Measuring Voting Power in Complex Shareholding Structures: A Public Good Index Approach

Aggregated Power Indices for Measuring Indirect Control in Complex Corporate Networks with Float Shareholders

“…In general, power indices are used to measure the power of a player i in group decision-making bodies. However, the interpretation of this value— —assigned to player i changes and depends also on the measure (power index) itself and the context in which it is applied, see Felsenthal and Machover (2005) [ 32 ], Laruelle et al (2006) [ 33 ], Gambarelli and Stach (2009) [ 34 ], Bertini and Stach (2011) [ 35 ], Bertini et al (2013) [ 36 ], Bertini et al (2015) [ 37 ], Bertini and Stach (2015) [ 38 ], Stach (2016) [ 39 ], Bertini et al (2016) [ 40 ], Bertini et al (2017) [ 41 ], Bertini et al (2018) [ 42 ], Bertini et al (2020) [ 43 ], Staudacher et al (2021) [ 44 ], Stach and Bertini (2021) [ 28 ], Stach (2022) [ 30 ], Stach and Bertini (2022) [ 45 ], and Stach, Mercik, and Bertini (2023) [ 17 ].…”

“…In this work, we consider the approach by Karos and Peters [ 1 ] and modify it by substituting the original Shapley and Shubik index with ten others to obtain so-called aggregated power indices. This idea has been just used by Stach, Bertini, and Mercik (2023) [ 17 ] and the Holler [ 54 , 55 ] index—also called the Public Good Index—substituted the Shapley and Shubik index in the Karos and Peters framework. The new index obtained was called the iPGI index.…”

“…The second group contains the power indices based on minimal winning coalitions. Stach, Bertini, and Mercik (2023) [ 17 ] argued widely the validity and incisiveness of the choice of the minimal-winning power indices to assess the real power of players in the context of indirect control. We refer the reader to this work, and here we just mention that in the context of a hostile takeover attack, it seems that a potential rider will look for a minimal winning coalition; not one that is expensive, but one that is stable and winning.…”

“…Note that Bertini, Mercik, and Stach (2023) [ 17 ] introduced this index recently and called it the iPGI index, where “ i ” refers to indirect control. To be in line with the other nine aggregated newly introduced indices in this paper, we denote the aggregated Holler index by Ah .…”

“…The game theory approach to measuring the indirect control power of firms as elements of a whole corporate network is known in the literature on the subject. Many scholars proposed methods based on power indices for measuring the indirect control power of a firm in an ownership network; see Gambarelli and Owen (1994) [ 4 ], Turnovec (1999) [ 5 ], Hu and Shapley (2003) [ 6 , 7 ], Leech (2002) [ 8 ], Crama and Leruth (2007, 2013) [ 3 , 9 ], Karos and Peters (2015) [ 1 ], Mercik and Lobos (2016) [ 10 ], Levy and Szafarz (2017) [ 11 ], Mercik and Stach (2018) [ 12 ], Stach, Mercik, and Bertini (2020) [ 13 ], Staudacher, Olsson, and Stach (2021) [ 14 ], Stach and Mercik (2021) [ 15 ], Staudacher, Olsson, and Stach (2022) [ 16 ], and Stach, Mercik, and Bertini (2023) [ 17 ], for examples. The reader can find the comparisons of some of these approaches in [ 18 , 19 , 20 ] and [ 12 ].…”