Abstract
•Voting systems with voters operating in different environments are considered.•Each voter is subject to an individual mission abortion policy.•An algorithm for evaluating the damage caused by wrong decision is suggested.•optimal aborting and voting rules, minimizing the damage are obtained.•An N-version programming cybersecurity system is analyzed.
Motived by abundant real-world examples in diverse domains such as drone-based target detection, sensor network-based environment monitoring, and cybersecurity defense, this paper pioneers the modeling of a weighted voting system (WVS) in which voting units (VUs) operate under distinct random shock environments and contribute to the system decision with varying weights. To mitigate the risk of VU loss, each VU follows an individual mission abort policy (MAP) determined by its shock exposure and operating time. We jointly model and optimize the MAP and the voting rule (defined by the VU weights and system voting threshold) to balance the risk of VU loss against the need to maintain sufficient active VUs for effective decision-making. A universal generating function-based method is suggested to evaluate the reliability as well as the expected cost of damage (ECD) of the considered WVS. An optimization problem is further formulated and solved to determine the optimal aborting and voting rules, minimizing the ECD. An N-version programming cybersecurity system is analyzed to demonstrate the proposed model. Detailed case studies are conducted to examine the effects of several cost and shock parameters on the ECD and optimization solutions, leading to important managerial insights.