Sociality As a Defensive Response to the Threat of Loss

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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, & 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 “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.

(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 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:

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 (2)

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.

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 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.