- Submitted By: idespi
- Date Submitted: 11/17/2008 4:29 PM
- Category: Science
- Words: 265
- Page: 2
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On Consensus Theory

Work in progress...

"The term consensus refers to a commonly agreed position, conclusion, or set of values, and is normally used with reference either to group dynamics or to broad agreement in public opinion. Additionally, however, it has come to be associated with the particular form of normative functionalism most fully developed in the writings of Talcott Parsons (see, for example, The Social System, 1951)". (A Dictionary of Sociology 1998, originally published by Oxford University Press 1998)

We will try to explain the mathematical background needed for an axiomatized consensus theory. There is an enormous interest nowaday for an axiomatic point of view coming from biologists, economists, politologs and even mathematicians as the field becomes more and more mature and stable. The main issue arises from an aggregation problem, the reduction of different individual preferences to a single group preference, that is given a set X of objects of interest, when present a tuple T of, say, k objects of X, find a rule that returns a single consensus object of X that in some aspect best represents the tuple T. We will enforce that any consensus rule should obey some axioms and so when solving this problem we check our rule against them. Of course, one can get an impossibility result when no rule obeys the axioms. Then she can play with the axioms (make them weaker) till the contradiction is eliminated. The axiomatic approch started in 1950 when K. J. Arrow proved that there is no rational democratic rule to obtain a consensus of a set of preference rankings.