Shapley-shubik power index

When I need a real value of shapley shubik index, how can I enlarge memory for calculation in R? in this case I had better use "apply" instead of "for loop". – Choijaeyoung Mar 29, 2013 at 14:34

The Shapley-Shubik power index was introduced in 1954 by economists Lloyd Shapley and Martin Shubik, and provides a different approach for calculating power. In situations like political alliances, the order in which players join an alliance could be considered the most important consideration. In particular, if a proposal is introduced, the ...We prove the validity of an alternative representation of the Shapley-Shubik (1954) index of voting power, based on the following model. Voting in an assembly consisting of n voters is conducted ...The Banzhaf and Shapley-Shubik power indices were first introduced to measure the power of voters in a weighted voting system. Given a weighted voting system, the fixed point of such a system is ...In this case, the Shapley value is commonly referred to as the Shapley–Shubik power index. A specific instance of simple games are weighted voting games, in which each player possesses a different amount of resources and a coalition is effective, i.e., its value is 1, whenever the sum of the resources shared by its participants is higher than ...(1+2)=(3 points ) A weightedFind the Shapley -Shubik power index of the last player, with weight 1, in this WVS voting system (WVS ) is described by [9 : 5, 4, 3, 2, 1] There’s just one step to solve this. Who are the experts? Experts have been vetted by …

A power index assigns to such an effectivity function a number for each agent, measuring the opportunities of that agent. We characterize a class of power indices by four axioms: the Transfer Property, the Dummy Property, Symmetry, and Network Neutrality. ... The Shapley-Shubik index is shown to be efficient in a vertex cover game for the ...Highlights • Application of the Shapley-Shubik index to determine the agents' strength in a dispersed decision-making system. • A new method for generating the local decisions within one cluster. Abstract In this paper, dispersed knowledge – accumulated in several decision tables is considered.Shapely-Shubik power index for P1 = 0.5 = 50%. Shapely-Shubik power index for P2 = 0.5 = 50%. Shapely-Shubik power index for P3 = 0%. This is the same answer as the Banzhaf power index. The two methods will not usually produce the same exact answer, but their answers will be close to the same value. Notice that player three …The Shapley–Shubik power index was formulated by Lloyd Shapley and Martin Shubik in 1954 to measure the powers of players in a voting game. The index often reveals surprising power distribution that is not obvious on the surface. The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players in an n ... The applet needs you to supply information for a weighted voting system and then press the Compute button to see the vote power distribution accoriding to the Shapley-Shubik power index.. There are several prebuilt voting systems available through the dropdown box at the bottom of the applet that appears under the Shapley-Shubik Index tab.. These can be modified and new ones can be created by ...

2.2. Shapley-Shubik power index. While for the Banzhaf power index the order in which voters join a coalition does not matter, i.e. the coalitions are just subsets of the set of voters, the Shapley-Shubik power index, introduced by Shapley and Shubik in 1954 [SS54] takes the order in which voters enter a coalition into account.The Shapley-Shubik power index was formulated by Lloyd Shapley and Martin Shubik in 1954 to measure the powers of players in a voting game. The index often reveals surprising power distribution that is not obvious on the surface. The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players in an n ...When a number is expressed with exponents, or one number to a power of another, it is considered to be in index form. For example, 27 can be written in index form as 3^3. This is because 27 is 3x3x3 or 3^3.Question: Variation of 120 in text Abe =49 shares, Ben =48 shares, Condi =4 shares, Doris =3 shares 2/3 majority needed Find the Banzhaf Power index and Shapely- Shubik index for each voter, Fill in the table for each index and include all relevant information: quota, number of coal tions, number of orderings. Describe what each of these indices tells about theseThe use of game theory to study the power distribution in voting systems can be traced back to the invention of “simple games” by von Neumann and Morgenstern [ 1 ]. A simple game is an abstraction of the constitutional political machinery for voting. In 1954, Shapley and Shubik [ 2] proposed the specialization of the Shapley value [ 3] to ...

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The Shapley-Shubik Power Index Terms: Sequential Coalition: a coalition where order matters, so there is a player who votes first, then second, etc. Pivotal Player: the player in a sequential coalition whose vote makes the coalition winning Shapley-Shubik Power index: a slightly different index on the power of each player in a weighted voting system Calculations 1.The Shapley-Shubik power index for Pi is then the total number of instances in which Pi is critical, divided by n!. The Banzhaf and Shapley-Shubik power distributions for a given WVS can some-times agree, but they can also be dramatically different. (Chapter 9 of Taylor's book [5] provides an example, and also other models of power.)shapely shubik power index. for each player the ratio: SS/N! where SS is the player's pivotal count and N is the number of players. shapely shubik power distribution.English Abstract: I define Shapley-Shubik Power Index per Person (SSPIPP) as the ratio of a political party's Shapley-Shubik Power Index in a parliament to the number of people who voted for the party. SSPIPP can be regarded as the political power each of them has. I calculate the optimal size of a political party that maximizes SSPIPP, and it ...Axiomatizations for the Shapley-Shubik power index for games… the title of the preface of Algaba et al. (2019) names it, the idea of the Shapley value is the root of a still ongoing research agenda. The remaining part of this paper is organized as follows. In Sect. 2 we introduceNote that if this index reaches the value of 0, then it means that this player is a dummy. When the index reaches the value of 1, the player is a dictator. Author(s) Sebastian Cano-Berlanga <[email protected]> References. Shapley L, Shubik M (1954). "A Method for Evaluating the Distribution of Power in a Committee System."

4 Agu 2010 ... JEL Classification Numbers: C71, D72. Keywords: Simple Games, Shapley$Shubik Power Index, Effi ciency Axiom. 1 Introduction. Shortly after the ...Power is a central concept in many disciplines in the social sciences, including political science, sociology, social-psychology, organization studies, urban ... Shapley—Shubik Index; Neorealism; Social Dominance Theory; McClelland, David; Social Power; Trust; Relational Power; Mann, Michael; Free Will; Shareholder Voting Power;Enter the email address you signed up with and we'll email you a reset link.b. (2 points) Briefly explain in a few sentences what your answer to part (a) tells you about the practicality of using the Shapley-Shubik approach to measuring power, even with the aid of a computer. It's not very practical to use the Shapley-Shubik approach to measuring power because it would take too long when a lot of players are involved. With only 23 players it'll take a computer ...This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Consider the weighted voting system [9: 7, 4, 1] Find the Shapley-Shubik power distribution of this weighted voting system. List the power for each player as a fraction: P1P1: P2P2: P3P3:Answer to The Shapley-Shubik Power Index Another index used to mea....After heated deliberations, Congress opted for the former, but in the very first exercise of the veto power by President of the United States, President Washington blocked the measure. ... Shapley-Shubik Power Index Calculator: Voting Methods and Social Choice: Webster's Apportionment Method: Weighted Voting and Power IndicesShapley-Shubik Power Index, σ, (sigma): Ratio of how often a player is pivotal to the number of sequential coalitions , where T = total number of sequential coalitions . Shapley- Shubik Power Distribution: Complete list of σ for each player. Find the Shapley - Shubik Power Distribution in each of the following examples: Example 1: [5: 3, 2, 1]The Shapley-Shubik index is immune to both bloc and donation paradoxes, but it does not satisfy the bicameral meet satisfied by the Banzhaf and MSR indexes. An index of power respects bicameral meet if the ratio of powers of any two voters belonging to the same assembly prior to a merge with a different assembly is preserved in the joint ...Shapley-Shubik Power Index, σ, (sigma): Ratio of how often a player is pivotal to the number of sequential coalitions , where T = total number of sequential coalitions . Shapley- Shubik Power Distribution: Complete list of σ for each player. Find the Shapley - Shubik Power Distribution in each of the following examples: Example 1: [5: 3, 2, 1]Power index. A numerical measure of an individual voter's ability to influence a decision the individual's voting power. Quota. The minimum number of votes necessary to pass a measure in a weighted voting system. Shapley-Shubik power index. The number of permutations of the voters in which a given voter is pivotal divided by the number of ...In what became known as the Shapley-Shubik index, the Shapley value became the default guide to analyzing all kinds of electoral situations. "He came up with a concept and proved mathematically that the voters in the medium-sized states have more power in the election of a president," Peter explains.

Advanced Math questions and answers. ☆ Consider the weighted voting system [15: 9, 6, 4). (a) Write down all the sequential coalitions, and in each sequential coalition identify the pivotal player. (b) Find the Shapley-Shubik power distribution of this weighted voting system. (a) Write down all the sequential coalitions, and in each ...

Question: Find the Shapley-Shubik power index for the weighted voting system [36: 20, 17, 15]. Find the Shapley-Shubik power index for the weighted voting system [36: 20, 17, 15]. Expert Answer. Who are the experts? Experts are tested by Chegg as specialists in their subject area. We reviewed their content and use your feedback to keep the ...The purpose of using the Shapley-Shubik index was to reduce the computational complexity compared to the approach proposed in the earlier papers.Elena Mielcová (2016) proposes the concept of the Shapley and Shubik index voting power under intuitionistic fuzzy sets. In the work , the Shapley and Shubik index is considered for the description of a voting game in parliamentary voting. A fuzzy coalition is a vector with coordinates called the membership degrees of a player in a coalition.Shubik and Shapley used the Shapley value to formulate the Shapley-Shubik power index in 1954 to measure the power of players in a voting game. Shubik's curriculum vitae lists over 20 books and 300 articles, with Shapley being his most frequent collaborator (14 articles). Nash also appears twice, including with Shapley and Mel Hausner on "So ...The Shapley-Skubik power index measures the power of a player in a weighted voting system.In this case, the weighted voting system is [10: 7, 5, 5], meaning player 1 has a weight of 10, and players 2 and 3 have weights of 7 and 5, respectively. To calculate the power index for player 1 using the Shapley-Shubik method, we consider all possible orders in which the players can vote.The Shapley-Shubik power index for these command games are collectively denoted by a power transit matrix Ρ. The authority distribution π is defined as the solution to the counterbalance equation π=πΡ. The basic idea for the counterbalance equation is that a person's power comes from his critical roles in others' command game; on the other ...Highlights • Application of the Shapley-Shubik index to determine the agents' strength in a dispersed decision-making system. • A new method for generating the local decisions within one cluster. ... This paper extends the traditional "pivoting" and "swing" schemes in the Shapley-Shubik (S-S) power index and the Banzhaf index to ...Any attempt to measure the power of a voting bloc in terms of the likelihood that it will be the swing voter, able to decide whether a proposition wins or loses. The first formal power index was proposed by Lionel Penrose in 1946 (although the idea was foreshadowed by the anti‐Federalist Luther Martin in 1787). The best‐known index is the Shapley-Shubik index.Shapley-Shubik Power Index, σ, (sigma): Ratio of how often a player is pivotal to the number of sequential coalitions , where T = total number of sequential coalitions . Shapley- Shubik Power Distribution: Complete list of σ for each player. Find the Shapley – Shubik Power Distribution in each of the following examples: Example 1: [5: 3, 2, 1]We show that the Shapley-Shubik power index on the domain of simple (voting) games can be uniquely characterized without the efficiency axiom. In our axiomatization, the efficiency is replaced by the following weaker requirement that we term the gain-loss axiom: any gain in power by a player implies a loss for someone else (the axiom does not ...

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Shapley - Folkmann lemma which settled the question of convexity of addition of sets (5) Shapley-Shubik power index for determining voting power. Moreover, stochastic games were first proposed by Shapley as early as 1953. Potential games which are extensively used by researchers these days were proposed by Shapley and Dov Monderer in 1996.A city council has 4 members in a weighted voting system (14 : 9,8,6, 4]. Compute the Shapley- Shubik power indices for each of the four council members. 2. Using your results from part (1), explain why the weights of the voters might be considered as deceptive in comparison to the power they hold, as indicated by the Shapley-Shubik index.args.legend = list(x = "top")) Calculating Banzhaf power index is more complex to implement in R in comparison to Shapley-Shubik power index but the code is faster. At the end of the code I plot comparison of both power indices. It is interesting to note that the results are very similar. Banzhaf power index slightly favors smaller ...This paper deals with the problem of calculating the Shapley-Shubik power index in weighted majority games. We propose an efficient Monte Carlo algorithm based on an implicit hierarchical structure of permutations of players. Our algorithm outputs a vector of power indices preserving the monotonicity, with respect to the voting weights. We show that our algorithm reduces the required number ...The Shapley-Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in the input and the output. The corresponding games are called (j, k) simple games. Here we present a new axiomatization for the Shapley-Shubik index for ...Voting is a fundamental aspect of democratic decision-making processes, but the distribution of power among individual voters can significantly impact the outcomes. To assess and quantify voting power, scholars have developed mathematical models and indices. In this article, we explore two influential measures: the Banzhaf Index and the Shapley-Shubik Index. These indices offer valuable ...Elena Mielcová (2016) proposes the concept of the Shapley and Shubik index voting power under intuitionistic fuzzy sets. In the work , the Shapley and Shubik index is considered for the description of a voting game in parliamentary voting. A fuzzy coalition is a vector with coordinates called the membership degrees of a player in a coalition.How to compute the Shapely-Shubik Power Distribution. Step 1– make a list of all possible sequential coalitions Step 2 –determine pivotal players. Step 3 --count the number of pivotal players. Step 4 –find the sigmas. Example 1. Let’s find the Shapley -Shubik power distribution of the weighted voting system [4:3,2,1] using the steps ... ….

The Shapley-Shubik index is used as the measure of centrality. The Shapley-Shubik index is shown to be efficient in a vertex cover game for the allocation of cameras in a transport network. Proceeding from the Shapley-Shubik indices calculated in this study, recommendations were given for the allocation of surveillance cameras in a ...Find the Shapley-Shubik power distribution for the system \([25: 17, 13, 11]\) This page titled 3.6: Exercises(Skills) is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman ( The OpenTextBookStore ) via source content that was edited to the style and standards of the LibreTexts platform; a detailed ...This is the case of the Shapley–Shubik power index (Shapley and Shubik, 1954) which has been applied to evaluate numerous situations, especially political and economic issues. The aim of this paper is to obtain both the extended Shapley–Shubik index for multi-criteria simple games, and axiomatization. Instead of defining the power index as ...This function computes Shapley - Shubik Power Index of a coalition. RDocumentation. Learn R. Search all packages and functions. GameTheory (version 2.7) Description. Usage Arguments. Details ... 0.370 0.148 0.156 0.141 0.0963 0.0667 0.0222 # Shapley-Shubik 0.533 0.133 0.133 0.133 0.0333 0.0333 0.0000 ...Shapley-Shubik is a natural choice when using an axiomatic approach. I will consider three axioms, Pareto Optimality, Equal Treatment Property,andMarginality,and show that the Shapley-Shubik index of power is the only power index that satisfies the three axioms simultaneously. 2. Voting Games and Power Indices Note that if this index reaches the value of 0, then it means that this player is a dummy. When the index reaches the value of 1, the player is a dictator. Author(s) Sebastian Cano-Berlanga <[email protected]> References. Shapley L, Shubik M (1954). "A Method for Evaluating the Distribution of Power in a Committee System."Consider the weighted voting system [16: 9, 8, 7]. (a) Write down all the sequential coalitions, and in each sequential coalition identify the pivotal player. (b) Find the Shapley-Shubik power distribution of this weighted voting system.Nonpermanent member has a Shapley-Shubik index of 2.44 billion/1.3 trillion or 0.19% Divide the rest of the 98% of power among 5 permanent members to get a Shapley-Shubik power index of 19.6% for a permanent member. Note that with large N's we need to use reasoning, approximation and computers rather than finding the power distribution by hand.III. Shapley-Shubik power index Shapley (1953) used three assumptions to develop “the value” an abstract measure of the value of playing a game such as buying a lottery ticket or influencing a Member of a Parliament. These games are a subset of … Shapley-shubik power index, the Banzhaf Power Index, we always write a coalition in numerical order. In the Shapley-Shubik Power Index, coalitions are formed differently. The order in which the players join a coalition is taken into consideration. For example, the coalitions <P 1, P 2, P 3> and <P 1, P 3, P 2> are not the same coalition. In the coalition <P 1, P 2, P 3> , P, I voted to close the other one instead. – user147263. Oct 8, 2014 at 6:06. You are correct, a dummy voter always has a power index of zero, both for Shapley-Shubik/Banzhaf. – Mike Earnest., Axiomatizations for the Shapley-Shubik power index for games… the title of the preface of Algaba et al. (2019) names it, the idea of the Shapley value is the root of a still ongoing research agenda. The remaining part of this paper is organized as follows. In Sect. 2 we introduce, Shapley-Shubik Power Index Calculator: The applet below is a calculator for the Shapley-Shubik Power Index. The instructions are built into the applet. The applet supplies six real world examples (Electoral College in the years 1990 and 2000, the UN Security Council, and the European Union in 1995, 2004, and 2007, with 15, 25, and 27 member countries, respectively) and provides means for ..., b. (2 points) Briefly explain in a few sentences what your answer to part (a) tells you about the practicality of using the Shapley-Shubik approach to measuring power, even with the aid of a computer. It's not very practical to use the Shapley-Shubik approach to measuring power because it would take too long when a lot of players are involved. With only 23 players it'll take a computer ..., The Shapley-Shubik power index has become widely known and applied in game theory and. political science.5 An unexpected practical turn was given to the problem of measuring voting power when the U.S. Supreme Court in the 1960s handed down a …, Banzhaf index: [0.6, 0.2, 0.2] Shapley-Shubik index: [0.6666666666666667, 0.16666666666666669, 0.16666666666666669] Plot results There's a possibility to plot the power distribution as a pie chart:, Mar 7, 2011 · Details. The Shapley–Shubik index of power of a player is the proportion of orderings of the players in which the given player is "pivotal". The pivotal player in a given ordering is the player whose vote(s), when added to the total of the votes of the previous players, result in enough votes to reach the quota and pass a measure. , In 1954, Shapley and Shubik [2] proposed the specialization of the Shapley value [3] to assess the a priori measure of the power of each player in a simple game. Since then, the Shapley–Shubik power index (S–S index) has become widely known as a mathematical tool for measuring the relative power of the players in a simple game., comparison of three power indices: the Shapley–Shubik, Banzhaf and newly defined Johnston power indices. We provide a huge class of voting games with abstention in ... and the Shapley and Banzhaf power indices considered in the paper are presented in Sect. 2. Section 3 is devoted to the definition and the axiomatization of the Johnston, We introduce the Shapley-Shubik power index notion when passing from ordinary simple games or ternary voting games with abstention to this wider class of voting systems. The pivotal role of players is analysed by means of several examples and an axiomatization in the spirit of Shapley and Dubey is given for the proposed power index., The literature is split on the usefulness of the Shapley-Shubik power index in computing voting power and the structure of corporate control in the ownership network [4, 6, 21,22], partly because ..., S and B denote the Shapley-Shubik index and the Banzhaf index, and the Owen index and the Banzhaf-Owen index if partition exist. J is used for obtaining the Jonhston index, CM determines the Colomer-Martinez index and JCM is used for obtaining the Jonhston-Colomer-Martinez index. partition. Numerical vector that indicates the …, The favorite power measure for many game theorists, especially if they have some mathematical inclination, is the Shapley-Shubik index (SS) which applies the Shapley value (Shapley 1953), a solution concept for cooperative games, to situations of weighted voting. Shapley and Shubik is the corresponding paper., The Shapley-Shubik power index 0 of a simple game (N, co) is defined as follows (Shapley and Shubik, 1954). Consider an ordering of N as representing the order in which the members of N will join a coalition in support of some bill. The, We provide a new axiomatization of the Shapley-Shubik and the Banzhaf power indices in the domain of simple superadditive games by means of transparent axioms. Only anonymity is shared with the former characterizations in the literature. The rest of the axioms are substituted by more transparent ones in terms of power in collective decision ..., Shapley-Shubik Power Definition (Pivotal Count) A player'spivotal countis the number of sequential coalitions in which he is the pivotal player. In the previous example, the pivotal counts are 4, 1, 1. Definition (Shapley-Shubik Power Index) TheShapley-Shubik power index (SSPI)for a player is that player's pivotal count divided by N!., The Shapley–Shubik power index (see Shapley, 1953; Shapley and Shubik,1954) assigns to each player \(i \in N\) the arithmetic mean of the contributions that a player makes to the coalitions previously formed by other players in the n! possible permutations of the players., THE SHAPLEY-SHUBIK POWER INDEX AND THE SUPREME COURT: A FEW EMPIRICAL NOTES Charles A. Johnson916 An article in this Journal recently argued that the Shapley-Shubik Power Index (hereafter SSPI) could be fruitfully used to study judicial behavior on the U.S. Supreme Court.1 In that article Saul Brenner reviewed and, Power Indices: Normalised Banzhaf index, Banzhaf index, Shapley-Shubik Indices, ... I have a data of thousands of companies (that means that in my SAS database I have thousands of rows) and each company has its capital structure . So I want to compute power indices of each shareholders in each company (e.g. Normalised Banzhaf index, Banzhaf ..., Downloadable (with restrictions)! The Coleman power of a collectivity to act (CPCA) is a popular statistic that reflects the ability of a committee to pass a proposal. Applying the Shapley value to that measure, we derive a new power index—the Coleman-Shapley index (CSI)—indicating each voter's contribution to the CPCA. The CSI is characterized by four axioms: anonymity, the null voter ..., The Banzhaf and Shapley-Shubik power indices were first introduced to measure the power of voters in a weighted voting system. Given a weighted voting system, the fixed point of such a system is found by continually reassigning each voter's weight with its power index until the system can no longer be changed by the operation. We characterize all fixed points under the Shapley-Shubik power ..., Shapley-Shubik Power (Chapter 2 Continued) Sequential coalitions – Factorial - Pivotal Player – Pivotal count - Shapley-Shubik Power Index (SSPI) – Ex 6 (LC): Given the following weighted voting system: [10: 5, 4, 3, 2, 1] a) How many Sequential Coalitions will there be? b) Which is the pivotal player in <P 1, P 2, P 3, P 4, P 5> ?, Shapley Shubik Power Index. the ratio of the number of times a player is pivotal to the total number of times all players are pivotal. Shapley Shubik Power Distribution. the complete list of Shapley Shubik power indices. factorial. multiplying a positive integer by each positive integer less than it (5! = 5x4x3x2x1), The Shapley-Shubik Power Index. Shapley-Shubik Power IndexList all permutations of all voters within a weighted voting system. Add weights of individual voters in each permutation, consecutively, from left to right., Find the Shapley-Shubik power distribution of the weighted voting system [13: 9, 4, 3, 2]. For your convenience, all the sequential coalitions are already written out; player in each., THE SHAPLEY-SHUBIK POWER INDEX AND THE SUPREME COURT: A FEW EMPIRICAL NOTES Charles A. Johnson916 An article in this Journal recently argued that the Shapley-Shubik Power Index (hereafter SSPI) could be fruitfully used to study judicial behavior on the U.S. Supreme Court.1 In that article Saul Brenner reviewed and, Compare it to the Banzhaf power distribution. Find the Shapley-Shubik power distribution for [34 : 11; 10; 9; 8; 7; 6; 5; 4; 3; 2; 1]. Compare it to the Banzhaf power distribution. In the electoral college, each state get a number of votes equal to its number of representatives plus its number of senators., シャープレイ＝シュービック投票力指数(シャープレイ＝シュービックとうひょうりょくしすう、Shapley–Shubik power index)は1954年にロイド・シャープレーとマーティン・シュービックによって考案された 、投票ゲームでのプレイヤーの投票力の分布を測る手法である。, Shapley LS (1962) Simple games: an outline of the descriptive theory. Behav Sci 7:59-66 Google Scholar; Shapley LS (1977) A comparison of power indices and a nonsymmetric generalization. P-5872. Rand Corporation, Santa Monica, CA Google Scholar; Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in a committee system., This paper presents new algorithms for computing the classical power indices, those of Shapley and Shubik (1954) and of Banzhaf (1963), which are essentially modifications of approximation methods ..., In a weighted voting system with three players the winning coalitions are {P1, P2} and {P1, P2, P3}. List the sequential coalitions and identify the pivotal player in each sequential coalition. Then, find the Shapley-Shubik power distribution of the weighted voting system. Im pretty sure these are the Coalitions: P1, P2, P3 P1, P3, P2 P2, P1 ..., Extending the Shapley-Shubik power index to networks, we propose a new measure and numerical method to calculate the indirect influence of investors on …