Integration of ordinal and cardinal information in multicriteria ranking with imperfect compensation

The method presented in this paper is a MCDA method, which outranks a certain number of choice options that are evaluated on a mixture of cardinal and ordinal judgement criteria. Characteristics of the method are a theoretically sound integration of cardinal and ordinal information and a decision-makers' preference structure that allows for less than perfect compensation between criteria. The method is based on a pairwise comparison of choice-options. It belongs to the family of decomposed scaling methods: the assessment of the relative importance of the criteria on one hand and the assessment of the scores (cardinal criteria) and rankings (ordinal criteria) on the other hand are performed separately. The assessment of the scores and rankings is realised by means of (marginal) value functions in such a way that the ordinal information is fully comparable with the cardinal information. Essentially, the ordinal information is translated into stochastical information without imposing any assumption on the probability distributions attached to the ordinal data. The relative importance of the judgement criteria is represented by a set of cardinal weights or by a ranking of weights. The final ranking of the choice options is based upon an overall value function that is some kind of weighed aggregation of the marginal value functions. In order to allow for less-than-perfect-compensation between criteria, the method uses a convex combination of two different CES-type value functions. The paper ends with an empirical application, on the planning of public transport systems in the Netherlands.