The Problem of Aggregation of Individual Economic Relations; Consistency and Representativity in a Historical Perspective

Ranking multidimensional alternatives and uncertain prospects

“…Another important connection is with the early microeconomic literature on consistent aggregation; see Green [18], and van Daal and Merkies [34,35] for surveys; the pioneering result is due to Nataf [29]. Once translated into numerical representations, our four axioms are seen to entail consistent aggregation, which is known from this literature to entail additive separability.…”

“…This section makes it more informative by introducing both 10 Though Nataf's [29] theorem is correct, its proof is rather obscure. The curious reader may consult the clarifications and improvements adduced by van Daal and Merkies [35]. 11 More obviously in Gorman [16] than in the other papers.…”

Sum representations of some functions and the aggregation equation

“…The left-hand sides of equations (5) and (6) are equal and consequently their right hands are too. However, from equation (4)…”

“…For historical background on the equation the reader is directed to [1] and [6]. The 1996 paper of Aczél and Maksa [2] was seminal in so far as it solved the equation for functions defined on abstract sets, subject only to surjectivity and injectivity conditions on their partial functions.…”

The generalized equation of bisymmetry: solutions based on cancellative abelian monoids

“…This alternate name arose from a model which links microeconomics and macroeconomics. A historical perspective of the economic model is to be found in [4]. More recently, Aczél [1] has presented an interesting overview of the GEB and related equations which traces the parallel development of the mathematical notion of bisymmetry and the economic concept of aggregating.…”