Reliability of decision making in human-organizations

In a human-organization system with n officers, a decision has to be made on whether to accept or to reject an innovation-oriented proposal that can either be good or bad. Each officer will review a given set of available information regarding the proposal in question and will thereafter return his or her decision. In the common formulation of this problem, the organization will accept the proposal if at least k officers decide for the project, where k is a prespecified threshold value. Hereby, each officer is subject to different errors and therefore, the final decision may be faulty as well. The reliability of such a system is the probability for the organization to make the right decision. In this paper, by imposing weights for each officer, generalized problem formulations are introduced and formulas for the corresponding reliability are derived