The trade-off between equity and efficiency is analyzed in a geometric framework for the problem of committee selection, which has recently attracted interest in the social choice literature. It is shown that this trade-off can be maximal in the precise sense of the antipodality of the outcomes...

In this paper we compare a minisum and a minimax procedure as suggested by Brams et al. for selecting committees from a set of candidates. Using a general geometric framework as developed by Don Saari for preference aggregation, we show that antipodality of a unique maximin and a unique minisum...

Following the recent generalization of social choice in the literature on judgment aggregation, we extend the analysis of freedom of choice from sets of alternatives to sets of opinions. We establish the analogue of the cardinality based freedom of choice measure and suggest an alternative...

In a paper published in 1952, the French mathematician Georges-Théodule Guilbaud has generalized Arrow's impossibility result to the "logical problem of aggregation", thus anticipating the literature on abstract aggregation theory and judgment aggregation. We reconstruct the proof of Guilbaud's...

It is well known that the literature on judgement aggregation inherits the impossibility results from the aggregation of preferences that it generalises. This is due to the fact that the typical judgement aggregation problem induces an ultrafilter on the set of individuals. We propose a...