Since its conception ELECTRE TRI has been widely used to deal with several problems in the problematic of sorting. However, the inherent limitation of this method lies in its working with only one decision-maker. Currently there is an ELECTRE TRI version that can be used with multiple decision-makers, but it lacks the tools to deal with non-cooperative situations. Thus, this paper puts forward a negotiation procedure to be applied when using ELECTRE TRI. The procedure was inspired by the last-diminisher procedure and a version of the Nash Demand Game, Divide-the-Dollar, in order to establish an envy-free Nash Equilibrium and to control greed. The method establishes a negotiation process between decision-makers, in order to define each player's degree of participation in determining the values of the ELECTRE TRI criteria, weights and parameters. Each parameter is divided into negotiable shares that will be distributed by means of the negotiation procedure, which represents the degree of participation of the decision-maker's preferences.