Nonemptiness of the Core: Low Multidimensional Decisions Spaces and One-Dimensional Preferences.

We consider a Society which as to make a finite dimensional collective decision, and study the "stability" of the public arrangements made in the Society when considering the threats that potential coalitions may generate. We refer for that to the standard cooperative approach based on the concept of Core, and its extension, the stable coalition structures. The present analysis aims at finding conditions with economic appeal that insures the non-emptiness of the Core.