Reliability optimization for weighted voting system

The voting system studied consists of n units, each of which provides a binary decision (0 or 1), or abstains from voting. The system output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction τ of the cumulative weight of all non-abstaining units. Otherwise the system output is 0. The existing method for evaluating the reliability of a weighted voting system can not be applied to real systems without imposing some restrictions because of its combinatorial complexity. In this paper a method is suggested which allows the reliability of weighted voting system to be exactly evaluated without imposing constraints on unit weights or threshold value. The approach is based on using a universal generating function technique. Using the suggested method an optimization procedure is developed for system reliability maximization by choosing proper unit weights and threshold values. A genetic algorithm is used as the optimization tool. Examples are presented.