12 research outputs found
Decisive Coalitions and Coherence Properties
In a seminal contribution, Hansson has demonstrated that the family of decisive coalitions associated with an Arrovian social welfare function forms an ultrafilter. If the population under consideration is infinite, his result implies the existence of nondictatorial social welfare functions. He goes on to show that if transitivity is weakened to quasi-transitivity as the coherence property imposed on a social relation, the set of decisive coalitions is a filter. We examine the structure of decisive coalitions and analogous concepts with alternative coherence properties, namely, acyclicity and Suzumura consistency, and without assuming that the social relation is complete
Product Filters, Acyclicity and Suzumura Consistency
In a seminal contribution, Hansson (1976) demonstrates that the collection of
decisive coalitions associated with an Arrovian social welfare function forms an ultrafilter. He goes on to show that if transitivity is weakened to quasi-transitivity as the coherence property imposed on a social relation, the set of decisive coalitions is a filter. We examine
the notion of decisiveness with acyclical or Suzumura consistent social preferences and
without assuming that the social relation is complete. This leads to a new set-theoretic
concept applied to product spaces
Arrovian juntas
This article explicitly constructs and classifies all arrovian voting systems
on three or more alternatives. If we demand orderings to be complete, we have,
of course, Arrow's classical dictator theorem, and a closer look reveals the
classification of all such voting systems as dictatorial hierarchies. If we
leave the traditional realm of complete orderings, the picture changes. Here we
consider the more general setting where alternatives may be incomparable, that
is, we allow orderings that are reflexive and transitive but not necessarily
complete. Instead of a dictator we exhibit a junta whose internal hierarchy or
coalition structure can be surprisingly rich. We give an explicit description
of all such voting systems, generalizing and unifying various previous results.Comment: 22 pages, 1 figur
Multi-Profile Intertemporal Social Choice
We provide a brief survey of some literature on intertemporal social choice theory in a multi-profile setting. As is well-known, Arrow’s impossibility result hinges on
the assumption that the population is finite. For infinite populations, there exist nondictatorial social welfare functions satisfying Arrow’s axioms and they can be described by their corresponding collections of decisive coalitions. We review contributions that explore whether this possibility in the infinite-population context allows for a richer class of social welfare functions in an intergenerational model. Different notions of stationarity
formulated for individual and for social preferences are examined. Journal of Economic
Literature Classification No.: D71
Quasi-Transitive and Suzumura Consistent Relations
We examine properties of binary relations that complement quasi-transitivity and Suzumura consistency in the sense that they, together with the original axiom(s), are equivalent to transitivity. In general, the conjunction of quasi-transitivity and Suzumura consistency is strictly weaker than transitivity but in the case of collective choice rules that satisfy further properties, the conjunction of quasi- transitivity and Suzumura consistency implies transitivity of the social relation. We prove this observation by characterizing the Pareto rule as the only collective choice rule such that collective preference relations are quasi-transitive and Suzumura consistent but not necessarily complete
Matroid, Ideal, Ultrafilter, Tangle, and so on: Reconsideration of Obstruction to linear decomposition
The investigation of width parameters in both graph and algebraic contexts
has attracted considerable interest. Among these parameters, the linear branch
width has emerged as a crucial measure. In this concise paper, we explore the
concept of linear decomposition, specifically focusing on the single filter in
a connectivity system. Additionally, we examine the relevance of matroids,
antimatroids, and greedoids in the context of connectivity systems. Our primary
objective in this study is to shed light on the impediments to linear
decomposition from multiple perspectives.Comment: 11 page