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Erschienen in:
A Probabilistic Model for Detecting Gerrymandering in Partially-Contested Multiparty Elections Kapitel lesen Erstes Kapitel lesen

2019 | OriginalPaper | Buchkapitel

Power in Networks: A PGI Analysis of Krackhardt’s Kite Network

verfasst von : Manfred J. Holler, Florian Rupp

Erschienen in: Transactions on Computational Collective Intelligence XXXIV

Verlag: Springer Berlin Heidelberg

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Abstract

This paper applies power index analysis to the well-known Krackhardt’s kite social network by imposing a weighted voting game on the given network structure. It compares the results of this analysis, derived by applying the Public Good Index and the Public Value, with the outcome of employing the centrality concepts - degree centrality, closeness centrality, and betweenness centrality - that we find in Krackhardt (1990), and eigenvector centrality. The conclusion is that traditional centrality measures are rather a first approximation for evaluating the power in a network as they considerably abstract from decision making and thereby of possible coalitions and actions. Power index analysis takes care of decision making, however, in the rather abstract (a priori) form of the potential of forming coalitions.

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Vorheriges Kapitel A Probabilistic Model for Detecting Gerrymandering in Partially-Contested Multiparty Elections
Nächstes Kapitel Orders of Criticality in Graph Connection Games
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Fußnoten
1
Krackhardt refers to Freeman (1979) for definition and discussion of these concepts. E.g., degree centrality is defined as the number of links connected to the person. Closeness centrality is defined as the inverse of the average path distance between the actor and all others in the network. The definition of betweenness centrality needs a formal apparatus which will not be given here (see, e.g., Krackhardt 1990). See Sect. 4 of our paper.
 
2
For a recent discussion of the PGI, see Holler (2019).
 
3
Think about a committee that decides about hiring a professor to the department. Nodes A to G represent the tight sub-network of incumbent professors, H, I and J are the representatives of the President of the University – also representing the bureaucratic personnel -, the assistants, and the students, respectively.
 
4
Fragnelli (2013) analyzes a weighted voting game with network structure applying the Banzhaf (power) index.
 
5
In general, parliaments do not change their majority rules if links between parties have increased or decreased, and, in the extreme, a party became unconnected to any other like going from Γ and Γ1.
 
6
For example, Aumann and Myerson (1988) identify links with players in the by now classical paper by Myerson (1977). However, links do not have preferences and do not gain payoffs.
 
7
For his analysis of the kite network Krackhardt applied degree centrality, closeness centrality, betweenness centrality only. His argument not to consider measures based on eigenvector centrality is that they “aimed more at the concept of asymmetric status hierarchy, or “being at the top”, than they are at the idea of “being at the center”, which is the idea behind the graph-theoretic measures used here” Krackhardt (1990: 351).
 
8
Krackhardt (1990) did not consider decision making. He focused on the cognitive problem of what network members know about the network and about other members of a network. Degree centrality, closeness centrality, and betweenness centrality might be reasonable instrument to evaluate one’s network position and the positions of the others – in fact, to recognize a network. “The central point” in his paper, however, is: “Cognitive accuracy of the informal network is, in and of itself, a base of power” (Krackhardt 1990: 343). The power index analysis dealt primarily with the formal structure, however, the links between the various nodes could be highly informal.
 
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Metadaten
Titel
Power in Networks: A PGI Analysis of Krackhardt’s Kite Network
verfasst von
Manfred J. Holler
Florian Rupp
Copyright-Jahr
2019
Verlag
Springer Berlin Heidelberg
Buch
Transactions on Computational Collective Intelligence XXXIV

Print ISBN: 978-3-662-60554-7

Electronic ISBN: 978-3-662-60555-4

Copyright-Jahr: 2019

DOI
https://doi.org/10.1007/978-3-662-60555-4_2

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