On the Borda Method for Multicriterial Decision-Making

The present paper discusses two issues with multicriterial decision-making methods of Borda type (when scores such as n, n-1,…, 2, 1 are given to the objects to be ranked and the hierarchy is obtained based on the totals of these scores). The first issue is related to the influence on the result of various transformations of the scores. We show that a linear transformation of the scores does not change the final ranking and that (almost) any polynomial of second degree or more, with positive coefficients, can alter the solution (ranking). The same happens if one changes the scores by employing the logarithm, exponential, or square root functions. In the second part of the paper we consider an iterated version of the Borda method. We show that this method is not robust: there are cases when different solutions are returned at different iterations.