Topsis Technique in Self-Government – Case Study of Košice Region

In the last decades, most of the democratic countries have reallocated tax revenues from collected taxes between the state budget and local government budgets. It is possible to monitor the effort to increase the relative financial autonomy of local governments, to strengthen own revenues of local self-government and to increase the autonomy of decision-making bodies regarding their use. The manuscript focuses on usage of TOPSIS technique as a tool for comprehensive evaluation in self-government in Slovakia. 8 criteria were used and their weight was calculated based Fuller triangle method and 25 experts. Based on this analysis, it is possible to recommend this method for usage not only in public sector, but also in private sector as well. Its use is also conditioned by the appropriate selection of the monitored indicators and their weighting, which significantly determines the overall results.


Introduction
Domestic and foreign researchers [1][2][3][4][5] noted that in the innovation economy, the efficiency evaluation based on multiple criteria is a more complicated option, but on the other hand, this evaluation gives more insight into the real state of public sector efficiency. According to [6], the basic advantage of these methods is the fact that they are not in a position to transform non-economic criteria into economic criteria at the cost of delicate, sometimes controversial operations. These methods include: scales and ranges (can be used separately or as a part of another method), methods of weight determination, methods based on partial evaluation of variants, methods based on pairwise comparison of variants.
All multi-criteria evaluation methods work with criteria (indicators) that are nonnegative and normalized, i.e. their sum is 1. The method of equal importance is not able to distinguish between the greater or lesser importance of the observed criteria, i.e., all criteria are evaluated equally. Ranking is based on assigning a point value based on certain preferences. The scoring method is similar to the previous method, but works with cardinal variables (preference of individual indicators). The principle of the Fuller's method is to allocate the points to each pair of indicators and then to sum up the points obtained. [7,8] used this method to evaluate municipalities in the Slovak Republic. Saaty's method works much like the previous methods. The only difference is that it also determines the size of this preference. The weighted sum method is particularly suited to determine quantitative criteria, assuming a linear dependence of the utility rate on criteria (indicators). The basic variant method determines the best or desired values and then calculates the utility rate of each alternative. The lexicographic method is based on the assumption that the most important criterion has the greatest influence. In the case of compliance, the second and the criterion after that shall be taken into account. When solving a problem, the AHP method takes into account all the elements that affect the outcome (the links between them and the intensity with which they influence each other). The TOPSIS method chooses the variant that is closest to the pre-set ideal and at the same time the furthest from the basal variant.
The identification of individual criteria for TOPSIS calculation was based on personal consultations with government employees of the Financial Control and representatives of municipalities. The common goal was to jointly identify a set of core indicators that best reflect the real status of a particular municipality's economy and that would offer an alternative to the currently valid law-based evaluation.  [7,8,17,18].
The whole process of statistical analyzes was carried out in MS Excel, Statistica 13.1 and Statgraphics XVII.

Application of TOPSIS technique in Košice region
Košice region (KSK) is the second most prosperous region in Slovakia. More than 55 % of its inhabitants live in the cities. The region is dominated by metallurgical, chemical and electrotechnical industry.  The ranking of municipalities achieved by applying the TOPSIS method with the same and modified weights, including the dependence of the individual monitored criteria on the achieved result is outlined in Table 2.  * district **ci -relative distance from PIS For the purposes of further analysis, the remote values identified by the Dean Dixon test were removed (Table 3). The Kolmogorov-Smirnov test did not confirm any match between the distribution functions of the results of the TOPSIS method (K-S = 0,252, p < 0,01). However, the relationship between both distribution functions was confirmed by the Kendall coefficient (rK = 0,938, p < 0,01). The Kendall coefficient tests the dependence between the result of the TOPSIS method and the number of inhabitants. This confirmed a weak negative correlation between the monitored variables (rK = -0.041, p = 0.194; rK* = -0.042, p = 0.180), however, it was not statistically confirmed.

Districts of Košice region
Change in the weights of the monitored indicators did not change the variance of results in the regions, however, what changed was the median in all districts except Spišská Nová Ves and Trebišov. As the normality of the results was not confirmed in any of the districts, the one-factor variance analysis was not used. By comparing the average rating in the districts (Figure 4), we can observe their minimum differences. The best-rated municipalities were found in the Sobrance district. With minimal differences, the worst-rated municipalities were found in the Košice district. Due to the change in monitored weights the evaluation of each district worsened by 0,97 %.

Conclusions
We consider the TOPSIS method to be a suitable multi-criterion assessment tool for the use of which it is necessary to have financial indicators (which in some cases may limit its use).
Its use is also conditioned by the appropriate selection of the monitored indicators and their weighting, which significantly determines the overall results. Based on a number of statistical analyzes in KSK we state that: a) the evaluation of the municipality depends primarily on the result of the management, which also determines the return on assets, b) the change in the weight, although retaining the variance, changed the median; the average result of the TOPSIS method in individual districts decreased by 0,97 %, c) from the point of view of the evaluation of municipalities the KSK's territory cannot be considered homogeneous.