Detection of Paradoxes of Power Indices for Simple Games

Within the context of weighted simple games, we consider some well–known postulates — relative normalized measures — for relative power indices. We essentially refer to the postulates: of monotonicity, donation and bloc; and to the power indices by: Banzhaf, Johnston, Deegan–Packel and Holler. We do not consider the Shapley–Shubik index because satisfies all these three postulates.
If a power index fails to satisfy one of the above postulates then the phenomena is regarded to be paradoxical. This work considers the paradoxes that arise from considering a particular postulate and a particular power index. The question that naturally appears for each simple voting game and pair, postulate & power index, is: how frequently does the paradox arise?
We develop some theoretical methods and experimental results to partially answer the above question.