||It has been observed that in single voting unanimity can rarely be reached. In many situations, however, members may not be aware that their preferences as expressed by their votes may contain room for compromise. This paper proposes a consensus-seeking methodology-the Negotiable Alternatives Identifier (NAI)-that searches for such a compromise. Starting with individual cardinal preferences on alternatives, NAI classifies alternatives into three classes of preferences: the most preferred, the preferred and the least preferred. Within each class, relatively small differences in preferences among alternatives may make it reasonable for a decision maker to consider them interchangeable. As a result of this flexibility, a collective solution acceptable to all decision makers can be generated. In this paper we provide some theorems and their proofs to address the extreme conditions of the proposed heuristic. Also we provide an example to illustrate how to use the proposed heuristic to solve a real-world problem.