The labeling problem in Multiple Target Tracking represents the problem of dealing with joint multi-target position uncertainties. This problem can be tackled by probabilistically characterizing the assignment of positions to labels [1]. The goal of this paper is to provide a performance evaluation criterion for such labeling characterization. In particular, an optimal decomposition of the association-free filtering posterior is derived analytically in a detection-based context. A particle-based implementation of this decomposition provides a definition of optimality regarding the labeling of the targets. This definition of optimality is also relevant for the characterization of labeling uncertainty in the track-before-detect context. An algorithm is provided for practical implementation of the method and used to evaluate the labeling uncertainty characterization proposed in [1].