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.

On the implementation of the L-Nash bargaining solution in two-person bargaining games

The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin, pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159, 1992) also implements the L-Nash solution.

Modifying the yield factor based on more efficient use of fertilizer — The environmental impacts of intensive and extensive agricultural practices

The aim of this article is to draw attention to calculations on the environmental effects of agriculture and to the definition of marginal agricultural yield. When calculating the environmental impacts of agricultural activities, the real environmental load generated by agriculture is not revealed properly through ecological footprint indicators, as the type of agricultural farming (thus the nature of the pollution it creates) is not incorporated in the calculation. It is commonly known that extensive farming uses relatively small amounts of labor and capital. It produces a lower yield per unit of land and thus requires more land than intensive farming practices to produce similar yields, so it has a larger crop and grazing footprint. However, intensive farms, to achieve higher yields, apply fertilizers, insecticides, herbicides, etc., and cultivation and harvesting are often mechanized. In this study, the focus is on highlighting the differences in the environmental impacts of extensive and intensive farming practices through a statistical analysis of the factors determining agricultural yield. A marginal function is constructed for the relation between chemical fertilizer use and yield per unit fertilizer input. Furthermore, a proposal is presented for how calculation of the yield factor could possibly be improved. The yield factor used in the calculation of biocapacity is not the marginal yield for a given area, but is calculated from the real and actual yields, and this way biocapacity and the ecological footprint for cropland are equivalent. Calculations for cropland biocapacity do not show the area needed for sustainable production, but rather the actual land area used for agricultural production. The proposal the authors present is a modification of the yield factor and also the changed biocapacity is calculated. The results of statistical analyses reveal the need for a clarification of the methodology for calculating marginal yield, which could clearly contribute to assessing the real environmental impacts of agriculture.

Modifying the yield factor based on more efficient use of fertilizer — The environmental impacts of intensive and extensive agricultural practices

The aim of this article is to draw attention to calculations on the environmental effects of agriculture and to the definition of marginal agricultural yield. When calculating the environmental impacts of agricultural activities, the real environmental load generated by agriculture is not revealed properly through ecological footprint indicators, as the type of agricultural farming (thus the nature of the pollution it creates) is not incorporated in the calculation. It is commonly known that extensive farming uses relatively small amounts of labor and capital. It produces a lower yield per unit of land and thus requires more land than intensive farming practices to produce similar yields, so it has a larger crop and grazing footprint. However, intensive farms, to achieve higher yields, apply fertilizers, insecticides, herbicides, etc., and cultivation and harvesting are often mechanized. In this study, the focus is on highlighting the differences in the environmental impacts of extensive and intensive farming practices through a statistical analysis of the factors determining agricultural yield. A marginal function is constructed for the relation between chemical fertilizer use and yield per unit fertilizer input. Furthermore, a proposal is presented for how calculation of the yield factor could possibly be improved. The yield factor used in the calculation of biocapacity is not the marginal yield for a given area, but is calculated from the real and actual yields, and this way biocapacity and the ecological footprint for cropland are equivalent. Calculations for cropland biocapacity do not show the area needed for sustainable production, but rather the actual land area used for agricultural production. The proposal the authors present is a modification of the yield factor and also the changed biocapacity is calculated. The results of statistical analyses reveal the need for a clarification of the methodology for calculating marginal yield, which could clearly contribute to assessing the real environmental impacts of agriculture.

A Note on The Weak Sequential Core of Dynamic TU Games

This paper addresses a problem with an argument in Kranich, Perea, and Peters (2005) supporting their definition of the Weak Sequential Core and their characterization result. We also provide the remedy, a modification of the definition, to rescue the characterization.