We propose a new level set model for representing multimaterial flows in multiple space dimensions. Instead of associating a level set function with a specific fluid material, the function is associated 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 designation. To represent a general M-material configuration, M(M-1)/2 level set functions need to be accounted for; problems of practical interest use far fewer functions, as not all pairs of materials share an interface, and level-set functions that coincide are grouped together. Under this model, regions of potential material ambiguity, i.e. overlaps or vacuum, are markedly reduced in size: in 2D, ambiguous regions are points, as opposed to lines in material-based level set models; in 3D, they are lines as opposed to surfaces. The model produces excellent results without the need for reinitialization, thereby avoiding additional computational costs and preventing excessive numerical diffusion.