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For the sake of leaving the suboptimal position, these contractors bargain with each other and form a social agreement which is mutually advantageous. However, bargaining needs a baseline which can determine the goods that each person brings to the bargaining table and that is not subject to bargaining. Without this baseline, one cannot understand the idea of advantage.²⁰ Hence, before bargaining, contractors have to know what goods they can legitimately own first. Gauthier suggests that this

‘initial distribution of goods’ is defined by a proviso on previous acquisition of resources. Gauthier, following Nozick, calls this proviso the ‘Lockean proviso’.²¹ Goods belong to a person when they are ‘acquired by him without taking advantage of any other person—or, more precisely, any other co-operator’.²² Here ‘taking advantage’ of another person refers to making the situation of another person worse in order to better one’s own. The function of this proviso is to exclude irrelevant factors such as coercion and free-riding. Under the constraint of this proviso, contractors can no longer acquire goods by coercive or predatory activities. They can get the goods only by their own labour. Since the Lockean proviso guarantees a fair initial situation without coercion, the hypothetical agreement which is reached under the constraint of this proviso will be a fair agreement.

20 Barry (1989: 12-15).

21 Nozick (1974: 175-182).

22 Gauthier (1986: 201).

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At the bargaining table, contractors have to think about how the cooperative surplus should be divided. They know that by cooperating with each other, extra goods will be created. The question is how these goods should be divided among contractors who create them together. According to Gauthier, since society’s members are rational utility-maximizers, they will seek to get as much cooperative surplus as possible during bargaining. If the claims of these society members are incompatible, there is a second stage in which each member offers concessions to the others by withdrawing some portion of their original claim and proposing an alternative outcome. Concession making continues until a set of mutually compatible claims are reached. According to Gauthier, this is reached when each member makes concessions that are relatively equal to the concessions of others. Here the relative concession refers to the concession that one has to suffer when one bargains with others in the division of cooperative surplus:

The relative concession that a person makes for a given option is the ratio of (a) the excess of (i) the utility for that person of his/her most favorable admissible option over (ii) the utility for that person of [the agreement] to (b) the excess of (i) the utility for that person of his/her most favorable admissible option over (ii) the utility for that person of the initial bargaining position option. An admissible option is one that is both feasible and accords everyone at least as much utility as the initial bargaining position.²³

Gauthier argues that the outcome of bargaining will be the ‘principle of minimax relative concession’, which is a bargaining solution that minimizes the maximum relative concession that anyone makes. This principle is most rational because it ‘is most favourable to [each society member], minimizing the costs of her restraint and maximizing the benefits she receives from the restraint of others’.²⁴ In every other alternative outcome, the maximum relative concession would be greater, which

23 Vallentyne (1991c: 8).

24 Gauthier (1986: 128).

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means that some society members would be disadvantaged and would be required to sacrifice more. As Vallentyne says, ‘the intuitive idea behind this solution is that, since one’s ground of complaint can be measured by one’s relative concession, minimizing maximum relative concession minimizes the grounds for complaint’.²⁵ Therefore, the principle of minimax relative concession is rationally the most acceptable solution to everyone, because any other alternative solution would impose more burdens on some members and would be rejected by these members.

The principle of minimax relative concession is the outcome of a joint strategy choice.²⁶ By following the principle of minimax relative concession, hypothetical contractors can overcome market failure and achieve an optimal outcome. However, someone might doubt whether, even if it is rational to make such an agreement, it is really rational to comply with it. It seems that, if individuals are by nature rational utility-maximizers, they should free-ride on others and break the agreement given that others must still honour the agreement. Gauthier disagrees that this is rational.

He distinguishes two strategies for maximizing utilities. One is straightforward maximization, which means that an individual ‘seeks to maximize his utility given the strategies of those with whom he interacts’.²⁷ Without concern about any other things. Another is constrained maximization, which means that an individual ‘has a conditional disposition to base her actions on a joint strategy, without considering whether some individual strategy would yield her greater expected utility…In other words, a constrained maximizer is ready to cooperate in ways that, if followed by all, would yield outcomes that she would find beneficial and not unfair’.²⁸ Gauthier argues that provided the government can guarantee a sufficient degree of

25 Vallentyne (1991c: 8-9).

26 Some theorists argue that rational contractors might choose other principles apart from the principle of minimax relative concession. This principle is only one of the possible joint choices. For a discussion of this question, see Hardin (1988).

27 Gauthier (1986: 167).

28 Gauthier (1986: 167). For the discussion of constrained maximization, see also Gauthier (1975)

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translucency, that is, other people can have a fairly good idea what we are really like and free-riding is difficult, constrained maximization is a more rational strategy than straightforward maximization. Individuals should be disposed to act on the basis of the agreement, rather than maximizing their utilities directly and free-riding on others.

This concludes the exposition of Hobbesian contractarianism. We can see how a Hobbesian contractarian develops a whole theory from the conception of rationality.

In Gauthier’s contract theory, hypothetical contractors are well-informed rational utility-maximizers, who model the rational deliberative process of actual people. The main problem for these contractors is market failure, which is the suboptimal situation that contractors would fall into if they maximized their utility without any agreement. So they have to make an agreement with one another in order to get rid of these suboptimal situations and enjoy a cooperative surplus. Before bargaining, contractors have to define what goods belong to them, so they first agree on the Lockean proviso which defines the initial distribution of goods. This initial distribution determines the bargaining power of contractors. Based on their bargaining power, contractors bargain with one another and at last agree on the principle of minimax relative concession. This principle acts as a public constraint which helps them to reach optimal, mutually beneficial outcomes. Contractors will also change into constrained maximizers and be disposed to maximize their utility under the public constraint. Hence, Gauthier shows how substantial political principles are derived from a formal conception of rationality by the contractarian method.