Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical...

Two different ways to model the diffusion of alternative choices within a population of individuals in the presence of social externalities are known in the literature. While Galam’s model of rumors spreading considers a majority rule for interactions in several groups, Schelling considers individuals interacting in one large group, with payoff functions that describe howcollective choices infl...

``Subset voting'' denotes a choice situation where one ®xed set of choice alternatives (candidates, products) is o€ered to a group of decision makers, each of whom is requested to pick a subset containing any number of alternatives. In the context of subset voting we merge three choice paradigms, ``approval voting`` from political science, the ``weak utility model'' from mathematical psychology...

In this paper, the authors investigate a basic assumption underlying most models based on social or mathematical psychology that consumers are rational in the sense of choosing the most economically efficient brand. Using Data Envelopment Analysis (DEA) for measuring the efficiency of individual consumer choice, they report the results of two empirical studies, one involving the social psycholo...

In this talk I will give a overview on the connections between closure operators and choice operators and on related results. An operator on a finite set S is a map defined on the set P(S) of all the subsets of S. A closure operator is an extensive, isotone and idempotent operator. A choice operator c is a contracting operator (c(A) ⊆ A, for every A ⊆ S). Choice operators and their lattices hav...

We consider a simple model of social choice where the voters find it costly to determine their true preferences. Since the influence of an individual voter decreases as the group size increases, each individual finds it optimal to invest less time in contemplating his values in larger groups than in smaller groups. This suggests that a desirable social choice mechanism might be to randomly choo...

The topological approach to social choice was developed by Graciela Chichilnisky in the beginning of the eighties. The main result in this area (known as the resolution of the topological social choice paradox) shows that a space of preferences admits of a continuous, anonymous, and unanimous aggregation rule for every number of individuals if and only if the space is contractible. Furthermore,...

This paper offers a short introduction to some of the fundamental results of social choice theory. Topics include Nash implementability, monotonic social choice correspondences, the Muller-Satterthwaite impossibility theorem, anonymous and neutral social choice correspondences, sophisticated solutions of binary agendas, the top cycle of a tournament, the bipartisan set for two-party competition...

The paper pays critical tribute to Arrow’s (1951) analysis of social choice by focusing on a number of the foundational, conceptual and interpretational issues to which it gives rise. It begins with a discussion of justifications of other formal requirements, namely unrestricted domain, Pareto optimality and independence of irrelevant alternatives, before proceeding to a detailed analysis of th...

I present a general mathematical modeling framework that can provide a foundation for the study of sustainability in social- ecological systems (SESs). Using basic principles from feedback control and a sequence of specific models from bioeconomics and economic growth, I outline several mathematical and empirical challenges associated with the study of sustainability of SESs. These challenges a...