Non-emptiness of the Core: Low Dimensional Decisions Spaces and One-Dimensional Preferences

We consider a Society which has 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 primarily aims at finding conditions with economic appeal that ensures the non-emptiness of the Core.