In this chapter, we extend the KSB distance metric to a signed and weighted matrix influence function in the context of group decision-making with mutual influence: we define the rule of how to transform each preference ordering into an ordering matrix and set a distance metric to compute the distance between any two preference orderings (i.e. ordering matrices); then, the theoretically feasible preference ordering that has the minimum weighted sum of distances from all influencing agents’ preferences is the resulting preference of the influenced agent. This function takes influencing agents’ preference orderings as input and give the influenced agent’s preference ordering as output. We use the same example of group decision-making with multiple sources of influence in previous chapter to apply and illustrate the matrix influence function.