On pairwise comparison matrices that can be made consistent by the modification of a few elements

Pairwise comparison matrices are often used in Multi-attribute Decision Making forweighting the attributes or for the evaluation of the alternatives with respect to a criteria. Matrices provided by the decision makers are rarely consistent and it is important to index the degree of inconsistency. In the paper, the minimal number of matrix elements by the modification of which the pairwise comparison matrix can be made consistent is examined. From practical point of view, the modification of 1, 2, or, for larger matrices, 3 elements seems to be relevant. These cases are characterized by using the graph representation of the matrices. Empirical examples illustrate that pairwise comparison matrices that can be made consistent by the modification of a few elements are present in the applications.

Spheres of Influence: A Few Reflections on the Concept

In the frame of the Ukrainian crisis the question of spheres of influence has returned to political discourse. This may be an awkward subject, but what if we only deny the existence of such power constellations as spheres of influence? Do spheres of influence exist, or are they relics of history, and mere rhetoric? And if they exist, where can we find them? The hypothesis in this article is that instead of being a tangible reality, spheres of influence are obscure and contested political constructions, which nevertheless can have an impact on political behaviour. To demonstrate this, the article will first introduce a few examples of the current use of the concept. Secondly, a few remarks follow concerning the different IR schools of thought, and conceptual history as a method. Next, the article turns to discussing a few dictionaries and the empirical material for the present inquiry, which consists of recent textbooks, i.e. the current political science curriculum in one particular university, at the University of Tampere, Finland. More empirical cases deal with the division of Africa, the post-WWII situation, and the Hungarian revolution of 1956.