justice as mutual advantage and the vulnerable - peter vanderschraaf

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DOI: 10.1177/1470594X10386566

2011 10: 119 originally published online 22 February 2011Politics Philosophy EconomicsPeter Vanderschraaf

Justice as mutual advantage and the vulnerable

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Special Issue article for Symposium on Game Theory and Justice

Justice as mutualadvantage and thevulnerable

Peter Vanderschraaf

University of California Merced, USA

Abstract

Since at least as long ago as Platos time, philosophers have considered the possibility thatjustice is at bottom a system of rules that members of society follow for mutualadvantage. Some maintain that justice as mutual advantage is a fatally flawed theory of

justice because it is too exclusive. Proponents of a Vulnerability Objection argue that justiceas mutual advantage would deny the most vulnerable members of society any of the

protections and other benefits of justice. I argue that the Vulnerability Objection pre-supposes that in a justice-as-mutual-advantage society only those who can and do con-tribute to the cooperative surplus of benefits that compliance with justice creates areowed any share of these benefits. I argue that justice as mutual advantage need notinclude such a Contribution Requirement. I show by example that a justice-as-mutual-advantage society can extend the benefits of justice to all its members, including thevulnerable who cannot contribute. I close by arguing that if one does not presupposea Contribution Requirement, then a justice-as-mutual-advantage society might requireits members to extend the benefits of justice to humans that some maintain are not per-

sons (for example, embryos) and to certain nonhuman creatures. I conclude that the realproblem for defenders of justice as mutual advantage is that this theory of justice threa-tens to be too inclusive.

Keywords

contribution requirement, Humean strategy, justice as mutual advantage, moral standing,Provider-Recipient game, Vulnerability Objection

Corresponding author:

Peter Vanderschraaf, School of Social Sciences, Humanities and Arts, 5200 North Lake Road, Merced CA

95343, USA

Email: [email protected]

Politics, Philosophy & Economics10(2) 119147

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Since you put your interest in the place of justice, our view must be that it is in your interest

not to subvert this rule that is good for all: that a plea of justice and fairness should do some

good for a man who has fallen in danger, if he can win over his judges, even if he is not

perfectly persuasive. And this rule concerns you no less than us: if you ever stumble, youmight receive a terrible punishment and be an example to others.

Thucydides, The Peloponnesian War

1. Justice as mutual advantage

Justice as mutual advantage has a distinguished history in political philosophy. Glaucon

proposes an early version of justice conceived of as mutual advantage in Platos Repub-

lic. Epicurus appears to revive this idea in his Key Doctrines.1 Thomas Hobbes develops

a brilliant proto-contractarian theory of justice as mutual advantage, most notably in De

Cive andLeviathan. David Hume presents a different, yet also brilliant, theory of justice

as mutual advantage using proto-evolutionary arguments rather than the device of a

social contract. Hume gives the core of his account of justice in Book III of A Treatise

of Human Nature and An Enquiry Concerning the Principles of Morals.2 Hobbes and

Hume have fine contemporary successors. David Gauthier (1986) and Gregory Kavka

(1986) offer contractarian theories of justice as mutual advantage that are informed by

elements of decision and game theory. Brian Skyrms (1996) and Robert Sugden

(2004) develop evolutionary accounts of justice as mutual advantage. Sugden and

Skyrms also incorporate game theory into their analyses, but they employ the evolution-

ary game theory pioneered by John Maynard Smith (1982), rather than the rational

choice game theory of John von Neumann and Oskar Morgenstern (1944) and John Nash

(1996), who originally established game theory as a branch of the social sciences in the

1940s and 1950s. Finally, Ken Binmore gives what is undoubtedly the most ambitious

new theory of justice as mutual advantage. Binmore combines elements of evolutionary

game theory and contractarianism and produces a theory of the social contract based

solely upon mutual benefit that he maintains can both explain the norms that actually

regulate current human societies and serve as a tool for achieving principled social

reforms (1994, 1998, 2005).Interestingly, philosophers have spent far less effort trying to identify the conditions

that characterize justice as mutual advantage than they have spent defending or criticiz-

ing specific accounts of justice as mutual advantage. In fact, these conditions are more

interesting than the name justice as mutual advantage suggests. Justice as mutual

advantage cannot be simply a system of rules that individuals follow for mutual benefit.

Taking an example from David Lewis (1969: 43), the individuals who follow a rule that

requires the initial caller to call again when a local phone connection is interrupted in

midconversation do so for mutual benefit. But an initial receiver who calls back by mis-

take right after a phone connection is lost and gets a busy signal is not guilty of an injus-tice. Similarly, if a couple, Julie and Bob, get separated while shopping in a mall, it is to

their mutual advantage that they follow this rule: When separated, head for the coffee

shop in the mall. Suppose they did not prearrange to follow this rule. When they get

separated each follows the rule: When separated, head for my partners favorite store

120 Politics, Philosophy & Economics 10(2)



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in the mall. Then Bob goes to the childrens clothing store and Julie goes to the kitchen

appliance store. They miscoordinate, but neither has committed an injustice in this

situation. The rules that help such individuals coordinate in problems like the two

described here are rules that individuals follow for mutual benefit. Yet these rules arenot rules of justice. For problems like the telephone and the shopping mall problems are

problems of pure coordination (Lewis, 1969; Schelling, 1960). In these kinds of prob-

lems, the interests of the individuals coincide perfectly. In such problems, no one cares

which rule they follow, just so long as the rule they do follow produces an outcome that

is best for all.

If justice as mutual advantage is not merely a set of rules that individuals follow for

mutual benefit, then what is it? The answer I propose below builds upon some sketchy

but important insights regarding justice as mutual advantage in works by David Gauthier

(1986), Brian Barry (1989, 1995), and Allen Buchanan (1990) as well as on some of the

literature that discusses the circumstances of justice (Barry, 1989; Hart, 1994; Hume,

1998, 2000; Rawls, 1971; Vanderschraaf, 2006). Barrys work provides a useful starting

point. While Barry fervently rejects justice as mutual advantage, he treats this theory of

justice with great respect. Indeed, in his Theories of Justice, Barry takes justice as mutual

advantage to be the one serious competitor to his own preferred theory of justice, a the-

ory Barry calls justice as impartiality (1989: 7). I will not discuss here Barrys account of

justice as impartiality or his claim in Theories of Justice that justice as impartiality and

justice as mutual advantage are the two main options for philosophers to consider.3 Here

I want to draw upon Barrys descriptions of justice as mutual advantage. In Theories of

Justice, Barry describes justice as mutual advantage thus:

Justice is simply rational prudence pursued in contexts where the cooperation (or at least

forbearance) of other people is a condition for our being able to get what we want. Justice

is the name we give to the constraints on themselves that rational self-interested people

would agree to as the minimum price that has to be paid in order to obtain the cooperation

of others. (Barry, 1989: 67)

In his laterJustice as Impartiality, Barry says that justice as mutual advantage consists of

an attempt to complete the following project:

we are to imagine people with different conceptions of the good seeking a set of ground

rules that holds out to each person the prospect of doing better (on each persons conception

of what doing better consists of) than any of them could expect from pursuing the good

individually without constraints. (Barry, 1995: 32)

I will not speculate as to why Barry gives different descriptions of justice as mutual

advantage in these two works. These descriptions are certainly compatible, and each

highlights what I think is an important condition that must be part of any account of jus-tice as mutual advantage. The second description addresses the structure of interaction.

Justice as mutual advantage is a system of rules or requirements. The system requires

individuals to restrain their pursuit of their personal interests to some extent. If the mem-

bers of a society conform their conduct with the system, then they all fare better than they

Vanderschraaf 121



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fare in a free for all in which each individual pursues her own interests without

restraint. They fare better by conforming than they fare in the free for all because their

individual interests conflict to some extent, so that no one can receive everything she

wishes from society unless others receive less than they wish for. Hobbess account ofcivil society is a classic example of such a system. Hobbes argues that if individuals all

follow the requirements of the civil society in which they live, they all do better than they

would do in their unconstrained natural condition or state of nature, which inevitably

deteriorates into a war of all against all. Barrys first description addresses motivation.

In justice as mutual advantage, each individual conforms for exactly one reason: each

wants the cooperation of the others in society. Hume summarizes this rationale for com-

pliance beautifully in A Treatise of Human Nature:

I learn to do a service to another, without bearing him any real kindness; because I foresee,that he will return my service, in expectation of another of the same kind, and in order to

maintain the same correspondence of good offices with me or with others. And accordingly,

after I have servd him, and he is in possession of the advantage arising from my action, he is

inducd to perform his part, as foreseeing the consequences of his refusal. (Hume, 2000:

3.2.5:9)

I now propose the following as necessary conditions for a system S of rules to be a

system of justice as mutual advantage for a society P. Note that the following three con-

ditions are compatible with Barrys two sketches of justice as mutual advantage quoted

above, but they omit one important element in his account, which I will address at theend of this section.

(M1) Conflicting Interests. Srequires each memberi ofP capable of pursuing interests

to restrain is pursuit of is own interests to some extent in order to advance the

interests of other members to some extent.

(M2) Pareto Improvement for Contributors. If no member of P violates the require-

ments ofS, then for each memberi ofP capable of pursuing interests who follows

the requirements of S, is own interests are better satisfied than they are if no

member of P restrains her pursuit of her own interests.(M3) Negative Mutual Expectations. Any given member i of P capable of pursuing

interests follows the requirements of S only because i expects that if she were

to violate these requirements, then other members of P would consequently

reduce their restraint of their conduct with respect to her, and is interests would

consequently be less well satisfied. Moreover, ifi violates the requirements ofS,

then the others subsequent reduction of their restraint of their conduct with

respect to i is compatible with the requirements of S (because i is a violator).

In this article, I will follow Gauthier (1986: 130) and call the additional benefits thatmembers of society generate by following any system of rules that satisfies conditions

(M1), (M2), and (M3) the cooperative surplus. I will assume that one contributes posi-

tively to the cooperative surplus exactly when one restrains the pursuit of ones own inter-

ests somewhat in order to allow others to pursue their interests more effectively. I will also




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assume that if one violates the requirements ofS by pursuing ones own interests without

restraint, then one subtracts from the cooperative surplus. Note that the motivation

for complying with the systems requirements is built into justice as mutual advan-

tage. The Pareto Improvement condition (M2) guarantees that those who add to the

cooperative surplus by their compliance receive the benefits of the cooperative sur-

plus and that they do better than they would do in the free for all of no restraint.

But those who pursue their own interests without restraint are to be denied some of

the benefits of the cooperative surplus. Also, conditions (M1)(M3) do not presup-

pose that the members of society have only selfish motives. In addition to their own

selfish concerns, members might wish to advance the conflicting agendas of variouscommunities represented in society, such as political movements or religions. Even

a society whose members interests are purely altruistic can satisfy (M1)(M3).4

Justice as mutual advantage requires only that the interests of the members of soci-

ety both coincide and conflict to some extent. Contributors to the system improve

their prospects over what they can expect in a free for all, and the system requires

the contributors to give in to the interests of others to some extent.

While I think (M1)(M3) are necessary parts of justice as mutual advantage, I do not

think that they constitute a full account of justice as mutual advantage. For suppose

that two individuals are matched in a Prisoners Dilemma, as summarized in Figure 1.Suppose further that S consists of a single rule, which requires one to follow strategy

D. Then conditions (M1)(M3) are satisfied, but rational parties will not follow the

D;D outcome, even if they know that D;D is a Pareto improvement over H;H .Since H strictly dominates D for each party, they will settle into the suboptimal

H;H outcome. In fact, Barry maintains that justice as mutual advantage has the struc-ture of a Prisoners Dilemma, and is consequently unstable (1995: 51). Here Barry blurs

the distinction between the structure of interaction and the rules that are to regulate con-

duct in this interaction. But if he were correct in thinking that the relevant interaction

structure is a Prisoners Dilemma, then indeed justice as mutual advantage would beunstable. I think Barry is not correct. The interactions that any system of justice regulates

in an actual society are too complex to be even roughly summarized by a single game.

But one can use specific games to illustrate specific rules of justice. Consider the

Hawk-Dove game summarized by Figure 2.

Party 2

D H

(1, 2)

(1, 0)

(0, 2)

(1,

2)

Party 1

H

i> i> i> 0, i {1,2}

D

Figure 1. Prisoners Dilemma

Vanderschraaf 123



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Sugden (2004: Section 4.2), Skyrms (1996: Ch. 4), and Vanderschraaf (1998) use

this game in their analyses of the problem of property acquisition. Suppose each

party would like to claim all of some good exclusively for herself (H). Each can also

offer to share the good (D). If both choose D, then they share the good. If one party

chooses H and the other chooses D, then the D-follower immediately backs down and

the H-follower gets all the good. If both choose H, then they fight the worst outcome

for them both. This is a much more complicated problem for the two parties than the

problem of the Prisoners Dilemma. In the Prisoners Dilemma, H is ones best choice

no matter what the other does. In Hawk-Dove, H is ones best choice only when one hasa sufficiently high degree of belief that the other will not also choose H. What are

the parties in Hawk-Dove to do? Hume argues that people will frequently solve problems

of original property acquisition by following a finders-keepers convention (1998: 3.2,

2000: 3.2.3). Suppose each party knows she is the first to find the good a third of the time.

Then if each party follows the rule: H if I know I found the good first, D otherwise,

they will follow D;D , D;H , and H;D a third of the time each. By following thisfinders-keepers rule, both restrain their conduct some of the time to allow the

other to receive more, and both do better than they do if neither restrains her conduct

and they both follow H. So this rule satisfies the conditions (M1)(M3) so faridentified as necessary parts of justice as mutual advantage. Moreover, given

what they know, neither party will want to deviate unilaterally from this rule.5 That is,

the finders-keepers rule characterizes a stable system or equilibrium of the Hawk-

Dove game.6

Of course, a rule that settles questions of original ownership is but one part of a

system of justice. But the finders-keepers convention illustrates a more general

point: if all of the rules of the system characterize equilibria of the relevant inter-

actions, then the system of justice as mutual advantage is stable. So I propose an

additional condition:

(M4) Positive mutual expectations. Any given member i of P capable of pursuing

interests expects that if she follows the requirements ofS, then the other members

of P will restrain their conduct with respect to her, as S requires.

Party 2

D H

D (1, 2)

(1, 2)

(1, 2)

(0, 0)

Party 1

H

i+i > i> i> i> 0, i {1,2}

Figure 2. Hawk-Dove




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Given (M3) and (M4), a given member of the population does better to follow the

requirements than to violate these requirements. So these conditions together guarantee

that each requirement of the system defines an equilibrium of the relevant interaction.

With (M4) I conclude my own explication of justice as mutual advantage. However,before continuing, I wish to note that the analysis that follows does not require, as

I require, that justice as mutual advantage be a stable social state. The arguments below

will still apply if one supposes that justice as mutual advantage requires (M1), (M2), and

(M3) only.

I must address one final and crucial point here. Condition (M4) implies that to follow

the requirements of the system is a sufficient condition for receiving the benefits of the

compliance of others with the system. Is following the requirements also a necessary

condition for receiving the benefits of the system? The answer to this question might

seem obvious, as condition (M3) explicitly states that if one violates the requirements

of the system, then one loses out on some of its benefits. Much of the best literature

on justice as mutual advantage does suppose that complying with the system is indeed

a necessary condition for receiving the benefits of others compliance. While Barry does

not say so explicitly, some of his criticisms of justice as mutual advantage plainly imply

that he thinks compliance is a necessary condition. Buchanan and Gauthier are explicit.

Gauthier (1986: 17) makes compliance a prerequisite for receiving benefits in his theory

and Buchanan (1990: 2301) maintains that justice as mutual advantage in general is

committed to this prerequisite. So I will attribute the following to Barry, Gauthier, and

Buchanan:

(M5) Contribution Requirement. S requires that members of P will restrain their con-

duct with respect to a given member i only if i increases the cooperative surplus

by following the requirements of S.

Condition (M5) might look redundant in light of (M3). Indeed, (M3) would be redundant

if each member necessarily either follows the requirements of the system or violates

them. But to assume this is to overlook an important third possibility. Perhaps some

members of society are simply unable to pursue interests at all. Such members might

have interests, but they are in no position either to pursue these interests or to limit thepursuit of their interests through their own efforts. Once one admits this possibility, one

must at once face the Vulnerability Objection.

2. The Vulnerability Objection

I will define the vulnerable members of a society as those humans living in this society

who are unable through their own efforts to contribute to the cooperative surplus. The vul-

nerable in a society might include very young children, some of the very elderly, the seri-

ously ill, and the seriously injured. Individuals who suffer from severe disabilities turn outto be a particularly troublesome class of vulnerable members of society for some critics

and defenders of justice as mutual advantage. For the present, I will limit the membership

of a society to humans, recognizing that some might wish to extend the analysis here to

members of other species. I also recognize that this definition of vulnerability is not

Vanderschraaf 125



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perfectly adequate. The ability to contribute to the cooperative surplus varies across

several dimensions. A healthy adult is likely to be able to contribute more to her

societys cooperative surplus than can a healthy ten year old child, who, in turn,

is likely to be able to contribute more to the surplus than can a healthy two yearold child. An adult battling a treatable form of cancer might be able to contribute

less to the surplus than other more physically healthy adults, but more than one who

is so ill as to be continually bedridden. Additionally, Buchanan rightly argues that

ones ability to contribute to the cooperative surplus can also vary according to the

way ones society structures its frameworks for cooperation. For example, Buchanan

argues that individuals who suffer from mild retardation and dyslexia might be vul-

nerable in a highly literate society in which contributing to the cooperative surplus

requires one to be able to follow complicated rules and practices often communi-

cated in writing. Yet these same individuals might be able to contribute to the coop-

erative surplus as well as anyone in a hunter-gatherer society (Buchanan, 1990:

237). Perhaps out of politeness to the academic profession, Buchanan did not add

that in all likelihood some university professors who could contribute in the literate

society would be vulnerable in the hunter-gatherer society.

In short, vulnerability is really best thought of as a matter of degree, varying both

according to ones particular society and to ones individual circumstances. However,

I will assume that if one holds the structures of society fixed, then one can identify some

members of society as vulnerable in the sense given here, that is, these members of soci-

ety cannot contribute to the cooperative surplus at all. This assumption is plausible, and

is all that is needed to develop the Vulnerability Objection. One can state the objection

quite simply: Justice as mutual advantage denies the vulnerable any of its advantages,

which shows that justice as mutual advantage is, in fact, no proper account of justice

at all. For those who are not instantly persuaded by this statement that justice as mutual

advantage is a nonstarter, one can supply a more developed argument, as follows.

P1. If a system of rules is merely a system of rules that members of a society follow

only for mutual advantage (and that satisfy (M1), (M2), and (M3)), then the vul-

nerable members of society have no claim to any of the benefits of the cooperative

surplus.P2. By definition, a member of society is owed benefits of justice if, and only if, this

member has some claim to some benefits of the cooperative surplus.

P3. So, if justice is merely a system of rules that members of a society follow only for

mutual advantage (and that satisfy (M1), (M2), and (M3)), then the vulnerable

members of society are not owed any benefits of justice.

P4. The vulnerable members of society are owed some benefits of justice.

C. So justice is not merely a system of rules that members of a society follow only for

mutual advantage (and that satisfy (M1), (M2), and (M3)).

The parenthetical requirements that the rules satisfy (M1)(M3) are included, despite

some redundancy, because as we saw in Section 1, justice as mutual advantage does not

purport to be just any system of mutually advantageous rules. The key moves in this

argument are, of course, P3, P4, and the modus tollens conclusion. The preliminary




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P1 and P2 serve two purposes. P1 and P2 together clarify what it means to say that one is,

or is not, owed the benefits of justice. More importantly, stating P1 explicitly makes it all

the more clear that the Vulnerability Objection relies upon the Contribution Rrequire-

ment. If ability to contribute to the cooperative surplus really is a prerequisite for receiv-ing any of the benefits of others contributions, then the vulnerable by definition are

ineligible to receive any benefits.

Since I will later argue against the Contribution Requirement, I do not include it as a

premise in the argument above. However, as noted already, some of the best critics and

defenders of justice as mutual advantage maintain that this theory of justice must contain

the Contribution Requirement. In addition, they take the Vulnerability Objection to be

an especially serious, even fatal, problem for justice as mutual advantage. Three repre-

sentative passages are worth quoting here. Barry, for one, believes that the Vulnerability

Objection is fatal. His criticisms of justice as mutual advantage are especially eloquent.

For example, in Theories of Justice Barry writes:

Is the theory of justice as mutual advantage really a theory of justice at all? It is surely nor-

mally regarded as a paradigm of injustice to kill some innocent person simply because that

person is in the way of your getting something you want, or to take what you want from

someone under threat of death. To say that this killing or taking is rendered just by the

inability of the victims to organize an effective resistance would surely be a hollow mockery

of the idea of justice adding insult to injury. Justice is normally thought of not as ceasing to

be relevant in conditions of extreme inequality of power but rather, as being especially rel-

evant to such conditions. (Barry 1989: 163)

Buchanan is even more forceful. He argues that if the Contribution Requirement is taken

to its logical conclusion, then justice as mutual advantage implies that

[If] all moral rights, including the so-called negative rights to refrain from injuring and

killing, are rationally ascribable only to potential contributors to social wealth, then we

violate no rights if we choose to use noncontributors in experiments on the nature of pain

or for military research on the performance of various designs of bullets when they strike

human tissue, slaughter them for food, or bronze them to make lifelike statues. (Buchanan1990: 232)

7

Even Gauthier admits that the presence of vulnerable members of society appears to

expose a serious weakness in his theory (1986: 17). Gauthier claims that care for the aged

might pose no serious problem for his theory, since even though they might be vulner-

able, they might still receive benefits from the cooperative surplus in payment for past

contributions to the surplus. The vulnerable who pose the real problem, according

to Gauthier, are the severely disabled: Speaking euphemistically of enabling them to

live productive lives, when the services required exceed any possible products, concealsan issue which, understandably, no one wants to face (1986: 18 n. 30). One might be

tempted to respond to Gauthier as follows, If even you dont want to face the conse-

quences of justice as mutual advantage for the disabled, lets all admit that justice as

mutual advantage is a sham.

Vanderschraaf 127



11/30

3. Three unsatisfactory responses

The task for a defender of justice as mutual advantage is clear. The defender must

respond to the Vulnerability Objection without turning justice as mutual advantage into

something else. A first response to the Vulnerability Objection is to simply accept that

the vulnerable fall outside the scope of justice. Hume appears to do just this when he

claims that if humans coexisted with another species of rational creatures who were

so relatively powerless they could not affect the humans prospects at all, then there

would be no justice between the humans and these weaker rational creatures (1998:

3.1:18). Gauthier eventually bites the bullet and declares that the vulnerable in society

indeed have no claim on any of the benefits of justice as mutual advantage (1986:

268, 2828).8 One might claim that the Vulnerability Objection has no real force,

because the objection assumes that the vulnerable are owed justice with no regard to

mutual advantage. In other words, the Vulnerability Objection assumes what it allegedlyproves, namely, that justice is not merely mutual advantage. Referring back to the sec-

tion 2 argument, defenders of justice as mutual advantage can complain that their critics

assume the truth of P4 far too casually, and assert that P4 is simply false and however

vehemently some might attack justice as mutual advantage, those who give this response

to the Vulnerability Objection can point out that at least they are not hypocrites. With char-

acteristic frankness, Binmore, who does not believe that justice as mutual advantage

necessarily excludes the helpless, describes the conduct of many who claim to oppose jus-

tice as mutual advantage:

The unwelcome truth is that practical morality the morality by which we actually live

does in fact endorse the exploitation of those powerless to resist. We dismiss the

homeless and the destitute as being an unfortunate consequence of the necessity that a

productive society provide adequate incentives for its workers. Is this not to accept that

an underclass must suffer in order that the rest of us can enjoy a higher standard of liv-

ing? We do not, of course, say this openly. Instead, we square things with our con-

sciences by dehumanizing those excluded from the feast. (Binmore, 1998: 258259)

A familiar criticism of utilitarianism directly parallels the Vulnerability Objection tojustice as mutual advantage. Alternative views of this criticism of utilitarianism illumi-

nate the strengths and weaknesses of this first response to the Vulnerability Objection.

Newcomers to utilitarianism sometimes raise the worry that the utilitarian principle

implies the doctrine, famously associated with Machiavelli, that the ends justify the

means.9 Indeed, in a sense, utilitarianism implies that the ends require the means. This

motivates an ends-require-the-means criticism of utilitarianism: The utilitarian principle

implies that one should commit an evil act (or actively support an evil institution or

policy) when doing so maximizes the utility of society. But one should not commit an

evil act (or actively support an evil institution or policy) under any circumstances. Soone should reject the utilitarian principle.

A first, and common, response to the ends-require-the-means criticism echoes the first

response to the Vulnerability Objection: this criticism assumes that some acts are evil (or

that some institutions or policies are evil) whether or not they meet the utilitarian




12/30

standard. The ends-require-the-means objection assumes what it allegedly proves,

namely, that utilitarianism is not the ultimate standard for evaluating the morality of our

actions, institutions, and policies. Indeed, utilitarians spread their gospel hoping converts

will reevaluate their beliefs regarding which actions, institutions, or policies are good orevil. So the ends-require-the-means criticism is no theoretical blow at all to utilitarian-

ism. Similarly, viewed as an priori criticism, the Vulnerability Objection does not under-

cut justice as mutual advantage in the slightest.

To be sure, not all critics of justice as mutual advantage accept this dismissal of the

Vulnerability Objection.10 But whether one accepts this first rebuttal or not, one can view

the Vulnerability Objection in a different way. Even if one concedes that the objection has

no a priori force, the objection raises a serious explanatory problem. A time-honored

method for evaluating any account of justice is to consider how well this account coheres

with and explains ordinary received views regarding justice. In particular, philosophers

take special care to examine how well an account of justice meshes with and explains what

John Rawls calls the considered judgments of society regarding justice.

These are questions we feel sure must be answered in a certain way. For example, we are

confident that religious intolerance and racial discrimination are unjust. We think that we

have examined these things with care and have reached what we believe is an impartial

judgment not likely to be distorted by an excessive attention to our own interests. These con-

victions are the provisional fixed points which we presume any conception of justice must

fit. (Rawls, 1971: 2021)

Again there is a parallel with utilitarianism. Utilitarians take seriously the ends-require-

the-means objection as an explanatory criticism of their theory. They argue that in the

main, utilitarianism actually requires us to refrain from doing what we ordinarily think

is wrong. In Utilitarianism, John Stuart Mill takes care to argue that a number of received

views regarding justice have a utilitarian basis. Henry Sidgwick devotes much of The

Methods of Ethics to discussing the relationship between commonsense morality and the

methods of intuitionism, utilitarianism, and egoism. In the concluding chapter, Sidgwick

summarizes his main positive conclusions, namely, that the methods of intuitionism and

utilitarianism are compatible and that these methods explain our commonsense moralbeliefs (1981: 4967).11

Similarly, taken as an explanatory criticism, the Vulnerability Objection has bite, and

on a standard otherwise favorable to justice as mutual advantage. Both defenders and

critics of justice as mutual advantage argue that one of the chief advantages of this theory

of justice is its explanatory power. Hume develops his conventionalist theory of justice in

large part to explain systematically the variety and complexity of systems of rules that

regulate real human societies. Barry thinks that the main reason one should seriously

consider justice as mutual advantage as the right account of justice is its substantial over-

lap with our ordinary beliefs regarding justice (1989: 163, 1995: 45 n. c). But the overlappresumably does not extend to our beliefs regarding the vulnerable. Even Gauthier

expresses some squeamishness regarding the way his theory treats the severely disabled.

I suspect that, like the hostile critics of justice as mutual advantage, Gauthier believes

that one considered judgment regarding justice is that the vulnerable must not be denied

Vanderschraaf 129



13/30

the benefits of justice merely because they are vulnerable. When the Melians appeal

to justice in their exchange with the Athenians, they invoke this considered judgment.

One can counter the Vulnerability Objection by denying P4. But to deny P4 is to deny

a considered judgment regarding justice. So if one tries this move, one shouldprovide a convincing case that all who hold and have held this considered judgment

are and always were mistaken. And this case had better include reasons other than the

consequences of assuming that justice as mutual advantage is the right theory of jus-

tice. Here I side with Barry, Buchanan, and the other critics of justice as mutual

advantage who press the Vulnerability Objection. I think there are no such indepen-

dent reasons for thinking that so many have been wrong and that the vulnerable really

are owed no justice because of their vulnerability. So I find the first response to the

Vulnerability Objection unacceptable.

Two other unsatisfactory responses to the Vulnerability Objection can be dealt with

more quickly. One could deny that the vulnerable make no important contributions to the

welfare of society. For instance, one could argue that since the vulnerable are incapable

of violating the requirements of justice, they support the system of justice as mutual

advantage in a passive way.12 I reject this proposal because I think such passive

contributions would give those who can contribute positively to the cooperative sur-

plus little reason to restrain their conduct with respect to the vulnerable. Indeed, these

contributors might be tempted to regard the care and other resources the vulnerable need

simply to continue living as a drain on the cooperative surplus, and consequently be

tempted to withhold such care and resources from the vulnerable. One might claim that

if contributors to the system for mutual advantage do not confer benefits to the vulner-

able, then the contributors will be more tempted not to contribute to the system at all. But

I see no reason to believe that this claim is true. Moreover, this claim assumes that ones

willingness to comply with the requirements of the system for mutual advantage depends

directly, to a certain extent, on how much of the benefits of the system the vulnerable

receive, and this plainly goes against the Negative Mutual Expectations requirement

of Section 1s analysis of justice as mutual advantage.

A variant of this response appeals to contributions that people value even though they

do not add to the cooperative surplus. Mother Teresa famously said, the poor are won-

derful. The poor are very kind. They have great dignity. The poor give us more than whatwe give them (1996: 83). In a similar vein, one might argue that even if the vulnerable

cannot increase the material wealth of society or other parts of this societys cooperative

surplus, they contribute invaluable intangibles such as love, and consequently should

not be stigmatized as noncontributors. Love and similar goods are without doubt terribly

important. Still, this variant is still an unsatisfactory response to the Vulnerability Objec-

tion. Many of the vulnerable, such as those who are comatose, are just as incapable of

expressing love or contributing other intangibles as they are of contributing to the

cooperative surplus. So the scope of this variant appears to be too narrow. Is a system

of justice satisfactory if this system extends some benefits to very young loving children,but none to more mature persons whose conditions leave them unable to give goods such

as love to others? Yet even if one sets this problem aside, the variant is still unsatisfac-

tory. By definition, the intangible goods referred to here are not contributions to the

cooperative surplus. If one appeals to such goods as reasons for extending the benefits of




14/30

justice, then one adopts an account of justice that is not a justice-as-mutual-advantage

account.

A third inadequate response is to argue that justice as mutual advantage will provide

the benefits of justice to the vulnerable without requiring that their interests be taken intoaccount directly. According to this line of reasoning, justice will protect the vulnerable

because they have active advocates, such as their friends and families, who want the vul-

nerable protected and cared for. Kavka, for example, suggests that Hobbesian contractors

would build provisions on behalf of the disabled into their system of justice. According

to Kavka, these contractors would want their own disabled friends and family members

covered in the system of justice. Moreover, as they are both a needy and a nonthreatening

minority, the disabled would be likely targets of whatever sympathy or altruism the con-

tractors might have (Kavka, 1986: 242). Perhaps Hobbes has a similar idea in mind when

he argues that children, fools and madmen that have no use of reason are to have deci-

sions made on their behalf by guardians approved by the civil society (1994: 16:10).

Morris (1991, 1998) presents a sophisticated account ofmoral standingto address the

general problem of providing benefits for the vulnerable in a contractarian system of jus-

tice. Kavka and Morris are not trying to rescue justice as mutual advantage as I have

defined it here, but their work provides a fine basis for developing this response to the

Vulnerability Objection. According to Morriss analysis, one has moral standing exactly

when one is owed moral consideration by others (1991: 81, 1998: 191). Put another way,

one has moral standing when others are obligated to treat one with some restraint, so that

one receives some of the benefits of justice. An individual i has primary moral standing

with respect to individual jifi andjcan restrain their conduct toward each other so that

the other benefits and, in fact, do restrain their conduct in this manner. An individual

i has secondary moral standingwith respect to individual jif for some individual k, jhas

primary moral standing with respect to k and k would be unwilling to restrain her con-

duct toward j if j were to fail to restrain his conduct toward i so that i benefits. In this

case, i is an object of ks preferences, that is, k cares fori enough that k would be willing

to punish someone who does not treat i with restraint (Morris, 1991: 8990). So a con-

tributor to the cooperative surplus could be required to treat a vulnerable individual with

some restraint if the vulnerable individual has secondary moral standing. For example,

one is required to treat an infant with some restraint if one has primary moral standingwith respect to the infants parents and the parents love their child to a degree that makes

their child an object of their preferences. As Morris notes, on this account moral standing

is a relational concept. One could have moral standing with respect to some of the people

with whom one interacts, but perhaps not with others, including those with whom one

never interacts or who are unwilling to treat one with restraint.

Moral standing is an ingenious framework for analyzing the obligations in contractar-

ian systems of morality. However, I think moral standing does not provide an adequate

basis for responding to the Vulnerability Objection. One can appeal to secondary moral

standing to explain why contributors to the cooperative surplus could have good reasonto treat the vulnerable with restraint. The vulnerable cannot punish nasty individuals

who treat them with no restraint, but others who are not vulnerable can punish these

nasty people. Indeed, I will employ this idea of indirect punishment to enforce com-

pliance with the requirements of a justice-as-mutual-advantage system in the following

Vanderschraaf 131



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section. But secondary moral standing relies upon motivating forces such as altruism and

affection that lie outside of the scope of justice as mutual advantage. Vulnerable mem-

bers of society have secondary moral standing when they have advocates who care for

them to the degree that they are objects of their advocates preferences. But if onesweetens the pool of motivating forces among the members of society to include

enough altruism and affection to generate secondary moral standing, then one no longer

has justice as mutual advantage.13 Moreover, moral standing would introduce an element

of partiality into the system of justice that jars with another considered judgment,

namely, that justice should be impartial. If one employs the moral-standing approach,

then in the human societies we know many of the vulnerable would receive no benefits

of justice simply because these vulnerable people have no family or friends. A final prob-

lem with moral standing, a problem Morris clearly acknowledges, is that this idea pro-

duces certain strikingly counterintuitive results. While secondary moral standing could

explain why individuals who care nothing for the welfare of certain vulnerable people

still have moral obligations to these vulnerable people, secondary standing cannot

always account for the relevant moral obligations of the advocates of these vulnerable

people. For example, if parents care for their infant child to a sufficient degree, then rela-

tive strangers who interact with the parents might have moral obligations to this infant

due to secondary moral standing. But if no one other than the parents happens to care for

this infant, then the infant has no moral standing with respect to her own parents. She is

not capable of having primary moral standing with respect to her parents, and she also

has no other advocates whose care for her would generate secondary moral standing with

respect to her parents (Morris, 1991: 95). Because of its dependence upon the motiva-

tions, or lack thereof, of relevant third parties, moral standing can fail to ground the obli-

gations of justice in sufficient generality. In particular, moral standing can fail to ground

the duties family members have toward each other.

4. Another response

As hinted above, I favor a different response to the Vulnerability Objection: leave the

Contribution Requirement out of the account of justice as mutual advantage. This move

allows one to deny P1, and so the argument from Section 2 does not go through, after all.But without the Contribution Requirement, can any system of rules still be a system of

justice as mutual advantage? In this section, I will show why one can give an affirmative

answer to this question.

Consider a community whose members interact repeatedly over periods of time.

Community members are sometimes active and sometimes inactive. Members play the

role of provider for a fraction a >1

2of the time periods when they are active and of

recipientfor the rest of the time. In particular, members are always recipients when inac-

tive. At each period, every recipient is matched with a provider. When she is a provider,an active member produces a quantity of a (perishable) good that can benefit herself as

well as others in the community. An active recipient can destroy the good his current

provider produces. An inactive recipient can do nothing. The benefit a memberi receives

from consuming a fraction l of a providers good is summarized by a payoff function




16/30

ui l , a von Neumann-Morgenstern utility function. Each members marginal payoff for

additional fractions of the good decreases. In particular, ui1

2

> aui 1 . So if, for

example, providers produce bread and a 59

, then a community member receives a

benefit from receiving half of the bread a provider produces at a given time that is greater

than5

9of the benefit of receiving all the bread.14 For simplicity, each payoff function ui

is scaled so that ui 0 0 Let ei1 denote the expected proportion of periods of amembers lifetime during which she is inactive and let ei2 denote the expected proportion

of periods that she is matched with an inactive counterpart.

Now suppose that providers may either be uniformly greedy, each provider consum-

ing all of the good she produces, or more generous, so that under certain circumstances a

provider shares half of the good she produces with her current recipient. The average

payoff for a given member i when all are greedy is a 1 ei1 ui 1 , since i receives apositive payoff only when she is a provider. On the other hand, if every provider in the

community offers half the good to her recipient at each period, then every member of the

community receives a one-half share of the good at every period, so the average payoff to

each community member is ui1

2

. Since

ui

1

2

> aui 1 > a 1 ei1 ui 1

the community whose providers always share half of the good they produce achieve a

Pareto improvement over the community whose providers are always greedy. If the pro-

viders share only with their active recipients, who can punish a greedy provider by

destroying the good? If the members of the community follow this harsher pattern

whereby inactive members receive nothing, then the average payoff for a given member

i is

gi 1 ei1 1 ei2 ui 12

1 ei1 ei2ui 1 :

Ifei1 ei2, that is, all members are inactive for the same portion of time periods, then

ui1

2

> gi and so the community whose providers always share half Pareto dominate

the community whose providers share only with active recipients.15 However, for

reasons that will become apparent below, it is important to consider cases in which ei1andei2 vary across members. In particular, if ei2 1, so that member i when active isalways matched with an inactive member, and if i follows the harsher pattern, then is

average payoff is 1 ei2 ui 1 :16 Note that even in this extreme case,

ui1

2

> 1 ei1 ui 1 when ei1 >

ui 1 ui12

ui 1

For example, if ui1

2

2 and

ui 1 3, then even one who when active is always a provider matched with inactives

Vanderschraaf 133



17/30

does better by sharing with all than by following the harsher pattern if ei1 >3 2

3

1

3.

Naturally, if one expects the others in the community to be generous, one might raise

a free-rider problem. Why not take advantage of the others generosity by being greedywhen I am a provider? The community may be able to forestall free-riding if members

follow a Humean rule: When a provider, always offer half the good to an innocentreci-

pient and nothing to a guilty recipient, and when an active recipient, accept the offer from

an innocent provider and destroy the good of a guilty provider. A community member is

innocent until she is greedy when matched with an innocent recipient, at which point she

becomes guilty. If a community member remains innocent, she receives an average

payoff ofui1

2

over time. If, when a provider, a member offers nothing to an innocent

recipient, then the best this now guilty member can achieve is an average payoff of

1 ei1 ui 1 , assuming she has the good luck to be matched always with inactivesafter her offense. As shown in the last paragraph, this payoff can be worse than the

average payoff of conforming to the Humean rule when ones own proportion of

inactive periods is sufficiently high. So each member of the community can have a

decisive reason to conform with the Humean rule. This informal argument is

developed in more detail in the Appendix. There it is shown that under fairly general

conditions, the Humean rule characterizes an equilibrium of this system of repeated

games.

What does this toy example show? This is a simple case of a community whose

members can enjoy mutual benefits when they provide for the welfare of others at

some personal costs. The state in which all providers are greedy corresponds to the

free for all in which no one restrains conduct so that anyone else may benefit.

The all-greedy state is an equilibrium of the system, since the best average payoff

any member can achieve if all her counterparts are greedy providers is the payoff

she achieves by being a greedy provider herself. The state in which all active mem-

bers follow the Humean rule can also be an equilibrium of this system, and this state

yields every member a higher average payoff than that of the all-greedy state. The

Humean equilibrium of the Provider-Recipient game is a simple example of justice

as mutual advantage, one of many such examples in the game-theoretic literature onnorms and conventions. When a provider meets an active recipient, they play an

Ultimatum game in which the provider offers a share of the good at stake to the reci-

pient, who may then either accept the offered share and leave the provider with the

rest or reject the offer, in which case both get nothing (Guth et al., 1982). When a

provider meets an inactive recipient, they play a degenerate Dictator game whereby

the recipient must accept any offered share of the good, including nothing (Forsythe

et al., 1994).17 So the Provider-Recipient game is really a system of sequential bar-

gaining games in which the recipient is completely powerless when inactive. The

reason a > 12

is that every recipient has a provider at every period, and some of the reci-

pients may be inactive. I call the strategy that characterizes the Humean equilibrium

Humean in part because this strategy resembles the rule that characterizes the conven-

tion of promises Hume describes in A Treatise of Human Nature (2000: 3.2.5), namely,




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members of a community exchange promises only with others who are not known to

have broken a promise in the past.18

The Provider-Recipient game differs from most other game-theoretic examples of

justice as mutual advantage in that members are not always able to affect the prospectsof their counterparts. The key idea behind the Humean equilibrium is that a norm of shar-

ing with all is enforced indirectly. A violator might not expect to be punished by the vic-

tim, who might be indefinitely or even permanently inactive. But a violator can expect

other active community members to punish her.19 Hume emphasizes the possibility that

one who violates the requirements of justice will be punished indirectly by parties other

than the victims of his injustice, which is another reason I call the strategy of the sharing

equilibrium described above Humean. The presence of inactive members in the system

mimics the facts that all humans are vulnerable at certain points in life and that some are

vulnerable all their lives. In this game, members might be inactive both early in life and

late in life, and even be inactive intermittently throughout their lives. This, of course,

reflects the actual life histories of most humans who live into adulthood, and who are

occasionally seriously ill or injured. The Provider-Recipient game even allows for the

possibility that some members are never active. Permanently inactive members corre-

spond to the severely disabled members of real human societies. The Provider-

Recipient game shows that a society whose members work together only for mutual

advantage can require that all its members receive the benefits of cooperation, even those

members who can never contribute to the supply of these benefits. This system satisfies

conditions (M1), (M2), (M3), and even (M4). So according to the account of justice as

mutual advantage proposed in Section 1, this is a system of justice as mutual advantage.

Of course, I do not claim that the Provider-Recipient game even roughly approximates

the cooperative structures of any actual human society. But the Humean equilibrium of

this game establishes the main point of this section: justice as mutual advantage need not

exclude the vulnerable from its benefits, after all.

5. Conclusions

I have argued that a system of justice as mutual advantage can require that the vulnerable

in society all receive some of the benefits of justice. The Provider-Recipient game ofSection 4 shows that it is even possible that a system of justice as mutual advantage pro-

vides the vulnerable with just as much of the benefits of the cooperative surplus as any of

the contributors receive. If I am right, then the Vulnerability Objection is not the silver

bullet that liquidates justice as mutual advantage, after all. To be sure, one must not

slide into the conclusion that justice as mutual advantage necessarily guarantees that the

vulnerable receive adequate benefits of justice. Human societies adopt many alternative

systems of cooperative equilibria that settle the competing interests of their members in

different ways. Such a system, a very complex equilibrium of the social possibilities

Binmore calls the game of life (1994: Section 1.2.4, 1998: Section 0.2.2), might providebenefits to only some of the vulnerable or even to none. Alternatively, the benefits the

vulnerable receive might fail to be adequate. An equilibrium of the game of life could

provide so little to the vulnerable that they cannot lead decent lives.20 Perhaps no actual

human society has yet adopted an equilibrium of the game of life that provides adequate

Vanderschraaf 135



19/30

benefits to all its vulnerable. All I maintain here is that nothing in the analysis of justice

as mutual advantage offered here blocks this possibility. Justice as mutual advantage can

ensure that the vulnerable receive adequate shares of the system of justice.

If society does follow a system of mutual advantage that benefits all of the vulnerable,then an important extension of the Vulnerability Objection is also avoided, or at least

significantly mitigated. As noted in Section 2, Buchanan argues that the personal char-

acteristics that will make one vulnerable can vary according to how a society structures

its frameworks for cooperation. This, Buchanan observes, leads to another serious prob-

lem for justice as mutual advantage. If the vulnerable are entitled to nothing from the

cooperative surplus, then some of the more powerful segments of society might be

tempted to alter societys cooperative frameworks with the aim of rendering certain other

segments of society vulnerable (Buchanan, 1990: Section 4). But if, as I claim, justice as

mutual advantage can require all of the vulnerable to receive their shares of the surplus,

then this temptation can be significantly reduced, and even eliminated. Suppose the sys-

tem grants all at least some minimum immunity rights, including rights not to be killed or

abused physically, and also grants all at least some of the means to sustain their lives.

These are plausible requirements if one maintains that all are to benefit from the coop-

erative surplus. Then if the relatively powerful do rig society so that more of a targeted

segment of the population become vulnerable, there are consequently more vulnerable

mouths to feed. So according to the account of justice as mutual advantage in section

1 no one would be tempted to create conditions that render any particular members vul-

nerable unless doing so somehow increases ones share of the cooperative surplus. This

is conceivable if, for example, according to the system, the costs of maintaining the vul-

nerable are so much lower than the costs of paying the least productive contributors their

shares that one actually nets savings by turning the least productive into vulnerable mem-

bers. I see no reason to think a society regulated by mutual advantage would have such a

peculiar incentive structure. In any event, there will be no temptation to make targeted

members of society vulnerable in a system that makes one responsible for the care of

those one renders vulnerable and requires that the vulnerable receive at least as much

from the cooperative surplus as the contributors who receive the lowest rewards in the

system. A system of justice as mutual advantage that requires that the vulnerable receive

benefits might even encourage the relatively powerful to alter the cooperative frame-works to make otherwise vulnerable members contributors.21

At this point, one might object that I have rescued what I call justice as mutual advan-

tage from the Vulnerability Objection by illegitimately tinkering with the account of

justice as mutual advantage that proponents such as Gauthier and critics such as

Buchanan and Barry adopt. My account of justice as mutual advantage replaces the

Contribution Requirement with a weaker requirement, one that, in effect, requires only

those who can contribute to the cooperative surplus to actually contribute. Does this not

just allow me to get a desired result on the cheap? In fact, I think clinging to the Contri-

bution Requirement leads to a surprise that gives an additional reason for relaxing therequirement. Before I discuss this surprise, I will first consider a different, but related issue.

Philosophers who think the vulnerable are owed justice frequently reject justice as

mutual advantage on the grounds that this theory of justice is too exclusive. If one

accepts the account of justice as mutual advantage proposed in Section 1, then one might




20/30

have the reverse worry. Justice as mutual advantage might turn out to be too inclusive, at

least for some. For if a system of justice as mutual advantage extends benefits to all of the

vulnerable, then apparently every human is to benefit, including those humans in the ear-

liest stages of life and those in a persistent vegetative state. Indeed, one might also arguethat if justice as mutual advantage has no Contribution Requirement, then a system of

justice could require that all of the nonhuman creatures that can benefit from the coop-

erative surplus are to receive benefits.22 However, a great many would object that this is

casting too wide a net, including some philosophers who defend unusually inclusive

accounts of which beings are to be treated with some restraint. Peter Singer would

approve of requirements in a system of justice as mutual advantage that forbid humans

from factory farming and slaughtering sheep and chickens. John Finnis would approve of

requirements in such a system that forbid the induced abortion of human fetuses and the

destruction of so-called excess embryos conceived in fertility clinics. But neither Fin-

nis nor Singer would approve of justice as mutual advantage if this theory of justice sets

no limits at all on the class of beings that are to receive the benefits of justice.

I do not think the potential inclusiveness of justice as mutual advantage is a problem for

the theory in principle. But I admit that there may be no way to set limits on the scope of

justice as mutual advantage that many will want to set if one uses the resources of the the-

ory only. One might try to exclude the nonhuman animals by arguing that only humans can

benefit from the system in a particular way. For example, one might claim that only

humans can benefit from certain primary goods the system provides and that Rawls argues

are the basis for self respect (1971: Section 67). But this move is a step outside of justice as

mutual advantage. Even if certain benefits of the system, such as goods that underwrite

self-respect, are characteristically human benefits, this alone is not a good reason to dis-

criminate against nonhuman creatures. Why not conclude that the system should be altered

so as to produce only benefits that all creatures can enjoy? Perhaps humans have some spe-

cial status that implies only they can be owed justice,23 but I think one cannot infer this

from the account of justice as mutual advantage presented here.24 One might also propose

that human embryos and at least some of the more developed human fetuses lie outside the

system of justice on the grounds that these humans are not persons. According to this now

familiar line of argumentation, embryos, fetuses, and even newly born infants cannot be

persons because they cannot function in certain ways thought to be necessary functions ofpersonhood, such as being aware of oneself and forming plans for ones life.25 I happen to

doubt that the inability to function in such special ways is proof that a being is not a per-

son.26 But even if one could establish on functionalist grounds that some humans are not

persons, to claim that personhood is a prerequisite for inclusion in the system of justice is

to appeal to a criterion other than mutual advantage.

Now I am ready to return to the charge that I should not have dropped the Contribu-

tion Requirement. I think that authors such as Barry, Buchanan, and Gauthier quite natu-

rally conclude that justice as mutual advantage includes the Contribution Requirement

because so many of the most important accounts of justice as mutual advantage, fromGlaucons account in Republic to Gauthiers account in Morals By Agreement, are

expressly contractarian. One might think that if a member of society can be a contractor,

then she can be a contributor. Suppose these authors reject the account of justice as

mutual advantage proposed in Section 1, and insist I include the contribution

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requirement. If I restore this requirement, so that justice as mutual advantage must satisfy

at least (M1), (M2), (M3), and (M5), then I agree that the Vulnerability Objection is

unanswerable. However, I now draw upon a distinction seldom made in discussions of

justice with respect to the vulnerable, namely, the distinction between the permanentlyvulnerable and the intermittently vulnerable. Gauthier hints at this distinction when he

says that his version of justice as mutual advantage might extend benefits to the aged,

but not to the severely disabled. Gauthier gives only the beginnings of an argument for

this claim, but his insights are crucial. The aged in his system can receive benefits

because they have already contributed to the cooperative surplus. Gauthier assumes that

the severely disabled are never able to contribute to the surplus, and consequently are

ineligible to receive benefits. According to Gauthier, the Contribution Requirement

necessarily excludes only the permanently vulnerable. Indeed, justice as mutual advan-

tage cannot exclude all of the intermittently vulnerable. Many of us are vulnerable late

in life, many are vulnerable for limited amounts of time long before the end of life, and

we are all vulnerable very early in life. So at least some of the intermittently vulnerable

must receive benefits if anyone receives benefits. Again, Gauthier has the key insight:

an intermittently vulnerable member of society can be eligible for benefits from the coop-

erative surplus, even when this member is vulnerable, because this member fulfills the

Contribution Requirement when she is not vulnerable. The Melians have a similar insight.

They warn that the Athenians should treat them justly even though they are currently help-

less, because otherwise the Athenians cannot expect just treatment should they ever find

themselves helpless in the future.

I suggest Gauthiers insight leads to a conclusion some will find unsettling: in a society

that rigorously enforces the Contribution Requirement, the severely disabled are owed no

benefits, but most, if not all, the unborn are owed some benefits. Again, I think it plausible

that these benefits include at the very least immunity rights against being killed or other-

wise physically abused and rights to sufficient resources to sustain life.27 Gauthier, in fact,

says that the unborn, being helpless, fall outside the scope of his theory (1986: 268). But

this need not be the case. Gauthier allows that the aged might receive benefits in payment

for past contributions to the cooperative surplus. Binmore shows by example that a

requirement to reward the elderly for past contributions can be part of a social equilibrium

(1994: 734, 1998: 32930).28

The Provider-Recipient game also shows this, but it showsmore. As shown in Section 4, the individuals in the Provider-Recipient game can follow an

equilibrium whereby providers share with all recipients, including the permanently inac-

tive. But they can follow another equilibrium in which providers are required to share only

with the intermittently inactive.29 This equilibrium incorporates the Contribution

Requirement. Furthermore, the equilibrium does not reward past contributions only. The

equilibrium also rewards expected future contributions. If members are inactive in the

early periods of their lifetimes, then providers share with them in these early periods

because they expect these currently inactive members to reciprocate when they become

active. Similarly, if aged persons in a Gauthierian society can receive benefits in paymentfor past contributions, then gestating fetuses can receive benefits in down payment for

expected future contributions.30 But the severely disabled would still receive no benefits

at all. This possibility is another reason I want to relax the Contribution Requirement. If

any purported system of justice requires that a human fetus receives benefits, this system




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should also require that a severely disabled six-year-old child receives benefits. The

Contribution Requirement leads to a violation of what I take to be an elementary consis-

tency requirement for justice, namely, that if the unborn are owed justice, then born chil-

dren, including vulnerable born children, are owed justice.To summarize, in this article I have argued that justice as mutual advantage, properly

understood, can be compatible with the considered judgment that the vulnerable are

owed benefits of justice. Of course, I have not shown that the account of justice as mutual

advantage presented here is the right account of justice. All I maintain is that this version

of justice as mutual advantage is better than the account that includes the Contribution

Requirement, because it avoids the repugnant consequences of the latter account. Indeed,

the following is one way to interpret the conclusions in this article: The vulnerable pose a

fundamental dilemma for any defender of justice as mutual advantage. With the

Contribution Requirement, justice as mutual advantage is too exclusive. Without the

Contribution Requirement, justice as mutual advantage threatens to be too inclusive.

Clearly, I prefer the second horn of the dilemma. The Contribution Requirement not only

excludes the permanently vulnerable from the system of justice, but it leads to results that

will appall both defenders and opponents of abortion rights. The account of justice as

mutual advantage developed here can ensure that the vulnerable receive their portions

of justice as we think they should. But, of course, in the end one might conclude that the

price of accepting either horn of the dilemma is too high, and give up on justice as mutual

advantage once and for all.

Appendix

I first give a formal description of how individual members in a community interact in

pairwise Provider-Recipient meetings. N f1; :::; ng is a set or community ofplayers inwhich n 2m, m 2 and m ! 2: O denotes a set of possible worlds. At each time

period or stage t, one worldo 2 O obtains at t. A description of each possible worldat t includes all of the information relevant to the agents decisions and acts at stage t,

including a description of the stage games, the status of each player at period t, and the

beliefs each player has regarding the counterparts, as in Aumann (1987). Each Playeri 2 N has a subjective probability distribution mi over the propositions in O, a privateinformation partition Hi ofO, and an expectation operatorEi based upon mi At eachstage t, Playeri 2 N is matched with a counterpart i t 2 N according to a bijective ran-dom vector X t : N N with no fixed points. The sequence X t is the matching

protocol. At each stage t, exactly one player in each pair is a provider and the other

player is a recipient. If Player i is a provider at period t and her counterpart Player

i t is active, then they play an Ultimatum game in which i offers i t a sharel 2 0; 1 and i t may either accept (A) or reject (R) the offer. If active recipient i t

chooses A, then i receives a payoff of ui 1 l and i t receives a payoff of ui t l .If active recipient i t chooses R, then both i and i t receive a payoff of zero. If Playeri is a provider at periodtand her counterpart Playeri t is inactive, then they play a Dic-tator game in which i offers i t a share l and i receives a payoff of ui 1 l and i t receives a payoff of ui t l .

Vanderschraaf 139



23/30

Now we define formally the strategies that the players in N can follow in the indefi-

nitely repeated Provider-Recipient game. A generic strategy for Playeri is a sequence of

functions fi ft

i where fi fti : O 0; 1 fA;Rg and fti is Hi measurable.f f1; :::;fn is a generic strategy profile. The set of all strategies Player i can followis denoted by Si and S S1 Sn denotes all of the strategy profiles that playersin N can follow. At a given stage t, fti o t 2 0; 1 fA;Rg defines the pure strategyai t that Player i follows in the Provider-Recipient game at stage t: The set of purestrategies a1 t ; :::; an t the players follow at t is given by

ft o t ft1 o t ; :::;ft

n o t

2 0; 1 nfA;Rgn

Note that when Playeri is a provider at periodt, then ai t is li 2 0; 1 , that is, i offerssome share li to her recipient. When Playeri is an active recipient at periodtthen ai t iseitherA orR that is, i either accepts or rejects the offer her provider makes to her. WhenPlayeri is an inactive recipient at period t then ai t R, that is, i makes no choice andsimply receives the share offered to her. Player i0s expected payoff at stage t given

o t 2 O is

Ei ui fto t

Xj6i

Ei ui ft

i o t ;ft

j o t

mi i t j :

Let pi 2 0; 1 be Player is discount factor. Player is overall expected payoff is

Ei ui f X1t1

Ei ui fto t pti:

A strategy profile f is a correlated equilibrium of the indefinitely repeated Provider-

Recipient game if, and only if, for each i 2 N,

Ei ui f ! Ei ui f0

i ; fi

for all f0i 2 Si.31

We now want to define the Humean strategy for playing this repeated game and showthat the members ofN can follow an equilibrium characterized by this equilibrium. First,

we identify two particular strategies for playing the base Provider-Recipient game at a

given stage t. Strategy s is defined as follows

s t Offerli

12

if I am a provider

A if I am an active recipient;

&

and strategy p is defined as follows

p t Offerli 0 if I am a providerR if I am an active recipient:

&Strategy s has one at stage t share half of the good when one is a provider and accept

any offer when an active recipient. Strategy p has one at stage t offer nothing when




24/30

one is a provider and reject any offer when an active recipient. For i 2 N, definezi : t f0; 1g by

zi t 1 if I i; t obtains

0 otherwise&

where I i; t obtains for each i 2 N and for t > 1,

I i; 1 8 T t 1 8 j2 N j i T ^I j; T ai T s T

^ j i T ^ :I j; T ai T p T :

In words, a player is innocent at stage t if she has always followed the sharing strategy

s over the first t 1 stages with other innocent counterparts and has always followed thepunitive strategy p with any counterpart who is not innocent orguilty. A player becomes

guilty if she ever deviates from strategy s when paired with an innocent counterpart orfails to follow p with a guilty counterpart. zi t is Player is marker and zi t 1 ifPlayer i is innocent and zi t 0 otherwise. Let o t z1 t ; :::;zn t . Then the

Humean strategy is defined by h h o t where

h o t s if zi t t 1p if zi t t 0:

&

The following result gives conditions under which a profile of Humean strategies forms

an equilibrium of the repeated Provider-Recipient game.

Proposition

Let ei1 denote the expected proportion of periods that Player i is inactive and let ei2denote the expected proportion of periods that Playeri is matched with an inactive coun-

terpart. Then, if for each i 2 N,

pi !ui 1 ui

12

ui 1 1 ei1 ei1ei2

1

then h h; :::; h is a correlated equilibrium of the indefinitely repeated Provider-Recipient game.

Proof

Given i 2 N, we have

Ei ui h X1t1

Ei ui s; :::;s pti

X1t1

ui 12

pti 2

Now consider any strategy f0i in which Playeri deviates from the sequence h o t .Let T0 be the first stage, such that f

0i o T0 6 h o T0 . Then

Vanderschraaf 141



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Ei ui f0

i ; hi

XT01

t1

ui1

2

pti

! ui 1 p

T0i 1 ei1 ei2

X1

tT01

ui 1 pti 3

because, first, if Playeri deviates from h for the first time at t T0, then at stage T0 he

will net at most the discounted gain ui 1 pT0i of exploiting Player i T0 and, second, at

each subsequent stag

justice as mutual advantage and the vulnerable - peter vanderschraaf

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