Incomplete pairwise comparison matrices and weighting methods

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the linear order preservation property if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen

Egy életminőség-rangsor a hazautalások alapján

A hazautalások a vendégmunkások és az őket küldő országok közötti kapcsolat egyik fontos mérőszámát jelentik. Ez egyben számszerűsített mutatója lehet annak is, hogy a saját hazájukhoz képest mely országokat részesítik előnyben az emberek, így egy életminőség jellegű rangsort állíthatunk fel azok között. Az elemzéshez a Világbank adatait használtuk 2010-től 2015-ig, az adatbázis a nemzetközi munkabér, illetve a személyek közötti bilaterális utalásokat tartalmazza. A javasolt mérőszám független az országok méretétől, és figyelembe veszi a teljes hálózat felépítését, azt feltételezve, hogy minden egységnyi átutalás felfogható egy preferenciaként a két érintett ország között

A new parsimonious AHP methodology: assigning priorities to many objects by comparing pairwise few reference objects

We propose a development of the Analytic Hierarchy Process (AHP) permitting to use the methodology also for decision problems with a very large number of alternatives and several criteria. While the ap- plication of the original AHP method involves many pairwise comparisons between considered objects, that can be alternatives with respect to considered criteria or criteria between them, our parsimonious proposal is composed of five steps: (i) direct evaluation of the objects at hand; (ii) selection of some reference objects; (iii) application of the original AHP method to the reference objects; (iv) check of the consistency of the pairwise comparisons of AHP and the compatibility between the rating and the prior- itization with a subsequent discussion with the decision maker who can modify the rating or pairwise comparisons of reference objects; (v) revision of the direct evaluation on the basis of the prioritization supplied by AHP on reference objects. Our approach permits to avoid the distortion of comparing more relevant objects (reference points) with less relevant objects. Moreover, our AHP approach avoids rank reversal problems, that is, changes of the order in the prioritizations due to adding or removing one or more objects from the set of considered objects. The new proposal has been tested and experimentally validated