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Game of Forgiveness

Forgiveness is a good strategy - mostly.

J. Krueger
The Max Planck Institute in Berlin
Source: J. Krueger

The weak can never forgive. Forgiveness is the attribute of the strong. ~ Gandhi

The psychology of forgiveness is a hot topic in discussions of morality and in research. The prevailing view is that of Gandhi and the Dalai Lama: forgiveness is good and we should have more of it. According to Desmond Tutu (2000), there is no future without it. Research showing the benefits of forgiveness to the giver is particularly intriguing because it raises the question of why we aren't more forgiving (e.g., Lawler et al., 2005). In other words, why do we withhold forgiveness to our own detriment? The conclusion that we should go forth and be more forgiving surely has merit, but I wonder whether a blind rush towards forgiveness is the best policy (see this post on grudge holding).

Talking with Jolene Tan at the Max Planck Institute for Human Development in Berlin, I was reminded that the decision to forgive is indeed that: a decision. It should be studied like other decisions. To make a decision, a rational person considers all possible outcomes and their respective probabilities. One way to do this is to treat the decision to forgive as a problem of signal detection. According to this perspective, the decision maker looks for a signal suggesting the presence of a particular condition. For example, a symptom may indicate the presence of a particular disease – or not. Signal detection is not a trivial task; it is difficult to the extent that the correlation between the signal and the underlying condition is low.

The condition a potential forgiver cares about is whether the forgiveness seeker is worthy. Worthiness is a fuzzy notion, and one that may only be known from the seeker’s future behavior. The giver prefers to forgive a worthy seeker, but to be unmoved by an unworthy one. The first case is a Hit (H), and the second case is a Correct Rejection (CR). This distinction is enough to question the notion that forgiveness is always best. The giver might make two kinds of errors. A Type I error is a False Alarm (FA), which occurs when forgiveness is granted to an unworthy seeker. A Type II error is a Miss (M), which occurs when forgiveness is withheld from a worthy seeker.

A giver values Hs and CRs, and tries to avoid FAs and Ms? Moreover, the giver may think that one type of mistake is graver than the other. From an outside, moralizing, perspective, it may seem that a Miss is more damaging than a False Alarm. The outside perspective takes into account the seeker’s pain of being denied forgiveness. From the giver’s perspective, however, a FA looms large. To forgive and then be proven wrong is aversive. For the giver, the FA is more salient and more bound up with her self-concept than the M. Let us therefore assume the giver values the outcomes in the following order: H > CR > M > FA. Turning to probability, we note that the probability of forgiveness will surely increase with the probability of the worthiness. Casting forgiveness as a decision problem recognizes the inner struggle people sometimes face when they are asked to forgive. It just is not always that easy. The general exhortation to be more forgiving glosses over this struggle; it neglects the giver’s legitimate desire not be appear weak or be taken advantage of.

J. Krueger
Pig unapologetically sharing the road in Storkow, Province of Brandenburg.
Source: J. Krueger

The decision-theoretic (signal detection) analysis of forgiveness takes the giver’s point of view. The seeker is assumed to be either worthy or unworthy. Her worthiness is the state that the giver tries to predict. The seeker too, however, is actively involved in the transaction. Seeking forgiveness and receiving it (or not) is an interpersonal exchange. We also need to take a look at the seeker’s preferences, which will, incidentally, help us understand why the giver may have reason to worry.

The seeker faces the question of whether she needs to actually ask for forgiveness. It would be nice to be forgiven without having to ask. Asking is an act of cooperation with the giver, and arguably it is a form of submission. Not asking is a form of defection. As we have seen, the giver has a choice between forgiving (cooperation) and grousing (defection). Her ranking of the outcomes - as presented above - is: to forgive after being asked (mutual cooperation) > to grouse after not being asked (mutual defection) > to grouse after being asked (unilateral defection) > to forgive without having been asked (unilateral cooperation). In contrast, the seeker feels that to be forgiven without having to ask (unilateral defection) > being forgiven after asking (mutual cooperation) > being groused at after not asking (mutual defection) > being groused at despite having asked (unilateral cooperation).

Supposing that the two sets of preferences are common knowledge in the game-theoretic sense, a smart seeker will cooperate and ask, knowing that giver plays tit for tat; the seeker too prefers mutual cooperation over mutual defection. Note, however, that mutual cooperation is not an equilibrium. The seeker would be better off defecting. Yet, only a myopic seeker would defect; the more foresighted realize that unilateral defection is not an equilibrium either. Giver might respond by defecting, and mutual defection is an equilibrium. Orthodox game theory (Binmore, 2007) sees no way out of this inefficient equilibrium; however, according to the theory of moves (Brams, 2011), seeker can ask forgiveness, which makes both players temporarily worse off, until giver grants forgiveness, thereby returning to a state of mutual cooperation. With the theory of moves, the game of forgiveness is not hopeless. The preferences we have assumed describe a degenerate prisoner’s dilemma, where both players prefer mutual cooperation, although mutual defection is the only equilibrium. Yet, players who can anticipate each other’s responses to their own moves should have no problem finding a cooperative agreement.

Many religious and philosophical traditions hold that forgiveness should be granted to an offender who asks for it. Not all offenders do, however, which raises the question for the giver if she should demand it. If ‘giver’ must demand from ‘seeker’ to actually seek forgiveness by offering an apology, giver faces a difficult decision. On the one hand, the ability to demand an apology and receiving it reflects interpersonal power. But the validation of this power is not guaranteed. Delivering an apology on demand is an act of submission. Yet, giver might also prefer to receive an apology without having to call it in. Let us consider both cases.

In the first case, giver (now ‘demander’) ranks her preferences as follows: demand an apology and receive it (unilateral defection) > be patient and receive an apology (mutual cooperation) > be patient and get no apology (unilateral cooperation) > demand an apology and get none (mutual defection). In contrast, seeker (now ‘apology maker’) feels that not being told to apologize and refusing to (unilateral defection) > no demand but apology (mutual cooperation) > demand and refusal (mutual defection) > demand and apology (unilateral cooperation). These preference rankings mean that demander is playing a game of chicken, whereas maker is playing a prisoner’s dilemma. Demander would like to have a compliant apologist, but if maker refuses, she would rather let it go. Maker would like an undemanding partner, but refusal is her own dominating strategy. Knowing this, demander would be well advised to let it go, which would, however, result in her second-worst outcome (unilateral cooperation). This is a game-theoretic equilibrium and hard to break. Out of hurt feelings or pride, demander might irrationally try to extract an apology, and thereby provoke a state of mutual defection to the great frustration of both. How can demander extract an apology if this outcome is most aversive to maker? If maker apologizes, the game theorist must rewrite her preference rankings and assume – after the fact – that maker rather accedes to the demand to apologize than to refuse it. Maker might choose to submit, for example, for fear of damaging the future of the relationship with demander. She must ask herself, however, how she weighs the expected benefits of future interaction against the cost of submission.

The second case is like the first, except that demander prefers mutual cooperation (receiving an apology without asking for it) to an extracted apology. This is a more genial demander, one that does not prize the exercise of social power above all. Yet, demander’s unilateral cooperation is still the equilibrium and a spiteful demand still hurts both parties. Demander’s overall greater geniality makes no difference.

If there is merit to this analysis, we must conclude that demanding an apology makes no sense. If the apology maker is not an apology seeker, the demanded of an apology only adds stress to the relationship. It is better to let it go, or look elsewhere for rewarding interactions. The religious and philosophical traditions that prize forgiveness in response to a request have a point. An apology or a request for forgiveness should be honored. Extracting a request to then grant it devalues the request and thereby the grant too.

Binmore, K. (2007). Game theory: A very brief introduction. Oxford, UK: Oxford University Press.

Brams, S. J. (2011). Game theory and the humanities. Cambridge, MA: MIT Press.

Lawler, K. A., Younger, J. W., Piferi, R. L., Jobe, R. L., Edmonson, K. A., & Jones, W. H. (2005). The unique effects of forgiveness on health: An exploration of pathways. Journal of Behavioral Medicine, 28, 157-167.

Tutu, D. (2000). No future without forgiveness. New York: Random House.