The Utilitarian Calculus
Having shown how indeterminacy can be removed by increasing the number of traders, Edgeworth turned to consider the role of arbitration in resolving the conflict between traders, in a ‘world weary of strife' (ibid.: 51).
The need for arbitration was stated by Jevons as follows:The dispositions and force of character of the parties...will influence the decision. These are motives more or less extraneous to a theory of economics, and yet they appear necessary considerations in this problem. It may be that indeterminate bargains of this kind are best arranged by an arbitrator or third party (Jevons 1957: 124-125).
Edgeworth’s statement of the same point was as usual rather less prosaic: ‘The whole creation groans and yearns, desiderating a principle of arbitration, and end of strifes’ (Edgeworth 1881: 51).
The principle of arbitration examined by Edgeworth was, not surprisingly, the utilitarian principle, which he had earlier used to examine optimal distribution. However, the new context of indeterminacy led him to a deeper justification of utilitarianism as a principle of distributive justice. Having arrived at this new link between “impure” and “pure” utilitarianism, Edgeworth had only to reorientate his earlier analysis of optimal distribution discussed above. His argument involved two steps. First, he showed that the principle of utility maximisation places individuals on the contract curve, because the first-order conditions are equivalent to the tangency of indifference curves. He exclaimed, ‘It is a circumstance of momentous interest that one of the in general indefinitely numerous settlements between contractors is the utilitarian arrange- ment...the contract tending to the greatest possible total utility of the contractors’ (ibid.: 53).
Edgeworth recognised that this result was not sufficient to justify the use of utilitarianism as a principle of arbitration.
It is only a necessary condition of a principle of arbitration that it should place the parties somewhere on the contract curve. His justification of utilitarianism was as follows:Now these positions lie in a reverse order of desirability for each party; and it may seem to each that as he cannot have his own way, in the absence of any definite principle of selection, he has about as good a chance of one of the arrangements as another...both parties may agree to commute their chance of any of the arrangements for...the utilitarian arrangement (ibid.: 55).
The important point about this statement is that Edgeworth viewed distributive justice in terms of choice under uncertainty. He argued that the contractors, faced with uncertainty about their prospects, would choose to accept an arrangement along utilitarian lines. A crucial component of this argument, also clearly stated by Edgeworth in this quotation, is the use of equal a priori probabilities. The importance to him of this new justification of utilitarianism cannot be exaggerated. Indeed, the whole of Mathematical Psychics is imbued with a feeling of excitement generated by his discovery of a justification based on a social contract. This provided the crucial link between “impure” and “pure” utilitarianism in a more satisfactory way than his earlier appeal to evolutionary forces.
Edgeworth believed that he had provided an answer to an age-old question, stating, ‘by what mechanism the force of self-love can be applied so as to support the structure of utilitarian politics, neither Helvetius, nor Bentham, nor any deductive egoist has made clear' (ibid.: 128). Nevertheless, this argument was neglected until restatements along similar lines were made by Harsanyi (1953, 1955) and Vickrey (1960). The maximisation of expected utility, with each individual taking the a priori view that any outcome is equally likely, was shown to lead to the use of a social welfare function which maximises the sum of individual utilities. This approach is now described as “contractarian neo-utilitarianism”.
In discussing the utilitarian solution as a principle of arbitration in indeterminate contract, Edgeworth did not indicate in 1881 that the utilitarian solution of maximum total utility could specify a position making one of the parties worse off than in the no-trade situation. This was later made explicit when, after proposing arbitration along utilitarian lines, he added, ‘subject to the condition that neither should lose by the contract' (Edgeworth 1925, ii: 102). This possibility depends largely on the initial endowments of the individuals.
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