This study presents a theoretical investigation of the rank-based multiple classifier decision problem for closed-set pattern classification. The case with classifier raw outputs in the form of candidate class rankings is considered and formulated as a discrete optimization problem with the objective function being the total probability of correct decision. The problem has a global optimum solution but is of prohibitive dimensionality. We present a partitioning formalism under which this dimensionality can be reduced by incorporating our prior knowledge about the problem domain and the structure of the training data. The formalism can effectively explain a number of rank-based combination approaches successfully used in the literature one of which is discussed.