It can be shown that sufficient statistics maintained by a multiple-hypothesis algorithm for a multiple-target tracking problem are expressed as a set of a posteriori Janossy measures. This fact suggests a new class of multiple target tracking algorithms without generating and evaluating data-to-data association hypotheses. Under a certain set of assumptions, including target-wise independent detection and measurement errors, a Janossy measure representation can be considered to be the symmetrization or scrambling of a posteriori joint target state distribution under a specific data association hypothesis. This paper explores the possibility of using Janossy measures directly to represent a posteriori joint target state distributions, instead of the product expression of the a posteriori joint target state distributions. By doing so, it becomes possible to combine any two data association hypotheses sharing the same number of detected targets they assume, thereby providing an effective method for combining data association hypotheses. When using Janossy measures as a method of representation, we are not forced to maintain the product structure, and hence, at least theoretically, we can combine two data association hypotheses without any approximation. Since we do not require track-wise independence under any hypothesis, this method allows us to treat split or merged measurements in a unified way.