Optimization under ordinal scales: When is a greedy solution optimal?

Mathematical formulation of an optimization problem often depends on data which can be measured in more than one acceptable way. If the conclusion of optimality depends on the choice of measure, then we should question whether it is meaningful to ask for an optimal solution. If a meaningful optimal solution exists and the objective function depends on data measured on an ordinal scale of measurement, then the greedy algorithm will give such a solution for a wide range of objective functions.