The distance measure on consensus decision making based on primal-dual programming models

This paper investigates the consensus problem based on minimum cost and maximum return by utilizing primal-dual programming models. The primal problem is a linear programming model based on minimum cost of reaching consensus, and its dual problem is a linear programming based on maximum return of reaching consensus. By using the dual linear programming theories, this paper not only discusses the relation between the minimum cost that the moderator paid the individuals and the maximum returns that the individuals expected to receive for changing the opinion, but also explored the relation between the unit cost that the moderator would pay each individual and the unit return that each individual would receive from the moderator.