Practical relevance of the weight of argument: preliminary analysis

Keynes does not make clear why one should take a decision on the basis of an argument having higher weight. As he stresses, Bernoulli's advice that we 'must take into account all the information we have, amounts to an injunction that we should be guided by the probability of that argument, among those of which we know the premises, of which the evidential weight is the greatest' (TP, p. 83, 345-6). He then recalls the decision rule suggested by Locke in the following maxim 'he that judges without informing himself to the utmost that he is capable, cannot acquit himself of judging amiss' (quoted in TP, p. 84, n. 2; see also p. 6). This second rule links in a crucial way weight of argument and learning: 'when our knowledge is slight but capable of increase, the course of action which will, relative to such knowledge, probably produce the greatest amount of good, will often consist in the acquisition of more knowledge' (TP, p. 83). If we take Locke's prescription too literally, we could undermine the practical relevance of the weight of argument by inferring that a rational agent should take a decision only when relevant knowledge is complete. However, Keynes rightly observes that, as soon as we take account of the practical constraints on decisions (the time horizon of the decision and the costs of acquiring new information), it is rational to reduce relevant ignorance and thus to reinforce the weight of argument only up to a threshold that in general is short of its maximum value (TP, p. 83). Therefore, the weight of argument cannot be ignored as its value affects the decision strategy of a rational decision maker (TP, p. 342).

The reason for taking into account the weight of argument in decision making is not made explicit by Keynes or Bernoulli or Locke in the passages cited. We could speculate that the higher the weight of argument is, the lower is the probability of deviating from the target. However, Keynes maintains that, in principle, the weight of argument is independent of the expected error or 'probable error': 'there is ... no reason whatever for supposing that the probable error must necessarily diminish, as the weight of argument is increased' (TP, p. 82). This observation is a source of perplexity for Keynes himself; we believe that this dilemma can be solved by recalling the distinction, routinely made in statistical inference and econometric estimation, between stochastic error and systematic error. We suggest that the weight of argument is altogether independent of stochastic error but is strictly correlated with expected systematic error. A greater weight of argument reduces expected systematic error; and it is exactly this property that confers practical relevance to the weight of argument. Stochastic errors are by definition inevitable as they depend on a host of (by definition) unknowable exogenous factors; however, stochastic errors have a practical relevance for decision making because their properties determine the nature and size of the risk associated with a decision. If we admit the presence only of stochastic errors, the weight of argument is maximum because relevant knowledge cannot be further increased. In contrast, a weight of argument inferior to 1 implies awareness of possible systematic errors that are the more significant the deeper relevant ignorance is. Systematic errors diminish with learning to the extent that learning diminishes relevant ignorance.

Although confidence in the conclusions of a non-demonstrative argument relies upon the expected value of both stochastic and systematic errors, these two determinants should be kept separate as they depend on completely different factors: risk and weight of argument. The practical relevance of risk depends on the attitude towards risk, while the practical relevance of the weight of argument depends on the attitude towards (second-order) uncertainty. The weight of argument, however, is important also for a second fundamental reason that breaks the symmetry with the analysis of risk as it may be interpreted as an index of potential learning. The crucial nexus between the weight of argument and learning is already altogether evident in TP, but it is only in GT that Keynes formulates the fundamental principle that gives the weight of argument a high degree of practical relevance, in particular in his analysis of liquidity preference: the lower the weight of argument, and thus the higher the potential learning, the higher is the degree of intertemporal flexibility sought by a rational agent (Basili and Vercelli, 1998).