We describe the fundamental groups of ordered and unordered k-point sets in C^n generating an affine subspace of fixed dimension.

We present a geometric model of social choice when the latter takes place among bundles of interdependent elements, that we will call objects. We show that the outcome of the social choice process is highly dependent on the way these bundles are formed. By bundling and unbundling the same set of...

Here the reader can find some basic definitions and notations in order to better understand the model for social choise described by L. Marengo and S. Settepanella in their paper: Social choice among complex objects. The interested reader can refer to [Bou68], [Massey] and [OT92] to go into more...

Suppose R is the complement of an essential arrangement of toric hyperlanes in the complex torus and ? = ?1(R). We show that H*(R;A) vanishes except in the top degree n when A is one of the following systems of local coefficients: (a) a system of nonresonant coefficients in a complex line...

A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present paper we prove that if T(W) is the toric arrangement defined by the cocharacters lattice of a Weyl group W, then the integer cohomology of its complement is...

In this paper we develop on a geometric model of social choice among bundles of interdependent elements (objects). Social choice can be seen as a process of search for optima in a complex multi- dimensional space and objects determine a decomposition of such a space into subspaces. We present a...

Recently, Marengo and Settepanella (2010) introduced a model of social choice among bundles of interdependent elements. In this paper we prove that their voting model is highly decidable, i.e. a group of agents that agrees to use such voting process has an high probability to reach a final...

The paper presents a new framework to assess firm level heterogeneity and to study the rate and direction of technical change. Building on the analysis of revealed short-run production functions by Hildenbrand (1981), we propose the (normalized) volume of the zonotope composed by vectors-firms...

We present a geometric model of social choice among bundles of interdependent elements, that we will call objects. We show that the outcome of the social choice process is highly dependent on the way these bundles are formed. By bundling and unbundling the same set of constituent elements an...