In this paper we present a result that relates merging of closed convex sets of discrete probability functions respectively by the squared Euclidean distance and the Kullback-Leibler divergence, using an inspiration from the Rényi entropy. While selecting the probability function with the highest Shannon entropy appears to be a convincingly justified way of representing a closed convex set of probability functions, the discussion on how to represent several closed convex sets of probability functions is still ongoing. The presented result provides a perspective on this discussion. Furthermore, for those who prefer the standard minimisation based on the squared Euclidean distance, it provides a connection to a probabilistic merging operator based on the Kullback-Leibler divergence, which is closely connected to the Shannon entropy.
Kullback-Leibler divergence, probabilistic merging, information geometry, Rényi entropy