On optimal completions of incomplete pairwise comparison matrices

An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uniqueness problem of the best completion for two weighting methods, the Eigen-vector Method and the Logarithmic Least Squares Method. In both settings we obtain the same simple graph theoretic characterization of the uniqueness. The optimal completion will be unique if and only if the graph associated with the partially defined matrix is connected. Some numerical experiences are discussed at the end of the paper.

Fiscal adjustment and economic growth in the European Union

The current world economic crisis induced countries to launch wide-scale spending programmes all over the world. Member states of the European Union have not been an exception to this trend. While deficit spending may increase the aggregate demand, it can also accelerate indebtedness and make the required spending cuts politically risky later on. However, deficit financing is not a new phenomenon in the EU; it has been widely practiced in the last couple of decades. As the crisis seems to come to an end, countries with huge deficits should adopt exit strategies now, thereby reducing deficit and debt and reintroducing fiscal discipline, a requirement laid down in the Stability and Growth Pact. Nevertheless, former adjustment processes can provide ample evidence for successful and politically viable fiscal consolidations. In certain cases, even economic activity started to accelerate as a response to the welldesigned adjustment measures. Based on the previous experiences of EU states, the aim of this paper is, therefore, to identify the conditions that may determine a fiscal consolidation to be successful in terms of a reduced debt ratio and a positive economic growth.