Consensus theories: an oriented survey

This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity

Poverty rankings of opportunity profiles

We address the problem of ranking distributions of opportunity sets in terms of poverty. In order to accomplish this task, we identify a suitable notion of ‘multidimensional poverty line’ and we characterize axiomatically several poverty rankings of opportunity profiles. Among them, the Head-Count and the Opportunity-Gap poverty rankings, which are the natural counterparts of the most widely used income poverty indices.Poverty, opportunity sets, head-count, poverty-gap.

Cognitive Constraints, Contraction Consistency, and the Satisficing Criterion

A theory of decision making is proposed that offers an axiomatic basis for the notion of "satisficing" postulated by Herbert Simon. The theory relaxes the standard assumption that the decision maker always fully perceives his preferences among the available alternatives, requiring instead that his ability to perceive any given preference be decreasing with respect to the complexity of the choice problem at hand. When complexity is aligned with set inclusion, this exercise is shown to be equivalent to abandoning the contraction consistency axiom of classical choice theory.Choice function, Perception, Revealed preference, Threshold

Axiomatic Foundations for Satisficing Behavior

A theory of decision making is proposed that supplies an axiomatic basis for the concept of "satisficing" postulated by Herbert Simon. After a detailed review of classical results that characterize several varieties of preference-maximizing choice behavior, the axiomatization proceeds by weakening the inter-menu contraction consistency condition involved in these characterizations. This exercise is shown to be logically equivalent to dropping the usual cognitive assumption that the decision maker fully perceives his preferences among available alternatives, and requiring instead merely that his ability to perceive a given preference be weakly decreasing with respect to the relative complexity (indicated by set inclusion) of the choice problem at hand. A version of Simon's hypothesis then emerges when the notion of "perceived preference" is endowed with sufficiently strong ordering properties, and the axiomatization leads as well to a constraint on the form of satisficing that the decision maker may legitimately employ.

Poverty Rankings of Opportunity Profiles

We address the problem of ranking distributions of opportunity sets in terms of poverty. In order to accomplish this task, we identify a suitable notion of `multidimensional poverty line', extend the most widely used income poverty criteria to opportunity profiles, and provide characterizations of a few poverty rankings that rely on such criteria.Poverty, opportunity sets, head-count, poverty-gap.