We consider the problem of choosing the best of a set of alternatives where each alternative is evaluated on multiple criteria. We develop a visual interactive approach assuming that the decision maker (DM) has a general monotone utility function. The approach partitions the criteria space into nonoverlapping cells. The DM uses various graphical aids to move between cells and to further manipulate selected cells with the goal of creating cells that have ideal points less preferred than an alternative. When the DM identifies such cells, all alternatives in those cells are eliminated from further consideration. The DM may also compare pairs of alternatives. The approach terminates with the most preferred alternative of the DM.