical evidence supports domain specificity in the particular case of certain
cogitative mechanisms involved with social decision making (Leda Cosmides & Tooby,
1992). A great deal of human cognitive architecture is now believed to involve domain
specific, special purpose mechanisms that have evolved in response to the adaptive
problems presented by life in complex groups of conspecifics (see, e.g., Byrne &
Whiten, 1988; Whiten & Byrne, 1997). This line of thought invites speculation—just
so stories, no doubt—about our present findings in the same terms. Early humans
undoubtedly stood to gain much from joint, cooperative action, most obviously in
hunting and the search for food. But it is equally certain that they stood to lose a great
deal from the failure of collective action when confronting external threat, perhaps from
predators but perhaps also from other groups or coalitions of humans. In that context,
joining other group members in defensive collective action would make, we propose,
even better adaptive sense than joining with them in efforts to acquire gains from
collective action.
In short, our findings raise the possibility that pressures favoring sociality in our
adaptive past were stronger in the context of threatened losses than in the context of
promised gains. Clearly, this is a domain specific hypothesis, and it remains to be
shown whether the effect reported here is independent of any more domain general
bias—or, indeed, whether any seemingly domain general bias exists as a consequence
of the huge adaptive importance of our ancestors’ decision making in the broad domain
of social relationships.
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Figure 1. Kahneman’s and Tversky’s proposed utility function for decision making
under risk.
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[Figure 1 footnote] With objective payoffs in the two frames on the horizontal,
subjective utility on the vertical, and the status quo at the intersection, the basic
prediction from expected utility theory is the diagonal utility function—with theorists
also acknowledging declining utility with respect to gains. But Kahneman’s and
Tversky’s findings support the heavy curved function as characteristic of human
decision-making, turning attention in particular to the importance of the status quo. The
PD payoffs in the losses frame are to the left of the status quo and payoffs in the gains
frame are to the right of it; the status quo is zero in both frames. The two sets of payoffs
are the same when the 10-point starting payout in the losses frame is incorporated.
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Figure 2
The structure of decision making in gains and losses frames
GAINS FRAME
(no endowment)
No Play
Play
Other
Chooses
X
Gain 5 points
You
Choose You gain
X
8
You
Choose You gain
Y
10
Other
Chooses
Y
You gain
0
You gain
3
LOSSES FRAME
(10 point endowment)
No Play
Lose 5 points
Play
Other
Chooses
X
You
Choose You lose
X
2
You
Choose You lose
Y
0
Other
Chooses
Y
You lose
10
You lose
7
14
[Figure 2 footnote] Subjects in the gains frame were presented the top game tree, while
those in the losses frame were presented the bottom one.
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Table 1: Outcomes in the gains and losses frames
Number of
Number Total
encounters “do not
of
enter”
Subjects between
Number
(and %) of
“enter”
decisions
Number (and
%) of decisions
to cooperate in
joined games
Gains frame
Losses frame
206
(57.4%)
289
(80.3%)
75
(36%)
110
(35%)
subjects
decisions
60
359
153
61
360
71
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Table 2: The distribution of "play and cooperate" choices across the losses and
gains frames—with each subject making about six such choices
Strategy chosen
Loss frame
Gains frame
0 play and cooperate
1 play and cooperate
2 play and cooperate
3 play and cooperate
4 play and cooperate
5 play and cooperate
6 play and cooperate
Subjects
25
8
16
9
2
0
0
60
22
3
16
12
4
1
3
61
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