Exactly what that structure is depends on how rational choice is formalised. For Pareto, who interprets rational choice in terms of constrained maximisation, the requirement is that tastes take the form of an ordering over the relevant set of end states.
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What kinds of facts are relevant, and what it means for tastes to conform to those facts, are not clear. What is clear is the assumption that, after sufficient repetition, each person has a stable system of tastes, structured in such a way that problems of instrumentally rational choice are well defined. A man who buys a certain food for the first time may buy more of it than is necessary to satisfy his tastes, price taken into account.
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But in a second purchase he will correct his error, in part at least, and thus, little by little, will end up by procuring exactly what he needs. We will examine this action at the time when he has reached this state. Similarly, if at first he makes a mistake in his reasoning about what he desires, he will rectify it in repeating the reasoning and will end up by making it completely logical , ch. On that interpretation, the transitivity of the taste relation would be implied by the hedonistic assumption that different pleasures for a given individual are commensurable on an ordinal scale.
However, although Pareto permits a hedonistic interpretation of tastes, he does not positively endorse it. Drawing a distinction between intrapersonal and interpersonal comparisons of sensations, he says that economics is principally concerned with that class of theories which has as its object:.
But it could be made up of theories of altruism if the meaning of that term could be defined rigorously , or, in general, of theories, which rest on any rule, which man follows in comparing his sensations. It is not an essential characteristic of this class of theories that a man choosing between two sensations choose the most agreeable; he could choose a different one, following a rule which could be fixed arbitrarily ibid.
What grounds do we have for this assumption? Repetition alone does not provide an adequate explanation. The significance of repetition is that it allows the learning of what Pareto calls objective facts.
The relationship between actions and sensations is such an objective fact, and we might expect that with repetition individuals would become able to predict the sensations that would result from alternative actions. Unless we can assume that people compare sensations as different quantities of some common objective attribute, we seem to have no grounds for assuming that these comparisons are logical i. Pareto was very conscious of this difficulty for his theory. In mathematical terms, this is the integrability problem.
But if there are more than two goods, how can we be sure that the marginal rates of substitution we observe at the different points can be integrated into indifference surfaces? Pareto struggled with the integrability problem for many years. He first mentions it in a letter to Pantaleoni in , and dedicated a good part of his energies to it in his last works on pure economics , Appendix; , p.
In a letter to Pantaleoni dated 14 December , Pareto , p. Pareto dedicated a long footnote in the French edition of the Manual , trying to convince himself first that there is a solution for such a crucial problem. Of course, the problem is swept under the carpet if one simply assumes that preferences are transitive, as became standard practice in choice theory in the mid-twentieth century.
If economics is to be a separate science, based on laws whose truth is to be treated as axiomatic, we have to be very confident in those laws. But the idea that indifference is transitive right across commodity space was only a speculative hypothesis, for which, at the time he was writing, no solid evidence existed. Pareto recognises that, in the overwhelming majority of cases confronted by economists, indifference curves are convex to the origin.
However, he also knows that there are occasional anomalous cases in which indifference curves are concave or, in general, not strictly convex , ch.
Presumably, and for this reason, he does not feel entitled to treat the convexity of indifference curves as a firmly established empirical law. Thus, for Pareto, the fact that convexity almost always holds can be registered only as a highly reliable but unexplained regularity in tastes.
There is an echo here of the scepticism with which many present-day economists view the suggestion that results from experimental psychology might be relevant for economics. They could reply that, while convexity is not a law of economics, the Fechner-Weber Law is a law of psychophysics, and that that a psychophysical law is useful in explaining the general tendency towards convexity of preferences. The hedonists believed that other reliable generalisations about preferences, beyond transitivity and convexity, could be derived from psychological hypotheses.
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They no doubt expected that as psychology and economics progressed, still more such generalisations would be found. In trying to achieve this objective and push it ever further, post-Paretian neoclassical economists Hicks, Allen, Samuelson faced a common set of methodological problems, two of which are particularly fundamental and particularly difficult to solve.
The first problem is to find and to justify a definition of the domain of economics within which rationality-based theories predict successfully: such a definition is not vacuous and is wide enough for economics to have something useful and relevant to say about the real world. Limits to the domain of rational choice theory were not discussed by Paretian microeconomics, and there was an implicit assumption that the theory was universal in its application.
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