Multi-criteria group consensus under linear cost opinion elasticity

Consensus is a pivotal concept in group decision making. Many times, such a consensus is achieved by the experts shifting their opinion towards a point of mutual consent. Such a shift in many cases is the result of laborious negotiations, which escalates the cost of reaching the consensus. Moreover, many times the group decision is multi-criteria oriented in which the experts need to agree on each criterion separately.This paper describes three problems where experts of unequal importance and with a linear cost of changing their opinion (opinion elasticity) consider a single and a multi-criteria decision consensus. These problems achieve a minimum cost consensus without a budget limit. It turns out that the optimal consensus point is at the median opinion for rectilinear cost function and at the weighted average opinion for squared geometric distance calculations.Linear-time algorithms are presented for all cost consensus problems with no budget limits. Proofs, computational complexity and examples are provided for these algorithms.