Collective Choice Functions Research Articles

On Generalized Nash Rationalization of Collective Choice Functions

This paper analyzes collective outcomes in games from a revealed preference perspective. A collective choice function is rationalizable if there are such “rational” individual preferences, that the observed choices are the only equilibria. We consider a generalized concept of Nash equilibrium, which should be robust to deviation by not only individuals but some exogenously given coalitions as well. The paper provides sufficient conditions as well as necessary conditions for the collective choice function to be rationalizable given some notion of rationality. In addition, we show that the conditions coincide and become a criteria if we relax the definition of equilibrium to the standard definition of Nash.

No-envy, efficiency, and collective rationality

We consider fair collective choice functions (hereafter fair CCFs) which associate with each profile of extended preference orderings and each set of feasible social states a subset of the set of Pareto efficient and envy-free states for the preference profile. Our main objective is to examine compatibility of fair social choices with collective rationality. We formulate desirable properties of collective rationality, and look for CCFs satisfying them. Next, we show that any fair CCF violates most of collective rationality properties. Moreover, one of our results implies that no fair CCF can be rationalized by a social preference relation.

Revisiting Proportional Fairness: Anonymity Among Users in Interference Coupled Wireless Systems

The paper revisits the problem of proportional fairness in interference coupled wireless systems. It models interference coupling in wireless systems based on an interference function framework through a set of axioms (introduced by Yates in 1995). It utilizes the collective choice function to represent resource allocation strategies and an axiomatic framework to emulate certain desirable properties of resource allocation strategies. We introduce the axiom of equal priority in the power domain (and in the interference domain) and motivate it as interference coordination fairness. We consider this as an anonymity among the users, from the perspective of a central controller, e.g. a base station or an operator. We show that the proportional fair resource allocation strategy is anonymous to the identity of the users at the signal processing layer. Such an anonymity is relevant to obtain interference coordination fairness in iterative resource allocation strategies frequently encountered in wireless systems.

Towards a general and unified characterization of individual and collective choice functions under fuzzy and nonfuzzy preferences and majority via the ordered weighted average operators

Towards a general and unified characterization of individual and collective choice functions under fuzzy and nonfuzzy preferences and majority via the ordered weighted average operators

Aggregation of ordinal and cardinal preferences: a framework based on distance functions

AbstractIn this paper a collective choice function (CCF), formulated within a p‐metric distance function framework, is proposed as a generator of several compromise consensuses. Even though, the proposed CCF is not smooth, it is however demonstrated that it can be straightforwardly transformed into easily computable goal programming models. Finally, several cases of individual preferences aggregation are obtained by providing different interpretations of the CCF parameters: ordinal and complete information, ordinal and partial information and a cardinal case through ‘pairwise’ comparison matrices. Copyright © 2009 John Wiley & Sons, Ltd.

Lattices of choice functions and consensus problems

In this paper we consider the three classes of choice functions satisfying the three significant axioms called heredity (H), concordance (C) and outcast (O). We show that the set of choice functions satisfying any one of these axioms is a lattice, and we study the properties of these lattices. The lattice of choice functions satisfying (H) is distributive, whereas the lattice of choice functions verifying (C) is atomistic and lower bounded, and so has many properties. On the contrary, the lattice of choice functions satisfying (O) is not even ranked. Then using results of the axiomatic and metric latticial theories of consensus as well as the properties of our three lattices of choice functions, we get results to aggregate profiles of such choice functions into one (or several) collective choice function(s).

Collective choice functions on non-convex problems

Collective choice problems on sets in \({\frak R}_+^n\) arise naturally in economics. Such problems have been extensively studied both in the theory of revealed preferences (Peters and Wakker, 1991) and in axiomatic bargaining theory under the assumption of convexity. However, our knowledge of collective choice functions on non-convex problems is still patchy. In this paper I study the existence and characterisation of continuous choice functions on the domain \(\Gamma\) of comprehensive problems. The main result completely characterises rational choice functions that are continuous and satisfy Weak Pareto Optimality: they form the class of Monotone Path Choice Functions on \(\Gamma\). I also show that any discontinuous rational and weakly Pareto optimal choice function must be non- anonymous.

Social learning and collective choice

To be pertinent to democratic practice, collective choice functions need not apply to all possible constellations of individual preference, but only to those that are “humanly possible” in an appropriate sense. The present paper develops a theory of humanly possible preference within the context of the mathematical theory of learning. The theory of preference is then exploited in an attempt to resolve Arrow's voting paradox through restriction of the domain of majoritarian choice functions.