In his recent book, Vanderschraaf sets out to develop an account of justice-as-convention, which is a form of justice-as-mutual-advantage. He certainly achieves this: the book provides a coherent and admirable account of why it is that rational agents might find it in their interest to share resources in an egalitarian fashion. His arguments are based on work by in particular Hobbes and Hume, but his own insights also throw new light on some of the problems that these authors discussed. Overall, the book is an important and impressive contribution to the literature on justice.

To consider justice as a form of convention means that we see justice not as rules or principles that reflect some deep truth about normative values, but rather as rules that we establish among ourselves in order to live peacefully together. A just distribution of resources, for example, is whatever distribution arises as a result of the rules we happen to agree on, given the different bargaining positions available to different actors. In a sense, then, justice as convention is arbitrary: we chose these particular rules, but we could have chosen other rules, and if we had, these, too, would have been just. The idea of justice as convention goes back at least as far as Plato, who discusses it, even though he does not himself agree with this view. Although it has never quite taken hold, it has never quite faded away either, and it often influences other theories of justice even if these other theories do not treat justice as fully conventional. But Vanderschraaf’s book is a careful and insightful defence of a pure theory of justice as convention. The aim is to make the theory of justice as convention a serious contender among modern theories of justice. He does this by showing that it is possible that rational agents could agree to govern their society democratically, and to share resources with vulnerable members of their group.

The book begins with an overview of interaction problems that concern interests that are partly overlapping, partly conflicting. These are well-known from previous literature, and include among others Hume’s example of farmers who consider helping each other with the harvest, and Braithwaite’s example of musicians who share housing and need to find time to practice their music without being disturbed by the other musicians. These work as an introduction to the kind of interaction dilemmas that motivate Vanderschraaf’s work on justice as convention and introduce non-cooperative game theory.

Vanderschraaf argues that one of the main reasons why the idea of justice as convention has not been more successful historically is that the notion of convention has been too vague. He therefore develops a more nuanced and specific notion of convention. Equipped with such a notion of convention, he then sets out to analyse what rules for peaceful co-existence rational agents would agree on. One important point is under what circumstances they would at all agree on rules that distribute resources among them in a regular and peaceful way, that is, the circumstances of justice. A lot has been written about the circumstances of justice, and Vanderschraaf carefully picks his way through the history of ideas to develop a slightly modified account. He then turns to the question of what would characterize a state of nature – in particular, whether Hobbes or Locke was right about the ability for rational agents to live peacefully in anarchy. He argues that Locke’s more optimistic view rests on a set of assumptions about what would be common knowledge among the agents, but agents would normally not have the knowledge Locke assumes. The conditions under which people would live in a state of nature would be very different depending on the level and content of common knowledge among the agents.

Would rational agents in anarchical conditions choose to “play fair”, that is, to share resources in ways that we intuitively think of as fair? Vanderschraaf investigates how strong reciprocity, including altruistic punishment, can evolve in at least a smaller population, and he does so without making use of group selection arguments, which is otherwise a common strategy for arguments about the evolution of strong reciprocity. However, although he shows that strong reciprocity and altruistic punishment can evolve in a small group, he also agrees with Hobbes that at some point, as the population grows, some form of government is necessary.

What kind of governance would emerge from such a population? Vanderschraaf argues that although each person would prefer to be the monarch themselves rather than to live as subject to someone else, their second-best option is to share governance with others. Although this is not anybody’s most preferred solution, it is salient because it allows people to avoid both the state of nature and being ruled by someone else. Inspired by Hobbes and Hume, Vanderschraaf thus puts forward an argument about a governing convention, and shows that it can be democratic.

Vanderschraaf then turns to three challenges raised in the literature against the notion that a rational person plays fair, that is, that a rational person complies with the rules of justice agreed upon. He calls these ‘The Foole’, ‘The Shepherd’ and ‘The Knave’. The Knave is based on Hume’s example, and concerns a person who acknowledges that complying with rules is generally a rational course of action, when opportunities arise for increasing individual benefit by breaking those rules, a rational agent takes them, as long as that does not seriously undermine the social fabric and threaten a general cooperative equilibrium. The Foole is based on Hobbes’ discussion, and concerns a person who is like the Knave except that he doesn’t worry about whether his actions destabilize the general cooperative society. The Shepherd, finally, is based on Plato’s story of Glaucon’s example of the shepherd who finds the ring of Gyges and – because invisibility makes him invulnerable to being sanctioned for his transgressions – goes on to break rules as soon as it suits him. All of these examples pose challenges to the claim that rational agents would comply with the rules of justice, even when they see opportunities to enrich themselves by breaking the rules. Responses to these challenges have traditionally tended to be given separately for each challenge, but Vanderschraaf argues that it is more effective to combine the responses to them. His response thus combines the desire to ‘have a soul free from corruption’ with considerations of reciprocity and social sanctions. His response to these three challenges forms the basis for the more developed model of how rational, self-interested agents can find it beneficial to behave justly.

It is common in the literature on justice-as-mutual-advantage to claim that a system characterized by such a notion of justice only requires agents to comply with certain requirements for their behaviour towards an agent i if agent i complies with those requirements towards them. Vanderschraaf calls this the Contribution principle. People often object to views of justice-as-mutual advantage by raising the so-called Vulnerability objection to this Contribution principle. This objection states, in one form or another, that justice-as-mutual-advantage implies that vulnerable people, who cannot for some reason or another contribute to the cooperative surplus, would not be included among those towards whom others have duties of justice. The vulnerable would have no right to a share of the resources. But our intuitions about justice tend to be that it is unjust to exclude them simply because they are vulnerable. Gauthier and others who discuss justice as mutual advantage tend to acknowledge that the Contribution principle must still require people to share with those that are temporarily unable to contribute, because we are all unable to contribute at the start of our lives, most of us towards the end of our lives, and most of us at various times in between those points too. But those that are never able to contribute, perhaps because they are severely disabled, would in such a system not be included among those towards whom others owe duties of justice.

Vanderschraaf rejects the Contribution principle. He describes a population of agents in which agents can have one of several roles. One such role is that of provider: this is a person who generates resources. A different role is that of receiver: a receiver does not generate resources herself. There are, however, two different kinds of receivers: active and passive. An active receiver can punish providers who fail to share resources with them. A passive receiver will do nothing even if providers do not share. An agent will occupy these roles at different times. In every turn in Vanderschraaf’s model, a provider is matched to a receiver, be it an active or a passive one. Vanderschraaf argues that a society in which providers share with receivers will be Pareto superior to one in which agents take all whenever they happen to occupy the provider role. Further, he argues, a society in which providers share with all receivers, not only the active ones, will be Pareto superior to one in which providers only share with active receivers. But this argument assumes that agents have the same likelihood of being paired with active vs passive receivers. If an agent knows that she will always be paired with a passive receiver she will benefit from being greedy. Further, if she knows that everybody else will share, she has an incentive to free-ride by being greedy when she is a provider but receive resources when she is a receiver. In order to avoid the problems these incentives generate, agents can punish guilty agents, that is, those that have failed to share with an innocent person. A community in which agents punish those that fail to share with innocent people can sustain sharing. Vanderschraaf mostly writes about those people who are incapable of generating resources or punishing guilty agents some of the time, but he claims that a community of people who work together for mutual advantage can require that members share with those that are never able to contribute to the general cooperative surplus, and that such sharing even with the permanently vulnerable can be sustained by the punishment of guilty agents.

I am not quite convinced that rational agents would not exclude those that will never contribute to the cooperative surplus from sharing that surplus. Vanderschraaf’s model shows that a system in which providers share with both active and passive receivers Pareto dominates one in which they only share with active ones. But he has not shown that such a system in which resources are shared with both active and passive receivers Pareto dominates a system in which providers share only with active receivers and with those passive receivers who will at some point in time occupy another role (as an active receiver, or as a provider). Why would rational agents concerned only with their own self-interest choose to share with those that are permanently unable to contribute? It seems to me that this is the critical question that Vanderschraaf would need to answer in order to successfully answer the Vulnerability objection. To claim that rational agents would punish those that fail to share allows us to establish that rational agents could be incentivized to share with everybody. But that does not answer the question of why rational, self-interested agents would find it in their interest to force productive members of their community to share with those that could never contribute to the cooperative resource surplus. If it is in their self-interest to share with the temporarily – but not with the permanently – vulnerable, then it might be in their self-interest to punish those that fail to share with the temporarily – but not the permanently – vulnerable.

Another problem for a theory of justice-as-convention – and one that Vanderschraaf readily discusses himself – is that there are too many possible convention equilibria. We need some way of determining which one of these we should take as reflecting a just state of affairs. Vanderschraaf argues that we should not make such a choice on the basis of some other theory of justice – for example by assuming that people have a particular kind of motivation or that some set of property rights are already in place. Most other theories of justice-as-mutual-advantage, he argues, do this. But he attempts to avoid this by introducing the concept of base-line consistency. Suppose we have engaged in bargaining over how to distribute a given total amount of resources, and have settled upon an equilibrium. When the total amount of resources changes (by either increasing or decreasing), we would have to engage in bargaining again in order to settle whether the changed total amount of resources should affect not only the absolute amount anybody receives, but also their relative share of the pie. But suppose now instead that we rule out all those equilibria which we would want to renegotiate if the resource pool changed. Base-line consistency means that whatever equilibrium for the relative shares of the total resources we choose should be stable even if the amount of resources to distribute changes. Whatever equilibrium we have settled on as a result of our bargaining therefore does not need to be renegotiated every time the amount of resources changes. The concept of base-line consistency allows Vanderschraaf to argue both that the set of possible equilibria is smaller than is otherwise thought, and, in particular, that it always includes the egalitarian solution.

This is a quite neat result: Vanderschraaf shows that rational agents involved in a bargaining problem with a common baseline could end up with an egalitarian system. But it would have been even better if Vanderschraaf had included a longer discussion about what his result implies about a theory of justice-as-convention. For example, that the egalitarian solution is possible does not mean that the egalitarian solution will be chosen. Had the egalitarian solution been the only base-line consistent equilibria for rational, self-interested agents, Vanderschraaf would have established that justice-as-convention would give us egalitarianism. But he has ‘merely’ shown that egalitarianism is not ruled out. Base-line consistency allows that people choose the egalitarian solution, but it also allows (in all cases in which there are vulnerable people) that those vulnerable people are not given an equal share. Presumably, according to Vanderschraaf’s own theory, those equilibria must also be considered just. And yet, they seem open to the Vulnerability objection. It would therefore have been very interesting to see what Vanderschraaf would say about these other, equally possible, equilibria that would fulfil the conditions for justice-as-convention just as much as the egalitarian solution would. We need an argument showing either that the egalitarian outcome is much more likely, or that even those other unequal outcomes fit with our intuitions about justice in important ways.

In such a discussion, I would also like to know a bit more about the justification for base-line consistency. As it is, the justification for the choice of this requirement is that it reduces the number of equilibria and that it does not import assumptions from other theories of justice. But surely there could be other requirements that would fulfil these conditions. If the requirement of base-line consistency is to serve a very important role in Vanderschraaf’s theory of justice, it would be good to have something more on which to base the choice of that requirement. The justification for base-line consistency could simply be that transaction costs make it more efficient to stick to base-line consistent equilibria rather than having to renegotiate every time the amount of resources changes. But as a justification for a normative theory of justice, this seems a bit thin, since it would depend on whether the cost for renegotiation really was high enough to outweigh possible benefits from renegotiating. Perhaps there are indeed reasons for renegotiating when the size of the cake we share changes. For example, if we were to agree to a threshold theory of justice, we could argue that the principles for distribution should be different depending on whether there are enough resources to get everybody above the threshold or not.

The general aim of the book is to develop an account of justice as convention. It certainly does this. But there are more ways to understand what the book does. For example, it could very well be argued that the arguments in the book demonstrate why we are the kind of creature that tends to have intuitions about justice, and whose intuitions about justice tend to lean towards sharing resources equally. After all, arguments about what kind of sharing principles would evolve and be stable among rational, self-interested individuals are often taken to be about explanations of why we have evolved to have the moral psychology we have. If one were to adopt such a take on the book, the discussion about the Contribution principle becomes less important, because there is no reason to believe that evolution of tendencies to think in certain ways is fine-tuned enough to explicitly exclude people who were born with serious disabilities. Suppose for example that tendencies to have justice intuitions along the lines of sharing more or less equally with people, regardless of temporary vulnerability, were mutually beneficial to people in a group. If vulnerability is a salient characteristic of everyone at least at some points in life, and only a small number of people are born so disabled that they can never contribute much to the (material) cooperative surplus, then our tendencies to think in terms of justice as equal sharing even with vulnerable people might evolve in a way that doesn’t distinguish between the temporarily and the permanently vulnerable. The stakes are not high enough for it to make evolutionary sense to use cognitive resources to distinguish between temporarily and permanently vulnerable people when it comes to our instinctive tendencies to share resources. Taken as an account of why it is that we are the kind of people we are, the normatively somewhat dubious principle of the base-line assumption can also be given a more robust justification in terms of the transaction costs involved in renegotiation, as discussed above.

Overall, Vanderschraaf’s book is thus focused on establishing that it is possible that rational agents could find it in their interest to comply with egalitarian rules. It achieves this aim admirably. But before we can conclude that justice should be understood as a convention, there are important questions still left unanswered. I hope that Vanderschraaf will turn to those questions next, and I look forward to reading about how he thinks they should be answered.