Analysis and optimization of weighted voting systems consisting of voting units with limited availability

The voting system studied consists of n voting units each either providing a binary decision (0 or 1) or abstaining 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. In this paper, we study the effect of limited availability of the voting units on the entire voting system reliability. Two different types of systems are considered. In the system of type 1, the absence of unit output (unit unavailability) is interpreted by the system as abstention from voting. In the system of type 2, the unavailable state of the voting unit and its abstention from voting can be distinguished and the system parameters can be adjusted to optimize its performance for each combination of available units. There are two ways to improve reliability of weighted voting system consisting of units with the given output probability distribution: optimization of system parameters (weights of units and threshold factor value) and units availability enhancement (for example, by choosing proper maintenance policy). This paper shows a method of incorporating information about unitsʹ availability into a procedure for determining the optimal system parameters. It also presents a method for determining indices that measure importance of voting units availability for both types of systems. These indices indicate voting units for which efforts of availability enhancement are the most beneficial from the entire system reliability improvement point of view. The approach is based on using a universal generating function technique and optimization procedure presented in . Examples are presented.