An Ordered Set Approach to Neutral Consensus Functions
Several authors have investigated consensus functions from the viewpoint of stability families. It will be shown that the stability family approach extends and enriches the ordered set approach to consensus theory. Our investigation will center on the notions of sup and inf-irreducible elements of a finite ordered set. We will see that irreducible elements give rise to natural internal stability families for a given ordered set X. We will investigate the relationship between these internal stability families and abstract stability families. Special attention will be paid to the study of different types of neutrality, thus extending earlier work of B. Monjardet. We will be particularly interested in the change in the available neutral consensus functions on an ordered set when a given internal stability family is changed.
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