Methods for Evaluating Power Distribution in Multi-level Structures

Evaluation of power of individuals and groups in systems where decisions are made by voting is important to both private (for example, power of potential investors, shareholders) and public sectors (for example, power of parties in parliament). However, in modern researches power assessment is usually limited to one level (for example, one house of parliament). In this research the method for usage classical power indices (Shapley-Shubik, Banzhaf, Johnston, Deegan-Packel, Holler-Packel and Coleman indices) to evaluate power in multi-level structures is described. Also, using Parliament of Ireland as an example, dependencies between values of these indices were assessed and comparisons with the results of indices approximations using alternative methods were shown. Finally, software for calculations of described indices was developed for this research. Using this dataset strong dependencies between values of almost every pair of indices were founded. In addition, it was shown that approximation technics which were chosen can return values considerably different from values of described indices.