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In economics, the Debreu's theorems are preference representation theorems—statements about the representation of a preference ordering by a real-valued utility function. The theorems were proved by Gerard Debreu during the 1950s.
Representation theory depends upon the type of algebraic object being represented. There are several different classes of groups, associative algebras and Lie algebras, and their representation theories all have an individual flavour. Representation theory depends upon the nature of the vector space on which the algebraic object is represented.
The concept of collective representation can be found in various normative theory and scientific works, but Weissberg (1978, 535) offered the first systematic characterization of it in the scientific literature and for the U.S. Congress, defining such representation as "Whether Congress as an institution represents the American people, not ...
An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes.
Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. [1] Social choice studies the behavior of different mathematical procedures ( social welfare functions ) used to combine individual preferences into a coherent whole.
In economics, a utility function is often used to represent a preference structure such that () if and only if. The idea is to associate each class of indifference with a real number such that if one class is preferred to the other, then the number of the first one is greater than that of the second one.
Hartley, however, finds these reasons for representative agent modelling unconvincing. Kirman [2] too, is critical of the representative agent approach in economics. Because representative agent models simply ignore valid aggregation concerns, they sometimes commit the so-called fallacy of composition.
In economics, a utility representation theorem shows that, under certain conditions, a preference ordering can be represented by a real-valued utility function, such that option A is preferred to option B if and only if the utility of A is larger than that of B.