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A social dichotomy function maps a collection of weak orders to a set of dichotomous weak orders. Every dichotomous weak order partitions the set of alternatives into approved alternatives and disapproved alternatives. The Borda mean rule returns all dichotomous weak orders that approve all alternatives with above-average Borda score and disapprove alternatives with below-average Borda score. We show that the Borda mean rule is the unique social dichotomy function satisfying neutrality, reinforcement, faithfulness, and the quasi-Condorcet property. Our result holds for all domains of weak orders that are sufficiently rich, including the domain of all linear orders and the domain of all weak orders. [ABSTRACT FROM AUTHOR]

In this paper we give an axiomatic characterization of a family of measures of success defined by Laruelle and Valenciano (Soc Choice Welf 27:171-197, ) for voting rules. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to provide an axiomatic analysis of incomplete social judgments. In particular, we clarify the underlying power structure of Arrovian collective choice rules when social preferences are allowed to be incomplete. We propose the concept of quasi-decisiveness and investigate the properties of the collection of quasi-decisive sets associated with an Arrovian collective choice rule. In the course of this, we offer a series of applications. [ABSTRACT FROM AUTHOR]

This article contributes to the literature on the evaluation of sets of opportunities. The starting point is Lancaster's characteristics approach. However, instead of assuming the existence of a canonical utility function, a reference point or reference level is postulated from which an agent evaluates set expansions in appropriate directions. One of the major tools for this exercise is the notion of directed cones. Desirability of characteristics is restricted to the interior of these cones. Satiation and non-monotonic evaluation is considered as well. An axiomatic characterization for various cases is provided. [ABSTRACT FROM AUTHOR]

problem of axiomatic construction of a social decision function is studied for the case when individual opinions of agents are given as m-graded preferences with arbitrary integer m ≥ 3. It is shown that the only rule satisfying the introduced axioms of Pairwise Compensation, Pareto Domination and Noncompensatory Threshold and Contraction is the threshold rule. [ABSTRACT FROM AUTHOR]

In this paper we present a constructive, behavioural and axiomatic approach to the notion of a stable set as a model of the standard of behaviour of a social organisation. The socially stable set we introduce is a generalisation of the von Neumann-Morgenstern stable set. In contrast with the original version, our stability concept is always solvable. The standard of behaviour, reflecting the established conceptual order of a society or organisation, emerges from a dominance relation on alternative conceptions that are relevant with regard to a certain issue. This common social choice phenomenon, that permeates our societies and organisations, we have tried to clarify. Two axiomatic characterisations as well as a construction algorithm for socially stable sets are presented. These characterisations are based on behavioural postulates regarding the individual or collective strategic behaviour of effective sets. Relations between socially stable sets and other notions of stability are discussed. [ABSTRACT FROM AUTHOR]

Hotelling (1929) studied two competing firms choosing their locations on a street. We consider instead a planner who builds two identical public facilities (e.g., libraries, parks, bridges, etc). We ask a normative question: Where should the planner build these facilities? We prove an axiomatic characterization of the efficient social choice rules that satisfy what is called the replacement-domination, which is a formulation of the idea of “solidarity” among the agents. [ABSTRACT FROM AUTHOR]