CONICET | Buscador de Institutos y Recursos Humanos

In this work we propose a method of opinion pooling based on pairwise interactions.We assume that each agent has a probability measure on the possible outcomes of somesituation, and they try to find a single measure aggregating their estimates. This isa classical problem in Decision Theory, where expert opinions contain some degree ofuncertainty, and a Decision Taker needs to pool these estimates.We study this problem using a kinetic theory approach, obtaining a Boltzmanntype equation for opinions which are symmetric probability measures defined on the realline. We obtain a non local, first order, mean field equation as its grazing limit whenthe parameter in the interaction goes to zero. Also, we prove the convergence to quasi-consensus with explicit estimates on the convergence time depending on the variance ofthese measures.Let us remark that this model can be interpreted as a noisy model of opinion dy-namics. In many models, the opinion of each agent is a point in the real line, the agentsinteract and observe other agents opinions. We can consider that observed opinions areperturbed or deformed by some noise in the transmission channel or in the interpretationof the agents, so we can think of agents opinions directly as random variables instead ofa single point