In the literature, as regards instrumental rationality, two different and conflicting criteria of rationality are distinguished: Bayesian reduction- ism and rational dualism (Mongin, 1984, p. 11). In section 12.3 we have argued that, according to Bayesian reductionism, agents, through the calculus of probability, are 'capable of reducing uncertainty to the same calculable status as that of certainty itself' (Keynes, 1973c , pp. 112-13). In this section, we will show how rational dualism works.
Rational dualism distinguishes situations (a) simple enough to be fully understandable by human mind, so that decision makers have reliable information and computing capabilities for applying the procedure of welfare maximization (substantive rationality); and (b) complex enough to be not fully understandable, so that decision makers have to simplify these situations in some rational way in order to make a choice (bounded rationality) since they do not have adequate information or computing capabilities for applying the maximization procedure (Marzetti, 1998).
Keynes, before Simon and Tinbergen, argued that the assumption of a calculable future wrongly interprets the principles of behaviour adopted in practice by agents, since it underestimates the situations in which they know very little or nothing, and gives rise to doubt, precariousness and fear. Therefore, the Keynesian view about right conduct leads to bounded rationality. This is a 'wild' research field, where there are numerous possibilities for modelling agents' behaviour that lack information. The bounded rational agent described by Sargent is only one possible kind of bounded rational agent. Simon (1987) generally speaks of cognitive limitations to decision making (internal constraints). Cognitive limitations mean that decision makers are never sure that a certain action will produce the maximum value. They cannot know, given certain circumstances, some of the conditions under which a specific action will determine its consequences, some of the consequences of these conditions, some of the events that will be influenced by the action in the future, and also the value of the action and that of some of its consequences. In addition, they cannot have information about all the possible alternative actions, and cannot know whether any other circumstances will interfere. This means that, as regards the structure of the model, the social welfare function and the representation of the economic system may be only partially known, or unknown. Furthermore, the model could be so complex that computational difficulties could hinder econometricians' efforts.
When due to cognitive limitations the basis for computing a mathematical expectation does not exist, agents have recourse to numerous practical procedures (heuristics) in order to behave rationally. In this case a decision depends not only on objectives and external constraints, but also on the procedure itself, which is the result of a process of choice (procedural rationality). In particular, when we relax one or more of the assumptions of the (expected utility) theory,
instead of assuming a fixed set of alternatives ... we may postulate a process for generating alternatives. Instead of assuming known probability distributions of outcomes, we may introduce estimating procedures for them, or we may look for strategies for dealing with uncertainty that do not assume knowledge of probabilities. Instead of assuming the maximisation of a utility function, we may postulate a satisfying strategy. 
- (Simon, 1987, p. 15)
- 18.104.22.168 An example: from a substantive procedure to a bounded procedure In order to give an example of the passage from substantive rationality to a bounded procedure, we may consider the theory of economic policy (Tinbergen, 1952).12
2. Tinbergen (1952, pp. 1-5) also maintains that in practice it is a difficult matter to estimate a social welfare function, and claims that in general social welfare
will not be considered consciously but intuitively by those responsible for the policy. In principle, it must not only depend on individual ophelimity functions... but on a certain measure of combining and hence the weighting of these individual 'interests' as well. In practice, the stage of fixing [the welfare function] and trying to maximise it will often be passed over and the targets chosen directly.
In other terms, model (1)-(3) cannot be applied.
Assume that rationality is limited by lack of data for estimating V(y), while h(y) = 0 is known. In this case a procedure that can be applied is that of the fixed target, which consists in the choice of a satisfying value for a certain number of target variables. Assume that y is distinguished in a subset of target variables x and instruments u, therefore h(x, u) = 0, and that x* is a desired or satisfying value fixed a priori, therefore x = x*. In this case the maximization procedure is substituted with a satisfying procedure as follows:
Given x = x*, the policymaking procedure consists in finding the values of instruments u which solve the system h(x*, u) = 0.
This procedure is used in many Keynesian models, and it works even in situations where probabilities are non-measurable. When probabilities are unknown, Keynes (1973c , p. 114) argues that the practical man or woman, in order to meet a minimum rationality requirement may ignore the prospect of future changes about which he or she does not know anything, and assumes that 'the present is a much more serviceable guide to the future than a candid examination of past experience'.
3. The procedure of fixed targets leaves some questions unsolved. In particular, how must the policymaker behave when the model has more than one solution, or has no solution? In these cases the approximate optimization procedure can be applied, which consists in the search for the best approximation of the desired fixed target x*, and therefore requires the use of a welfare loss function L(x - x*, u). The model is as follows:
The policy-maker will choose u in order to make the value of L(x - x*, u) a minimum, where x - x* is the difference between the actual value x and the desired value x* (Preston and Pagan, 1982).
-  Consider first a situation of substantive rationality, where a policymaker has all the information for maximizing social welfare. For thesake of simplicity, let us assume a static context, and assume thatin some sense and to some extent the ethical value is numericallymeasurable and described by the welfare function V(y), where y > 0is a vector of target variables. Uncertainty is included in V(y) by usingsubjective probabilities for weighting the utilities of the differentstates of nature. Assume that the structure of the economic systemh(y) = 0 is known. Therefore, we write:
-  where u.c. means 'under the constraint'. According to this model,the policymaker will choose y in order to make V(y) a maximum,given h(y) = 0.