The questions of whether people form expectations about others in social dilemmas and whether such expectations affect strategic decisions are separable. With regard to the first question, there is empirical support for the idea that people form expectations projectively: they think that others are likely to choose whichever strategy they themselves prefer. Dawes et al. (1977) presented evidence for this hypothesis (see also Messé and Sivacek, 1979) and Dawes (1989) derived a Bayesian rationale for why people should use their own strategic choice as a projective cue to predict the choices of others, and proved by backward induction that even a sample of one ought not be ignored lest a sample of any size would have to be ignored. This logic is particularly compelling in an information-poor environment such as an anonymous one-shot social dilemma.

With regard to the second question, it has been argued that once projection is admitted as a judgment heuristic, it cannot be ignored as a decision heuristic (Krueger and Acevedo, 2005). In the PD, for example, the rational expectation that most others – by definition – are more likely to make the same instead of a different choice will leave a person caught between the prospects of mutual cooperation and mutual defection. Being able to only predict mutuality by using the projection heuristic, a self-interested player has no reason not to choose cooperation. Choosing cooperation does not imply a magical belief that the other person’s behavior can be influenced but simply reflects respect for the statistical rule that one’s own choice is diagnostic of the choices of most others (Krueger, 2013; Krueger and Acevedo, 2005; Krueger et al., 2012). Social projection is beneficial in the PD because mutual cooperation is best for both the individual and the group, whereas in the VoD, projection is problematic because mutual cooperation (2R) is worse than unilateral cooperation (T+R). Ideally, a player would choose whichever strategy the other player is not choosing. If Tom knows that Dick volunteers, Tom defects. If Tom knows that Dick defects, Tom volunteers. The structure of the VoD thus challenges the human tendency to project. A player who volunteers and then estimates that the other player will also volunteer will be dissatisfied with the prospect of mutual, that is, inefficient, volunteering. A player who defects and then estimates that the other player will also defect will be unhappy with the prospect of mutual loss. In other words, these players find themselves in Popper’s dilemma of love.

If the VoD does not reward social projection, one might think that projection is low or even reversed in this dilemma. Our working hypothesis, however, is that projection will be strong nonetheless. We draw this hypothesis from past research, which has shown that projection is a reliable social heuristic even under conditions discouraging its use (Krueger and Clement, 1994; Krueger, 2003). We predict that in the VoD players’ strategy choices will be positively correlated with the choices expected of others.¹

Classic game theory is not concerned with individual differences, identity, or social categories. The theory does not simply happen to ignore such variables. Its axioms affirm their irrelevance. There is only one standard of rational choice, and everyone is assumed to meet it. In contrast, social psychology and evolutionary psychology recognize the relevance of prosocial motives and how these motives are differentially activated by the nature of the relationships between or among actors (Murphy and Ackermann, 2014; Kurzban et al., 2015). The broadest generalization emerging from theory and data is that the probability of prosocial choice decreases with social (or psychological or genetic) distance. Hamilton’s (1964) theory of inclusive fitness provides an elegant Darwinian rationale. Assuming that the survival of genes is the ultimate adaptive coin, organisms will make sacrifices if and only if the net effect on the survival of their genes is positive. Prosocial behavior will therefore decrease as the beneficiaries of these sacrifices become biologically more distant. In a classic study, Burnstein et al. (1994) showed that people come to the aid of close over distant kin in hypothetical life-and-death scenarios, whereas less serious contexts activate social norms concerning need and deservingness. Genetic relatedness is difficult to display and assess, and humans and other animals have evolved a range of cues to honestly or deceptively signal relatedness (Dawkins, 1976). Perhaps the crudest way to differentiate between close and distant others is to categorize them into ingroups and outgroups. The general finding is that people like their ingroups more than outgroups (Krueger and DiDonato, 2008), describe them in more favorable terms, and – importantly – are more willing to help ingroup than outgroup members in need (Rabbie and Horwitz, 1969; Tajfel and Turner, 1979; DiDonato et al., 2011).

From the perspective of biology, anthropology, and psychology, “bounded prosociality” is a stylized fact (De Dreu et al., 2015). Its robustness presents a challenge to traditional game theory. There is much evidence to show that people cooperate more readily with presumed ingroup members than outgroup members in a variety of social dilemmas (Balliet et al., 2014). Importantly, the increased willingness to cooperate in the context of “parochial morality” comes with the expectation that ingroup members, but not outgroup members, will also cooperate (Yamagishi and Kiyonari, 2000; Brewer, 2008). In other words, differential projection (Robbins and Krueger, 2005) tends to be accurate. Extrapolating from this research, we hypothesize that people’s readiness to volunteer and their expectations that others will volunteer both diminish over social distance. Although such a decline runs counter to the precepts of traditional game theory, it is consistent with certain social preference models of interdependent behavior (e.g., Van Lange, 1999; Fehr et al., 2005; Archetti, 2009).

Archetti (2009) developed a social-preference model to quantitatively predict the probability of volunteering for degrees of social distance. With our payoff notation, Archetti’s (2009, p. 476) equation becomes pv=1−T−R(T−P)⋅[1+(1−d)]. The probability of volunteering, p_v, increases as the temptation to defect, T - R, or the cost of mutual defection, T - P, decrease and as social distance, d, increases. The parameter d captures the idea that the utility of volunteering is high to the extent that the other person is socially or genetically close to the self. Consider the payoffs in Figure 1, namely T = 2, R = 1, and P = 0. For maximum distance (d = 1), we find that p_v = 0.5, which is the conventional Nash equilibrium. Neither orthodox game theory nor a biologically informed social-preference theory would assume a probability of volunteering below this benchmark.² For zero distance p_v = 0.75. Here, the player weights the outcomes of the other as much as his or her own outcomes, and if both players do this, the sum of their outcomes is maximized. Note, however, that this is not an equilibrium in the Nash sense. A player who knows or expects the other to volunteer with a high p_v might choose to defect for sure and thereby increase his or her payoff and reduce the other’s. In other words, using this ‘superrational’ strategy (Diekmann, 1985) requires the expectation that the other player will do the same.

Our third hypothesis is more subtle and thus riskier. We predict that many individuals will volunteer too much relative to formal standards and relative to the implications of their own expectations regarding others’ choices. They will, in other words, stumble into Popper’s dilemma of love. How might this happen? We submit that the social-distance heuristic is frugal in the sense that it has no non-monotonic provisos (Gigerenzer and Gaissmaier, 2011). There is no check as to whether there may be too much volunteering. Not having such a proviso works well in social dilemmas where mutual cooperation is the most efficient collective strategy (i.e., were 2R > T + P [or T + S]). In the VoD, however, heuristically thinking individuals may choose to volunteer for a very close other without working out the implications. As both individuals have this tendency, the outcome is inefficient. In other words, we predict that Archetti’s social preference model will offer a good description of volunteering over social distance, but that against this background of adaptiveness, there will be a systematic error precisely where individuals would want to avoid it the most.

When adding expectations to the picture, the possibility of over-volunteering becomes more poignant. If, as we hypothesize, people will be most likely to volunteer when the other is psychologically close, and if, as we also hypothesize, people project their own choices most strongly onto those who are close, then we will find that respondents over-volunteer even by the lights of their own expectations of reciprocity. To illustrate this hypothesis, imagine a pair of siblings. Both want to ‘do the right thing’ and sacrifice for the other. At the same time, they predict that their sibling is equally willing to make that sacrifice. Yet, they choose to volunteer. This outcome, if obtained, would suggest that projective predictions are difficult to alter. The player cannot escape the dilemma by defecting because this would suggest the worst personal and collective outcome. To avoid over-volunteering, the person would have to find a way to predict that the other person is less likely to volunteer than the self. This, in turn, might be a difficult psychological maneuver because it would suggest that the self is a more socially responsible person than the other. In doing so, it would undermine the perception of social closeness (there is, however, evidence for such self-enhancement in volunteering, Heck and Krueger, 2016, unpublished).

We tested these hypotheses in three studies. In study 1, we sought to demonstrate the social-distance effect and provide evidence for over-volunteering at very short social distances, as evaluated against a game-theoretic standard. In study 2, we considered a full range of social distances and introduced respondents’ expectations. Here, we tested all three hypotheses (social projection, social distance, and over-volunteering) over multiple samples. In study 3, we manipulated expectations experimentally. Assuming that expectations are not epiphenomenal to behavior, we predicted that respondents would consult expectations when making a decision, but that the effect would be limited and result in over-volunteering.

The results of this multi-sample study supported the main hypotheses. In support of the social-projection hypothesis, we found positive correlations between respondents’ willingness to volunteer and their predictions of what the other person would do. These correlations emerged for each level of social distance, and they were strongest for short distances. It is worth noting that some “differential projection” (Robbins and Krueger, 2005), that is, a decrease of perceived similarities over social distance, is warranted because actual similarities also tend to decrease. Closely related and connected individuals share more similarities than do mere strangers. Expecting such similarities in behavior from one another is therefore a generally adaptive strategy.

As predicted, the willingness to volunteer and correspondent expectations both decreased over social distance, thereby allowing errors of over-volunteering to creep in. For the two shortest social distances, willingness to volunteer exceeded game-theoretic benchmarks. While this result suggests over-volunteering, it is not yet definitive. Respondents might rationally exceed these benchmarks if they (have reason to) believe that the others are less likely to volunteer. The clearest case for over-volunteering requires that both, own willingness to volunteer and others’ expected willingness to volunteer, lie above the benchmark. We find such evidence for the shortest social distance.

Given the moral overtones of volunteering, we predicted and found evidence of self-enhancement. At each level of social distance, respondents claimed that they were, on average, more willing to volunteer than the other person. The self-enhancement bias is not a striking discovery on its own, but it is relevant in that it makes over-volunteering more difficult to detect. Had self-enhancement been any stronger, volunteers would have expected others to defect, in which case they would have expected successful (anti-)coordination to the benefit of the other.

Following theory and research on social projection, we submit that people construct expectations about others on the basis of their own behaviors rather than vice versa (see Van Veelen et al., 2016, for a comprehensive review of the evidence for this claim and its boundary conditions). This causal flow has good support in research on both social projection and self-enhancement (Krueger, 2007; Heck and Krueger, 2015). Yet, it is difficult to draw firm inferences in the VoD because, as in other social dilemmas, decisions and expectations are dynamically interdependent. To open a window into the potential role of expectations on volunteering decisions, we manipulated expectations in our final study. Induced expectations are available before respondents make strategic decisions (Gaschler et al., 2014). This design let us test two hypotheses: First, expectations will inversely affect volunteering decisions. Second, the effect of expectations will be smaller than full rationality demands. A consequence of this underuse of expectations is over-volunteering. Respondents will be willing to volunteer even when they expect the other person to volunteer as well.

We recruited 296 residents of the United States on Amazon Mechanical Turk and collected no further demographic information. Each participant received a small payment of c75 and a lottery ticket for a $25 Amazon.com gift card. Each participant responded to all four scenarios of the 2 (social distance: high vs. low) by 2 (expectation: high vs. low) design.³

The structure of the VoD and the social distance scale were introduced as in the previous studies, using a standard platform (Qualtrics Research Suite [Survey software], 2014). Participants were asked to consider only the closest (distance rank 1) and the remotest person as a partner in the VoD (social distance rank 100). For each dilemma, they were to assume either that this person was very likely to volunteer (with a 80% chance) or very unlikely to volunteer (20% chance). The order of the four scenarios was randomized over participants in a 2 (distant or closest partner first) × 2 (for the first partner: high or low expectations first) × 2 (for the second partner: high or low expectations first) design. Participants then entered their own likelihood to volunteer using a percentage scale.

Figure 4 shows the findings as bean plots with means and confidence intervals. Visual inspection reveals clear evidence for both the social distance hypothesis and the expectation hypothesis. We again used linear mixed models with random effects and bootstrapped confidence intervals for statistical analysis and effect-coding (-0.5 and 0.5) for the predictor variables social distance and expectation. The main effect of social distance, b = -14.13, 95% CI [-10.84, -17.54], R² = 3%, indicated that participants were approximately 14% less likely to volunteer for the distant other compared with the close other. The main effect of expectation, b = -23.30, 95% CI [-18.52, -28.08], R² = 9%, indicated that participants were about 23% less likely to volunteer when they expected the other to volunteer with a probability of 80% vs. 20%. The interaction term was not significant, b = -2.92, 95% CI [-8.64, 2.72], R² < 0.1%.

The data also support the over-volunteering hypothesis. When the other was expected to volunteer with an 80% probability, the optimal response was to not volunteer at all. Yet, participants announced that they would volunteer with a 51 and 35% probability, respectively, for the close and distant other (see Figure 4). This is prima facie evidence for over-volunteering. Yet, there was also the converse effect of undervolunteering when the other was expected to volunteer with a 20% probability. Although the optimal response was to volunteer with certainty, participants announced that they would volunteer with a 72 and 60% probability, respectively, for the close and distant other.

The results of Study 3 replicate and extend the body of correlational findings accumulated in Studies 1 and 2. The social distance effect on volunteering is robust, consistent with the ideas of inclusive fitness (Hamilton, 1964) and strong reciprocity (Gintis, 2000). As the social distance heuristic uses a single cue, it opens the door to predictable error. We have identified over-volunteering as one such an error and we saw that respondents violate their own expectations regarding the choices of others when they arguably care the most about an efficient outcome. Study 3 shows that this violation of expectation occurs not only when these expectations are self-generated but also when they are externally provided.

Volunteer’s Dilemmas pervade social life, although they are rarely recognized as such. Who will buy the wine for dinner? Who will start work on the co-authored manuscript? Who will punish the loafers and jaded bystanders (Przepiorka and Diekmann, 2013)? The VoD has received little research attention apart from the specific issue of bystander intervention and apathy in emergency situations (Darley and Latané, 1968; Krueger and Massey, 2009; Fischer et al., 2011). We suspect that the VoD is neglected because of the belief that it is easily resolved with a little goodwill and coordination, particularly among kin and the well-acquainted (Sir Karl Popper dissenting). Most research remains focused on social cooperation in public-goods and resource dilemmas involving unrelated strangers (Dawes, 1980; Norenzayan et al., 2016). In those dilemmas, collective outcomes continue to improve as more individuals contribute. In contrast, the relationship between collective welfare and the frequency of prosocial behavior is non-linear in the VoD. It is inefficient to have more than one volunteer or to have none at all. This non-linearity poses a psychological challenge. A prosocial person must consider the risk of making a redundant and thus inefficient contribution.⁴

An excess of prosociality can occur when individuals are close and when the effects of volunteering or mutual failure to volunteer are negative. Our principal explanation of this finding is the idea that people use a social-distance heuristic when deciding whether to accept the cost of volunteering. They are willing to make a sacrifice to the extent that the other person is socially, psychologically, or genetically close to them. This heuristic works well in many contexts of interdependence, providing adaptive advantages that are recognized by evolutionary biologists and game theorists (e.g., Ferrière and Michod, 2011; Locey et al., 2013). Indeed, we find that the mean probability of volunteering tracks the predictions of a formal equilibrium model, which uses relatedness to weight and integrate the other person’s outcomes with one’s own (Archetti, 2009). When social distance is zero, the model assumes that players care for the outcomes of the other player as much as they do for their own.

Our findings suggest that many pairs of close individuals will end up with the same outcome, the R payoff for mutual volunteering, although they would have fared better if their probability of volunteering had been lower. It is not clear yet whether this effect is large enough so that individuals can gain insight into its non-optimality. Perhaps they will focus instead on the equality of their two payoffs, consider it fair, and find reassurance in the successful avoidance of the most aversive outcome of mutual defection (Leliveld et al., 2009). Alternatively, our findings point toward a mistaken sense of altruism (Krueger, 2011; Oakley et al., 2011), which, under certain conditions, can do great harm. For instance, when individual and group identities fuse, the eagerness to act prosocially can beget tragedy (Whitehouse et al., 2014).

Now consider the relevance of the findings regarding expectations of volunteering. With pain at stake, people expect close others to volunteer, and even over-volunteer. Why do respondents not scale back their own probability of volunteering to restore maximum efficiency? The logic of social projection suggests an answer (Krueger, 2013). Consider a person who is ready to volunteer and who expects others to do the same. This person cannot switch from ‘volunteer’ to ‘defect’ without assuming that others will do the same. If projection is a valid heuristic for inferring the actions of others, it is valid regardless of one’s particular strategy. Like prosocial behavior, social projection decreases over social distance (Robbins and Krueger, 2005); this general finding emerges in the present data too (Studies 1 and 2) and thus helps explain the tenacity of over-volunteering among close individuals.

If – as we believe – respondents generated their expectations about the likely behavior of others after they had made their own decisions, we can make sense of a final finding: respondents thought that the probability of others to volunteer was lower than their own. With volunteering being a socially desirable act, declaring oneself to be more willing to volunteer than others amounts to a better-than-average-effect (Alicke and Sedikides, 2009). Self-enhancers claim dual moral credit (Heck and Krueger, 2016). They not only volunteer but also predict that they volunteer more than others do. Self-enhancement is consistent with the general projective pattern (Heck and Krueger, 2015). If respondents derive expectations about others from their own decisions, these expectations should be more regressive (i.e., less extreme) than own decisions (Moore and Healy, 2008). Indeed, expectations were overall closer to the 50% mark than were judgments of own intended volunteering.

In light of the bounded rationality with which people approach the VoD, we may ask what options exist for efficient solutions. In contrast to the prisoner’s dilemma and the assurance game, but like the game of chicken (Van Lange et al., 2014), the VoD yields best results if the two players act differently. Over repeated encounters, turn-taking in volunteering yields mutual benefits. In a one-shot episode, however, communication is of little help. If both individuals declare their intention to volunteer (or defect), additional factors must be brought in to break the tie. One reasonable social rule is to put the burden of volunteering on whomever can afford it the most (Przepiorka and Diekmann, 2013). When Linda and Laura reach for the lunch bill, jobless Linda may yield to working Laura (Abele et al., 2014). When there is no difference in wealth, timing is critical. Whoever announces their decision first forces the other to do the opposite (Schelling, 1960). We suspect that in such a sequential arrangement social distance will remain a moderating factor.

Our study designs reflect choices made under constraints and in the interest of expediency. Future research needs to identify and test pinpoint hypotheses to sharpen our theoretical understanding of the volunteer’s dilemma and to enhance the generalizability of the findings.

First, there is the finding that over-volunteering occurred only for aversive outcomes. It may be too soon to declare valence a robust moderator as we had only one sample with a positive game frame. If, however, the valence effect survives further testing, we may note that the departure from rationality and adpativeness occurred where participants would arguably be most motivated to avoid it: in the domain of pain (Kahneman and Tversky, 1984; Baumeister et al., 2001).

Second, the task of mapping the effects of social distance onto the predictions of a rational equilibrium model limited us to a artificial methodology. To scale social distance with precision, we sacrificed the real-life experience of encountering others in the dilemma. As future research meets the challenge of mundane realism, it will be critical to remain wary of confounds. Individuated partners will introduce a host of additional information or assumptions that might increase the variability of results in random or systematic ways.

Third, the use of five levels of social distance presented in non-random order may raise the specter of experimental demand. Yet, we remain sanguine because the demand hypothesis makes no specific predictions. What particular slope or which specific intercept, for example, should a respondent feel called upon to produce when scaling her own willingness to volunteer onto social distance?

Fourth, we presented the VoD as a choice problem of the type used in scenario research in the psychology of judgment and decision-making (see, for example, Murnighan et al., 1993, or Kim and Murnighan, 1997, for such work on the VoD). In contrast, behavioral economics prizes consumable payoffs. Recent work in our laboratory suggests that in the VoD, symbolic payoffs yield the same results as material ones do (Krueger et al., 2016, unpublished).

Many ordinary people and the scientists who study them operate from the simple, reasonable, and adaptive heuristic that prosocial behavior is socially desirable. Their moral concerns take the form of asking what can be done to make such behavior more common. Our excursion into the volunteer’s dilemma suggests structural and psychological factors can combine to undercut the effects of good intentions and expectations. More is not always better.