Much has been written of coalition formation and duration but most of the literature overlooks the legislative and electoral environments in which coalitions are formed. How polarized or center oriented are the parties that may or may not join the coalition? What is the likelihood that the coalition that forms may last? What is the likely coalition policy that those who think about joining the coalition may expect of the coalition? Is this policy going to be controversial in the eyes of the electorate or is it going to be a good fit with the center of gravity of the electorate as a whole? While some of these questions have been answered in the literature and some have actually been dealt with in some rigor and tenacity, they have almost always been addressed in isolation and in parallel lines of inquiry. In this paper we propose a general concept, the uncovered set, that allows a new line of research to integrate all of these questions in one analytical and empirical research program. We use a very rich and original data set from Israel to illustrate the usefulness of this approach for theoretical and empirical inquiry and call upon our colleague to invest in future research guided by this unifying approach.