The binary chief executive officer (CEO) problem with an arbitrary number of agents is considered in this paper. A scheme which separates the reconstruction of observations and the final decision of a common source is assumed. Hence, we first derive the outer bound for the rate- distortion region by providing the converse proof of a binary multiterminal source coding problem which is the key to solve the binary CEO problem. The distortion of the binary CEO problem is then determined by the Poisson binomial process based on the using majority voting logic for the final decision. The rate-distortion behavior of the binary CEO problem is then analyzed based on the outer bound by solving a convex optimization problem. It is found that the distortion decreases until it converges to a certain level, as the sum rate and/or the number of agents increases.