R2. What are the entailments of claiming that cognitive mechanisms for revenge and forgiveness are adaptations with identifiable functions?

Some commentators believe our analysis of revenge and forgiveness leads to implausible hypotheses about the widespread occurrence of revenge in human societies (Gintis), that the analysis “sheds very little light on the evolution of these purported cognitive systems” (Wereha & Racine), and that adaptations for revenge and forgiveness are unlikely to exist at all (Holbrook, Fessler, & Gervais [Holbrook et al.]). Barclay is right in pointing out that one major risk of adaptationist analysis is that readers might misperceive functional claims as universal claims. The claim that the revenge system is an adaptation emphatically does not entail that all instances of revenge (or forgiveness) will be adaptive (Andrews et al. Reference Andrews, Gangestad and Matthews2002; West-Eberhard Reference West-Eberhard, Keller and Lloyd1992; Williams Reference Williams1966).

Gintis bases his skepticism of our central claims, which he calls “implausible,” on (a) evidence from economics experiments indicating that third parties will, under some laboratory conditions, pay costs to punish a stranger who has been stingy or greedy with regard to another stranger; (b) educated guesses about ancestral population structure; and (c) the results of his and his colleagues' evolutionary simulations. Gintis's claims, and the evidence he adduces in support of them, have recently been addressed extensively elsewhere (e.g., Guala Reference Guala2012; West et al. Reference West, Mouden and Gardner2011), so we restrict our comments to Gintis's first point, which bears most strongly on our central claims.

Although the data from economics experiments used to support the concept of strong reciprocity are interesting and important (but see sect. 3.1.3 in the target article for difficulties surrounding interpretation), the finding that people will sometimes pay costs to punish harmdoers even when (by experimental constraint) the punishers cannot benefit economically or reputationally from doing so does not damage our claim that humans have adaptations for punishment that were designed by natural selection because of their deterrent effects. Zooming out to a broad conceptual level, adaptationists since Williams (Reference Williams1966) have hewed to a definition of an adaptation as “a characteristic of an organism whose form is the result of selection in a particular functional context” (West-Eberhard Reference West-Eberhard, Keller and Lloyd1992, p. 12). A critical entailment of this definition is that a trait's status as an adaptation must be evaluated from the perspective of the historical selection pressures that gave rise to the trait's gene-propagating effect. The operation of the adaptation within the organism's contemporary ecology (or within a laboratory experiment) might accurately reflect the function that natural selection designed the adaptation to perform, but to the extent that the organism's contemporary ecology (or the laboratory experiment) fails to capture key elements of the ecological backdrop against which natural selection gave rise to the adaptation in question, contemporary results from both the field and from the laboratory can be deeply misleading (Burnham Reference Burnham2003; Hagen & Hammerstein Reference Hagen and Hammerstein2006). Indeed, an adaptation can appear to be “misfiring,” even though it is merely executing its proper function in response to environmental stimuli whose sensory properties are close enough to approximate the ancestral conditions under which the adaptation was naturally selected to operate.

Biologists frequently encounter initially puzzling costly contemporary behaviors. In Colorado, for example, yellow-bellied marmots have not encountered wolves since the 1930s, when farmers and ranchers eradicated them. Nevertheless, when exposed to life-sized two-dimensional images of wolves during field experiments, these marmots immediately suspend their foraging activity to run and hide – a costly pattern of behavior that is unlike their responses to equivalent images of extant predators or control animals (Blumstein et al. Reference Blumstein, Ferando and Stankowich2009). Costly fleeing in marmots, therefore, can be explained with reference to benefits that existed in the past but no longer do. The fact that marmots receive no benefits in the modern ecology from fleeing from images of wolves does not make implausible, as Gintis's argument would have it, that the mechanisms for fleeing were selected for by virtue of the fitness benefits those behaviors used to provide (viz., avoiding predation by wolves) under ancestral circumstances.

Therefore, for some stimulus-response relationships, it is more plausible that the adaptation that causes a given behavior is firing in response to a stimulus that is outside of the adaptation's proper domain (i.e., the range of stimuli whose biological function it is to process; see Sperber Reference Sperber, Hirschfeld and Gelman1994), than it is that the adaptation's proper domain is broader than scientists had previously apprehended. To the extent that in ancestral human environments repeat interactions were common (Hagen & Hammerstein Reference Hagen and Hammerstein2006), cooperation-regulation mechanisms might embody the ex ante assumption that interactions are likely to be repeated (Delton et al. Reference Delton, Krasnow, Cosmides and Tooby2011) even though some social interactions might have turned out (ex post) to be one-shot. And if this were the case, people in modern (e.g., laboratory) environments should be expected to execute behaviors that promote cooperation or deter exploitation (including punishment) even when they are aware (i.e., have an explicit representation) that the interaction is likely to be one-shot. Thus, for some of the same reasons why misfiring arguments are better suited to explaining some aspects of contemporary marmot behavior, we also think that misfiring interpretations are better suited than is Gintis's account for explaining the existing experimental results about “strong reciprocity.”

R3. What are the advantages of carefully distinguishing between ultimate and proximate levels of causation?

Several commentators seem unconvinced that our model presented an exhaustive account of the causal forces that are operative within revenge and forgiveness systems. Potegal, for example, claims that we fail to give adequate weight to the “reinforcing value of aggression” as part of the causal apparatus that makes revenge happen. Other commentators (e.g., Fatfouta, Jacobs, & Merkl [Fatfouta et al.]; Dellis & Spurrett; Yu; Ross) have suggested in one way or another that our analysis gave insufficient attention to neurological evidence (or the lack of neurological evidence) about the systems that might be involved in the production of revenge and forgiveness.

Some of these misgivings, we think, are traceable to confusion about the differences between ultimate and proximate causation (Scott-Philips Reference Scott-Philips, Smith, Smith and Ferrer-i-Cancho2008). In the target article, we took pains to point out in sections 2.1 and 2.2 that explanations for revenge that are based on statements about proximate causation (e.g., that people enact revenge because it feels “satisfying”) are inadequate for explaining the evolution of such mechanisms in the first place. Ultimate causal explanations must always be with respect to the fitness-enhancing (i.e., gene-propagating) effects of rival designs (Scott-Philips Reference Scott-Philips, Smith, Smith and Ferrer-i-Cancho2008). So, when Ross suggests that “a key condition for the existence of equilibrium strategy vectors that include revenge and forgiveness” (by which we take him to mean that the conditions under which revenge and forgiveness can become evolutionarily stable strategies; Smith Reference Smith1982) is the human susceptibility to shame, we believe that more careful attention should be paid to the proximate/ultimate distinction: Shame, which is an emotion, is a proximate causal force (which, one is free to argue, is put to use by cognitive systems for revenge and forgiveness) rather than a statement about the effects of rival designs on gene frequencies (Scott-Philips Reference Scott-Philips, Smith, Smith and Ferrer-i-Cancho2008). Consequently, shame cannot be invoked to describe the ultimate casual forces that lead to the assembly of mechanisms for revenge and forgiveness. A similar conflation of ultimate and proximate levels of causation occurs when Yu writes that “Revenge is not always future-oriented and may have evolved for other reasons, such as the fairness instinct.” Sell's commentary is an elegant example of how considering ancestral selection pressures (viz., for up-regulating a harmdoer's WTR for oneself versus reducing someone's capacity for harming oneself) can yield fine-grained predictions about the distinct proximate characteristics of the psychological systems that generate anger versus hatred.

R4. Does our theorizing ignore the role of development?

Wereha & Racine take us to task for using a “fundamentally non-developmental evolutionary paradigm,” and commend as an alternative their own “evolutionary systems perspective.” Their critique gets its traction, however, by assigning views to us that we do not endorse, and by substituting a set of bold but largely empty propositions about understanding the development of the adult revenge system. Most flagrantly, they claim that, “In the particulate, additive, non-developmental stance popular in EP [evolutionary psychology], the ‘system’ with all its potentialities are developmentally predetermined, a perspective that is contrary to the probabilistic nature of development.” Many researchers in evolutionary psychology, however – including those whose views we would associate with our own – take development very seriously indeed (Belsky et al. Reference Belsky, Steinberg and Draper1991; Ellis Reference Ellis2004; Ellis & Bjorklund Reference Ellis and Bjorklund2005; Frankenhuis & Del Giudice Reference Frankenhuis and Del Giudice2012; Geary & Bjorklund Reference Geary and Bjorklund2000), and have taken pains to distance themselves from the particulate, additive, adevelopmental caricature that Wereha & Racine set up as representative of evolutionary psychology's stance on development (Tooby et al. Reference Tooby, Cosmides and Barrett2003). Tooby et al. (Reference Tooby, Cosmides and Barrett2003) pointed out that the idea that development is a complex interaction between genes and environment is the starting point for evolutionary psychologists.

Wereha & Racine's critique is further undermined by a category error. Seeking to contrast our view that “‘evolved cognitive mechanisms underlie decision making processes” (their phrasing), they write that “Decisions, however, are made by people with life histories.” Cognitive mechanisms at any given moment both cause decisions and have developed over time, so setting the two in opposition to each other is illogical. Further, our colleagues in evolutionary psychology who study development draw heavily from life history theory (Ellis Reference Ellis2004), a feature that distinguishes their approach from other developmental approaches, thereby hollowing out this critique. Although it is true we did not focus on development in the target article, we do not think that the revenge system magically appears in adult form; indeed, in section 3.3.2, we discussed the role that people's life histories can play in altering the operation of mechanisms for revenge (see also Barclay). We take for granted that the unique elements of people's life histories likewise influence the operation of mechanisms for forgiveness. Similarly, the idea that we “do not seriously consider” that people still face the problem of deterrence is a striking misrepresentation of our work. We discuss examples from the lab and the field in which people are faced with the category of problem that we believe selected the behavior, which is that aggression now predicts aggression later.

Finally, we note that “systems” theories have been criticized for yielding only predictions that are vague at best. Indeed, Tooby et al. (Reference Tooby, Cosmides and Barrett2003) suggested that “developmental systems theory makes no predictions.” Vindicating this bold assertion, the closest Wereha & Racine come to a positive statement about what their view predicts is the claim that the “complexity of the ‘system’ would constantly change (i.e. develop) over time, with various factors changing it in sometimes non-obvious ways.” It is difficult to imagine what pattern of empirical data might put such a claim in jeopardy.

Generally, we emphatically agree that explaining and understanding the development of revenge systems is an important priority. Indeed, work such as Sell et al.'s (Reference Sell, Tooby and Cosmides2009) research on anger points to a potentially profitable direction: identifying factors – in Sell et al.'s case, variation in size and attractiveness – that might be expected to systematically influence developmental outcomes. Hypotheses about the privileged roles of ecological factors such as local life expectancies, frequencies of within-group interpersonal violence and intergroup warfare, the strength of fraternal interest groups, and the harshness of one's family environment during early childhood likewise merit exploration in future developmental work on revenge and forgiveness.

R5. What does it mean to refer to systems for revenge and forgiveness as computational? What does it mean to refer to them as systems?

Several commentators express reservations about our claim that the mechanisms underlying revenge and forgiveness are computational systems. More specifically, some argue that it is important to consider that these systems might not be “rational” (O'Connor & Adams) as opposed to emotional (Aureli & Schaffner; Leiser & Joskowicz-Jabloner), and that our explanation was either, on the one hand, unnecessarily complex (Aureli & Schaffner) or, on the other, insufficiently so (Stein, van Honk, & Ellis [Stein et al.]).

First, we wish to clarify that we were not trying to be tendentious in making a computational claim. Following convention in the cognitive sciences (e.g., Carruthers Reference Carruthers2006; Pinker Reference Pinker1999), we take computation to be the information-processing description of what the brain's functions entail. Computational mechanisms take as inputs select types of information (including possibly information from other computational systems), represent that information in some sort of physical format, perform operations on those representations, and pass the outputs of those operations to other neural or somatic systems for further processing or action production. So, in our view, systems for revenge and forgiveness are computational because their function is to represent and process particular types of information – specifically, information that would have led them to cause good (i.e., fitness-raising) decisions in the domains of the adaptive problems for which they were naturally selected (i.e., deterring future harms and updating aggressors's intrinsic WTRs for the self peaceably).

We hope it goes without saying that we take for granted that natural selection is the only cause of complex functional design in biology – computational design included. Neural systems can only be called computational to the extent that they physically represent states of the world with a non-zero degree of fidelity; thus, to the extent that computational systems are beset by mutations or otherwise influenced by other non-adaptive causal process, the effect of these non-adaptive causal processes will generally be to reduce the fidelity with which the systems can represent true states of affairs. Consequently, their computational powers will be reduced. For this reason, the concepts of adaptation and computation tend to go hand in hand. To the extent revenge and forgiveness systems exist, we assume that it is fitting to conceptualize them as computational systems, and that “good computation” within their respective domains is shorthand for computations that ancestrally would have provided reasonable tradeoffs between the benefits of deterrence to be gained by imposing a retaliatory harm on the harmdoer and the relationship-mediated benefits to be gained by signaling one's willingness to withhold revenge and return to mutually beneficial relating, conditional on better treatment from the harmdoer in the future (Burnette et al. Reference Burnette, McCullough, Van Tongeren and Davis2012).

Referring to revenge and forgiveness systems as computational systems explicitly is useful, we think, because it keeps one mindful of the need for clear information-processing specifications when investigating how these systems might perform their tasks. On the basis of computational reasoning, for example, Burnette et al. (Reference Burnette, McCullough, Van Tongeren and Davis2012) made five novel predictions about the cognition of individuals who are actively making decisions about whether to forgive or avenge a recent harm:

These predictions resulted from applying computational thinking to how a well-designed forgiveness system might operate, as we tried to do in the target article.

The emotions such as those alluded to by the commentators as potential alternatives to the computational steps that might be involved in motivating revenge and forgiveness (e.g., anger), by our reckoning, are also computational in nature (see, e.g., Tooby & Cosmides Reference Tooby, Cosmides, Lewis, Haviland-Jones and Barrett2008). Indeed, we are unsure what else the systems that produce emotions might be, though admittedly emotions seem special because they are associated with complex conscious experiences in a way that non-emotional cognitive processes (e.g., vision) are not. The question is not whether anger plays a role in the production of revenge (it certainly seems like it does – perhaps along with hatred, as Sell perceptively proposes), but, rather, what the computational processes are that make anger happen, and how those subroutines lead to outputs that can then be put to use in the production of revenge. In the target article, we intentionally refrained from implicating anger and similar emotions as causal elements in the information processing stream that leads motivation for revenge and forgiveness because our goal was to articulate the computations these systems must perform, but this was not a move on our part that was designed to exclude emotions in any sense. So, we find little reason to quarrel with Aureli & Schaffner's suggestion that “emotional mediation” is important for revenge and forgiveness: The computations involved in the production of revenge and forgiveness no doubt involve emotions; emotions are, from our point of view, fundamentally computational in nature, too.

Further, our claim was not that the computational systems we propose are “rational” as economists use the term. “Anger” might be well designed to deter, as we have proposed, yet give rise to “irrational” behavior, such as (vengeful) rejections of low offers in the Ultimatum Game. According to this view, emotional systems execute their evolved function in a way that respects ancestral computations of costs and benefits, but far from the way envisioned by standard bloodless economic analysis (Frank Reference Frank1988). So, (emotional) deterrence systems need not be “deliberative,” and we reject as ill-formed the persistent “tension between affect and deliberation” to which O'Connor & Adams allude (Tooby & Cosmides Reference Tooby, Cosmides, Lewis, Haviland-Jones and Barrett2008).

As for the complexity required for such systems, we did not intend to take a strong stand on this, though would resist the flavor of Aureli & Schaffner's remarks that emotional systems are necessarily simpler than non-emotional systems. In our view, emotional systems embody potentially intricate complex computations (Tooby & Cosmides Reference Tooby, Cosmides, Lewis, Haviland-Jones and Barrett2008), and we look forward to work from people from differing perspectives helping to shed light on the intricacies of the involved computations. For example, Johnson-Freyd & Freyd point out that one way to engineer “acceptance” is to engineer the systems to ignore – or at least appear to ignore – intentional harms. We agree that ignorance can have strategic advantages (Kurzban Reference Kurzban2010b; Schelling Reference Schelling1960), and we are sympathetic to the view that one means of accepting an offense, in terms of the outcome for the relationship, is to ignore or pretend to ignore an offense.

Holbrook et al. are not sanguine about the claim that human brains contain computational systems whose function is to deter future harms. Comparative data illustrate that nonhuman animals from multiple taxa impose retaliatory harms on other organisms that have previously harmed them, and that by doing so, the retaliators deter the recipients of their retaliatory behaviors from harming them again in the future (e.g., Aureli et al. Reference Aureli, Cozzolino, Cordischi and Scucchi1992; A. Bshary & Bshary Reference Bshary and Bshary2010; R. Bshary & Grutter Reference Bshary and Grutter2005; Hoover & Robinson Reference Hoover and Robinson2007; Jensen et al. Reference Jensen, Call and Tomasello2007). Such data make the parallel claim for humans plausible.

Instead of revenge mechanisms designed for deterrence, Holbrook et al. propose as an alternative hypothesis that the deterrence function we have in mind is more parsimoniously handled by anger along with a variety of domain-general systems (e.g., norm acquisition, future forecasting, and perspective taking) and “systems related to other motivations, such as reputation management.” However, we would argue that their proposal that revenge is subserved by “evolved capacities to categorize events, assume others' perspectives, forecast the future, and weigh costs against benefits” lacks substantial theoretical or predictive force because it constitutes a far too general gloss of a computational system. The capacities that Holbrook et al. catalogue are all, to be sure, important in executing a deterrence function, but the organism that is effective at deterring others from imposing harms upon it in the future must be motivated – by, for instance, the experience of anger – to take appropriate adaptive action out of all the possible actions that one might take. Categorizing events and so on is also insufficient; particular events (intentional harm) need to be met with appropriate behavior (e.g., return harm) to bring about adaptive outcomes. The suggestion that people choose how to react to a situation through categorizing it and forecasting the future allows no predictive mapping between situation and behavior, specifying only the sorts of mechanisms that are recruited as opposed to what strategies those mechanisms ought to implement.

To put it another way, the claim that there is no deterrence system per se implies that to the extent that people's propensity to harm in response to harm does deter, this comes about as an incidental side-effect of the action of systems designed for some other (perhaps more general) function. What function might anger have, such that it is not designed to deter but happens, as a lucky side-effect, to deter? The answer to this cannot be “reputation management” without a more explicit and specific account of precisely how one ought to manage one's reputation. Why not cultivate a reputation to be unmoved, or even happy, when one is harmed? There is an arbitrarily large vocabulary of reputations one might cultivate; one cannot cultivate a “good” reputation unless one specifies the problem that having a reputation is supposed to solve. Our posited deterrence function explains why people experience anger rather than joy at being harmed; a “reputation management” function, in itself, does not (see Tooby & Cosmides Reference Tooby, Cosmides, Barkow, Cosmides and Tooby1992, pp. 109–13; 2008).

So, even if it is the case that the devices that are wired together to generate revenge within human brains are also used for other functions (as Holbrook et al. posit), then an explanation is required for how these devices came to be wired together in just the sort of bricolage, to use their favored term, that causes that bricolage to create retaliatory behavior that returns fitness-enhancing deterrence benefits to its bearer. Neural wiring is expensive and needs an explanation in terms of natural selection every bit as much as do the structures that get wired together (Anderson Reference Anderson2010; Cherniak et al. Reference Cherniak, Mokhtarzada, Rodriguez-Esteban and Changizi2004).

Finally, we respectfully disagree with Holbrook et al.'s claim that we have reified a folk category, a claim which seems to rely wholly on their observation that “[t]here are many kinds of deterrence that do not stem from the anger-hatred nexus.” In fact, we never claimed that revenge was the only system that deters, and their example of swatting a begging dog to deter future begging shows only that some deterrence is not revenge. The poisons of poison frogs and the thorns of roses are also deterrence mechanisms, for instance. Therefore, we of course agree that there are other systems beyond the ones we posit that can be deployed for deterring predators from attacking or, perhaps, training domesticated animals. More generally, we are comfortable with the notion that the revenge system, as a whole, makes use of subsystems such as the ones that Holbrook et al. identify.

Dellis & Spurrett have a different problem with our specification of the systems involved in revenge and forgiveness: They suggest that there is no reason to postulate two separate systems when one “reciprocity” system will do, suggesting that the key dispositive evidence would be a dissociation due to, for instance, “local brain damage” or “genetic intervention.” To clarify our position, we believe that evidence for a putative function can be aided by these empirical patterns, though behavioral evidence of special design is similarly of value (Andrews et al. Reference Andrews, Gangestad and Matthews2002; West-Eberhard Reference West-Eberhard, Keller and Lloyd1992; Williams Reference Williams1966). We similarly believe mechanisms ought to be (and generally are) individuated by virtue of their function (Barrett & Kurzban Reference Barrett and Kurzban2006). Therefore, we think that it will continue to be useful, in guiding empirical research, to distinguish the function of deterring others from harming oneself, from the function of encouraging others to deliver benefits to oneself.

In short, in broad strokes, we are very pleased to agree with Aureli & Schaffner, as well as with Leiser & Joskowitz-Jabloner, O'Connor & Adams, and Holbrook et al. that emotions do important jobs in the production of revenge and forgiveness; but our view is that emotions are computational entities, and if they are to be deeply understood, the function of the computations they execute should be made explicit in order to make good predictions about the nature and details of these computations.

R6. Did we neglect important individual differences?

Several commentators, including Potegal, Yu, Fatfouta et al., Balliet & Pronk, Karremans & van der Wal, Konrath & Cheung, and Roberts & Murray, feel that we gave inadequate attention to important individual differences. Karremans & van der Wal, for instance, call self-control one of the “basic processes that lead to forgiveness,” and worry that its neglect might limit our model's ability to explain “how revenge and forgiveness actually occur.” Many individual differences are related to variation in people's propensities to forgive and to seek revenge, including empathy and narcissism, as Konrath & Cheung point out, as well as agreeableness (or social concern; see Balliet & Pronk), conscientiousness, self-esteem, and religiosity (Balliet Reference Balliet2010; Fehr et al. Reference Fehr, Gelfand and Nag2010; Hoyt et al. Reference Hoyt, Fincham, McCullough, Maio and Davila2005; McCullough Reference McCullough2001; McCullough & Hoyt Reference McCullough and Hoyt2002; McCullough & Worthington Reference McCullough and Worthington1999; McCullough et al. Reference McCullough, Bellah, Kilpatrick and Johnson2001; Riek & Mania Reference Riek and Mania2012). We are not overly concerned about our model's failure to specify all individual differences that are associated with forgiveness and revenge. Nevertheless, we do look forward to more work in this area by people with expertise in individual differences – perhaps explicitly incorporating some of the common theoretical tools that evolutionary biologists use to make sense of individual differences (Buss Reference Buss2009; Nettle Reference Nettle2006; Reference Nettle2009; Tooby & Cosmides Reference Tooby and Cosmides1990a).

Our interest in writing the target article was to outline the set of computations that function to deter (the proprietary computations of the revenge system) and to select behaviors that inhibit the revenge system and signal a willingness to re-establish positive relations, contingent on improved behavior from the harmdoer (the proprietary computations of the forgiveness system). We grant that the inputs to and outputs from the proposed revenge system and forgiveness system can be modified by other systems. However, the mechanisms that act on those inputs before they enter the revenge or forgiveness system, and the mechanisms that act on them after they have left the system for further processing, are not necessarily “basic” (though no less interesting as a consequence).

Narcissism, which Konrath & Cheung encourage us to consider, for instance, might indeed influence one's proneness to respond to harms with retaliation rather than forgiveness (Riek & Mania 2011), but this does not make narcissism an individual difference that must be incorporated into the computational theory per se. (It also does not make narcissism a “bias”: We see little reason to discard the hypothesis that narcissistic people simply believe that they are entitled to better treatment from everybody [i.e., expect others to hold high WTRs for them] because narcissistically entitled people, it appears, really are both physically stronger [Sell et al. Reference Sell, Tooby and Cosmides2009] and better looking [Holtzman & Strube Reference Holtzman and Strube2010; Sell et al. Reference Sell, Tooby and Cosmides2009]). As long as narcissism's associations with revenge and/or forgiveness are due to its influence on computational events taking place outside of the revenge or forgiveness systems, it doesn't necessarily require specification within the computational architecture itself. Barclay also helpfully describes how individual differences in people's perceptions of others' actions will change the information that computational systems for revenge and forgiveness end up processing, consequently changing their behavioral outputs.

Another individual difference that emerges repeatedly in the commentaries is “self-control” or “executive control” (e.g., Yu; Fatfouta et al.; Balliet & Pronk; and Karremans & van der Wal). Impulsivity (which is often pejoratively called “low self-control” or “poor self-control”) might be caused in part by mechanisms whose function is to motivate organisms to exploit local opportunities (i.e., to capture resources, or to avert bad outcomes) whose payoffs can be realized on short time horizons or acceptably high probabilities of attainment (Daly & Wilson Reference Daly and Wilson2005). In other words, humans might discount the value of rewards by the time required to wait for them or by the certainty with which they will come to fruition when that wait time has ended (Ballard & Knutson Reference Ballard and Knutson2009). If the deterrence benefits of revenge can be realized sooner, or with greater certainty, than the relationship-restoration benefits of forgiveness, then natural selection might lead to the evolution of a psychology that, ceteris paribus, produces stronger motivation to execute revenge than to execute forgiveness.

In an alternative specification, one might propose that mechanisms for revenge (as is the case with, say, mechanisms that “like” ice cream) themselves have lower discount rates than do mechanisms for forgiveness (as would be the case with mechanisms that “like” to go on diets). After all, there are good reasons to think that a propensity for action now, or for taking a sure bet over a more speculative one, will result, effectively, in the inhibition of mechanisms that are designed to motivate for restoring relationship-bearing benefits: Generally, reaping the fitness advantages of reciprocal cooperation, for example, seems to require that the benefits, which are realized only over a relatively long temporal horizon, not be discounted too steeply (Stevens et al. Reference Stevens, Cushman and Hauser2005). Additionally, individual differences in temporal discount rates (i.e., the rates at which people downgrade the subjective value of future rewards as a function of the time until their receipt) are negatively associated with cooperation during the iterated prisoner's dilemma and similar social dilemmas (Curry et al. Reference Curry, Price and Price2008; Yi et al. Reference Yi, Buchhalter, Gatchalian and Bickel2007).

A plausible hypothesis, then, about the associations of individual differences in “self-control” with revenge and forgiveness, is that dispositionally impulsive people are more vengeful and less forgiving not because, as Karremans & van der Wal suggest, their “executive control resources are…depleted” (a view that is, we acknowledge, highly influential in social psychology, but theoretically and perhaps also empirically problematic; Kurzban Reference Kurzban2010a; Molden et al., in press; Navon Reference Navon1984), but, rather because humans have cognitive mechanisms that weight the value of particular courses of action by the probability that the payoffs associated with those courses of action will be realized (see also Barclay, who describes how misperceptions of the costs and benefits associated with revenge and forgiveness can lead to individual differences in revenge and forgiveness broadly). When these valuation-assigning mechanisms estimate that one's time horizon is short, they may motivate courses of action (viz., revenge) whose payoffs (viz., direct or indirect deterrence) can be realized over shorter time horizons (McCullough et al. Reference McCullough, Pedersen, Schroder, Tabak and Carver2012).

Such a hypothesis finds precedent in work suggesting that people from homes in which nurturance, discipline, and parental care were inconsistent, or from neighborhoods in which violence and economic disadvantage were high, engage in more impulsive and risky behavior as young adults (Griskevicius et al. Reference Griskevicius, Tybur, Delton and Robertson2011; Hill et al. Reference Hill, Jenkins and Farmer2008). By extension, some of the ecological factors that we discussed in section 3.3.2 of the target article could influence people's propensity for revenge because those factors might ancestrally have been correlated with a shorter average lifespan, thereby creating a selection pressure for psychological mechanisms that can use those cues as inputs to regulate impulsive decision-making.

There is an interesting developmental angle here, which might please Wereha & Racine: The impulsive behavior associated with adolescence and young adulthood is often viewed pejoratively, as if there were something wrong with the adolescent brain that causes it to make dysfunctionally impulsive choices (Gullo & Dawe Reference Gullo and Dawe2008; Hill & Chow Reference Hill and Chow2006). However, it is important to bear in mind that every single one of our hominid ancestors successfully negotiated the challenges of adolescence. Thus, it is highly improbable that adolescent impulsivity is caused by something gone wrong in the brains of adolescents, as such frailties would have been subjected to millions of years of negative selection before they could have become part of the species-typical brain design (Daly & Wilson Reference Daly and Wilson2005). Accordingly, we assume that youthful impulsivity is caused by mechanisms that “know,” thanks to the operation of natural selection, that the only way to improve fitness when one has not yet reproduced is to increase one's reproductive prospects – which, for adolescents, ancestrally came largely from inter-sex competition (i.e., fighting and displays of mate value) and efforts to manipulate opposite-sex choice by demonstrating one's possession of desirable mate characteristics – that is, by showing off (Geary Reference Geary2010). In this light, perhaps it is no surprise that the modal homicide among non-relatives is perpetrated by a young, unmarried male against another young, unmarried male during an “escalated showing-off dispute” or as “retaliation for previous verbal or physical abuse” (Wilson & Daly Reference Wilson and Daly1985).

R7. Is our theorizing applicable to revenge and forgiveness between groups?

Do the deterrence model of revenge, and the “social-benefit capture” model of forgiveness, apply to groups as well as to individuals? Certainly Beckerman's as well as Stein et al.'s remarks along these lines are intriguing, and the presence of revenge in diverse societies during the course of human history and cross-culturally represents a set of phenomena well worth pursuing.

Still, as Pietraszewski suggests, the strategic dynamics get considerably more complex when we move from considering only dyadic interactions to multiple agents, with the case of even just three already introducing considerable nuance and texture. It is for this reason that we worry that the leap from individuals to groups, as intimated by Crisp & Meleady, might not be completely straightforward.

Specifically, Crisp & Meleady contend that “systems for regulating intra- and intergroup behavior should be intimately linked because they involve precisely the same computational requirements.” However, we would be cautious about such a claim. In particular, moving from dyads to groups raises several additional issues. First, even if a third party represents himself or herself as belonging to the same “group” as a person who was harmed, the third party still must compute the extent to which it is worth the costs of taking revenge to deter subsequent harms that might later be directed toward the third party as a consequence of the shared group membership with the victim. Just to take one of many possible complications this raises, the third party must infer whether the harm to his or her fellow group member was (a) because of their group membership, in which case revenge might be worth the cost because the third party could be the next victim, or (b) due to some other cause, in which case taking revenge on behalf of one's group member may be less profitable.

This raises the further complication Crisp & Meleady point to, the usual issue of free riding. It might be that I indeed would benefit from taking revenge when a member of my group is harmed, but I would be better off still (if no additional benefit from being a punisher can be expected) if someone else from my group bore the costs of revenge rather than bearing them myself. These factors imply that the computations involved in revenge in group contexts might be different from those in the more simply dyadic case. We note, in this regard, that the literature cited by Crisp & Meleady showing punishment in Public Goods games has a somewhat ambiguous interpretation, for the reasons discussed in section 3.1.3.

As Pietraszewski points out, computational requirements increase substantially in complexity as we move even the single step from dyads to triads, and, as he indicates, the proximate systems are indeed likely to be “interestingly different.” Because humans can, unlike most other species, form relatively long-lasting, non-kin based alliances, coordinating activities in the service of cooperative, potentially antagonistic activities (Harcourt & de Waal Reference Harcourt and de Waal1992; Kurzban et al. Reference Kurzban, Tooby and Cosmides2001; Tiger Reference Tiger1969), we face strategic complications surrounding building and maintaining alliances (DeScioli & Kurzban Reference DeScioli and Kurzban2009a; Reference DeScioli and Kurzban2009b; Reference DeScioli, Kurzban and Krueger2012), which includes keeping track of where one stands in others' alliance hierarchies (DeScioli et al. Reference DeScioli, Kurzban, Koch and Liben-Nowell2011b), an important factor in being able to predict others' actions in the kind of triadic conflicts Pietraszewski has in mind.

Indeed, the problem is even worse than that because humans do not always take the side of close allies when conflicts emerge, instead using the moral value of the acts of those involved in the conflict to choose sides (DeScioli Reference DeScioli2008; DeScioli et al. Reference DeScioli, Bruening and Kurzban2011a; Kurzban et al. Reference Kurzban, DeScioli and Fein2012). So, although we agree with Uhlmann that often people desire that those who violate a social norm should be punished even if the target or the target's allies were not harmed (Kurzban et al. Reference Kurzban, DeScioli and O'Brien2007), we believe – and suspect that Pahlavan would agree – that it will be useful to distinguish revenge from moralistic aggression, which we believe evolved for a different function (Szymanska Reference Szymanska2011).

We are similarly skeptical of Uhlmann's suggestion that people's reactions to harmless moral violations are designed around inferences about character (DeScioli et al. Reference DeScioli, Gilbert and Kurzban2012; Gray et al., in press) – why the accompanying desire for punishment as opposed to mere avoidance, if the goal is simply character evaluation? – but we agree that this remains an open and interesting question (DeScioli & Kurzban Reference DeScioli and Kurzban2009a).

For these reasons, we are optimistic that the overall approach we suggest here might be fruitfully applied to groups, but we continue to believe that additional theoretical development will be needed to bridge the gap from dyad to collective.

R8. What are the implications for criminal justice and restorative justice?

We appreciate Roberts & Murray's, and Petersen's suggestions that our ideas about revenge might be productively applied to understanding how humans make decisions in the context of contemporary criminal justice systems. Roberts & Murray note that when people empathize with victims (e.g., when the costs to the victim are high), they are more likely to “view the costs of the crime in a personal manner,” leading to an increase in their motivation to retaliate on behalf of victims via their decisions about guilt versus innocence or about punishment severity. We appreciate this point, and Petersen shows that even more subtle predictions are possible. In particular, he notes that third parties will inevitably disagree about how much punishment versus restorative action a specific offender should receive because social value is a dyadic phenomenon. As Petersen writes, “different selves will compute the social value of the same target differently, and a single self will compute the social value of different targets differently.” Consequently, disagreement among jurors or other third parties regarding the sanctions that should be delivered to a criminal (as a function, say, of racial or ethnic similarity, or other cues of social value), particularly in information-sparse decision-making contexts where the ancestrally valid cues for making such determinations are generally unavailable, is not only unsurprising, but probably also inevitable. The applications of this insight, both for research and policy, are considerable.

R9. Do people ever genuinely forgive?

Finally, McCoy & Shackelford raise doubts as to whether people ever “genuinely” forgive. We actually agree with their analysis suggesting that systems for regulating behavior with respect to others are unlikely to be designed to discard entirely past information about harms; indeed, past information should be used in some more or less Bayesian fashion to update expectations. Our proposal regarding forgiveness was not meant to imply that the past behavior did not influence subsequent behavior in any way. In fact, we take for granted that a “genuine forgiver” will also be “prepared to exact revenge” if a future harm occurs in the same way that McCoy & Shackelford envision their so-called “feigned forgiver” would be. Our model does not imply that someone who forgives at time one necessarily will permanently forego revenge in the future. Moreover, we note, after Petersen et al. (Reference Petersen, Sell, Tooby, Cosmides and Høgh-Olesen2010) that forgiveness-based strategies for addressing exploitation are dicey propositions because failures to impose retaliatory harms can easily be confused for weakness or failures of nerve, inviting further exploitation from one's harmdoer.

Still, we doubt that all forgiveness signals are disingenuous (i.e., serving only to lull others into complacency) for two principal reasons. First, if all such signals were false, then they would be ignored, for the usual reasons associated with the evolution of signaling systems (Dawkins & Krebs Reference Dawkins, Krebs, Krebs and Davies1978). Second, we believe that harms occur within the context of relationships that are, with some probability, likely to produce positive sum outcomes over time, which means that reconciliation along the lines we propose carries a higher expected value in some contexts than exacting revenge would. We think that forgiveness might serve to put relationships (back) on a positive sum footing while still leaving open the possibility of revenge, should further harms occur.