Level-sets are a convenient model for representing immiscible multilateral fluids in multiple space dimensions. Material interfaces are embedded as zero level-curves of the function, which are used determine material designations. Traditional models assign to each material its own level-set function, whose zero level-curve defines the boundary of that material. This approach is known to produce indeterminate states, i.e. regions that are not claimed by any material, or regions that are claimed by more than one material. Algorithms to remove ambiguities exist, but involve decisions that appear arbitrary. We present a new level set model, in which the level set function is not associated with a specific fluid material, but with a pair of materials and the interface that separates them. A voting algorithm collects sign information from all level set functions and determines material designations. The new model is less prone to producing indeterminate material states, and outperforms existing material-based level set models without the need for reinitialization schemes. We will present both traditional and new approaches, discuss their respective merits and present numerical results. This is joint work with D. Starinshak and P.L. Roe.