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 multidimensional space and objects determine a decomposition of such a space into subspaces. We present a series of numerical and probabilistic results which show that such decompositions in objects can greatly increase decidability, as new kind of optima (called local and u-local) are very likely to appear also in cases in which no generalized Condorcet winner exists in the original search space.
Amendola, G., Marengo, L., Pirino, D., Settepanella, S. and Takemura, A. (2015). Decidability in complex social choices. Evolutionary and Institutional Economics Review, 12(1), 141-168.