Designing Envy-Free Fair Distributed Detection Systems With Minimum Operational Cost

Consider the operator of a distributed detection sensor system that serves multiple communities, each with a certain Receiver Operating Characteristic (ROC) curve. To minimize operational costs, the operator may be inclined to configure the various detection probabilities using the Bayes decision rule; however, members of communities that receive lower probabilities of detection may consider the system unfair. To avoid dissatisfaction among communities, we argue for the adoption of envy-free fairness, in which all communities receive the same probability of detection. As shown in our previous work, envy-free fairness can be achieved by adjusting the probabilities of false alarm at each community. In here, we extend our results by considering a-priori probabilities and a decision cost model; and we propose that operators design their systems such that all communities operate at the common probability of detection that minimizes the operational cost. We provide guidelines to allow operators estimate the additional cost of the envy-free fair system and better plan system expansions. Lastly, we propose a sensor allocation procedure among communities to design envy-free fair systems under different constraints.