In the third stage of descriptive theory building, correlations and associations are made explicit and models developed to account for the differences between the categorised data and the outcomes of interest. In this process of anomaly identification, ‘normal science’ proceeds to push the current paradigm to its limits (Kuhn, 1962). In this thesis the outcome of interest is the extent to which male and female patterns of organization in mixed gender networks are similar or different and whether women- only and random networks differ from mixed gender networks. This thesis therefore tests current WOB paradigms by incorporating network concepts from other disciplines into WOB theorising.
The list below is a preliminary statement of Glass Network theory, derived from the initial description and categorisation of gendered director networks and is the starting point for the empirical investigation that follows.
102 a. Glass Network theory is a general and inclusive theory equally applicable to male and female directors. It can be extended to include directors categorised by other attributes such as race or ethnicity.
b. Directors are changeable entities in a director network, which accommodates a flow of directors through the network while maintaining a stable structure. Director networks show high levels of director turnover. The turnover of women directors in mixed gender networks is unknown.
The organising principle is a power law, namely, the rule of the critical few and trivial many. The effect of this law may be observed in global and national networks, as well as gendered and random director networks. Power laws have already been observed in some measures of director networks, such as degree and betweenness and it is likely that more instances will be found. Director network data as a consequence does not follow normal distributions. In this thesis a close approximation of the underlying power laws can be derived by fitting trend lines to the director network data.
c. The underlying equations describing the trend lines will show variations in different segments of director networks at different times, particularly where local legislation and other social factors influence the network, that is, these are organic networks adapting to environmental conditions such as governance and affirmative action pressures.
d. The power laws vary within a set range. Predictive range limits can be set using a characteristic of power laws, which produces a straight line on a graph when the data is transformed by logarithms on both axes. This permits a comparative methodology whereby the equation for this straight line can be determined, allowing different networks at different times to be compared. These can be used to compare networks on multiple measures, in this thesis, component size, seat spreads, degree and betweenness. Glass Network theory predicts that most director networks will fall between the ranges for these networks measures.
103 e. Gendered director networks are small-world networks as they show high
clustering and short path lengths. The derived SW quotient will be greater than 1 and related to network size. Director networks show low density but high reach as a result.
f. Gendered director networks are a form of scale-free network as they are driven by power laws and show self-similarity, irrespective of categorisation. As the number of multiple seats held by a director is limited, the scale free nature of director networks is truncated. Individual merit and ability is irrelevant at the network level. Gender differences are likewise irrelevant, as male and female director networks are similar in function and structure, in proportion to their presence in the network. This is also likely to be true of other director attributes such as ethnicity. This property is also illustrated in networks created by the allocation of random attributes. This explains the finding that degree and betweenness follow a power law in director networks because these are measures derived from seat spreads, which will also be shown to follow a power law.
g. The structure in director networks is, in complex network terminology, an emergent structure whose organization is the result of many seemingly random and unrelated director selection processes. The underlying power laws are the result of innumerable selection decisions that are driven by ‘shoulder tapping’ or inviting peers to join other boards, and by connector directors with multiple seats, ‘cherry picking’ the less risky and more prestigious board seats.
h. One mechanism that drives the creation of scale-free networks is ‘preferential attachment’, where new nodes have a preference to attach to nodes that already have edges. This mechanism is also a driver in director networks, where recruiting boards prefer directors who are like them and who already have board appointments. Two forms of this are known. Firstly, ‘homophily’ or preference for the similar, whether by gender, ethnicity or other social factor, leading to the creation of ‘old boy’ groupings. Secondly, ‘assortativity’ or the preference for
104 directors of the same ‘degree’ or number of links to other directors. Gendered director networks as a consequence will also be positively assortative. Gender preference and assortativity interact determining the gendered structure of director networks.
i. Power laws determine the component structure of director networks. If the largest connected component is included or excluded, the ranking of the components by size, or number of directors in each component, also follows a power law. A frequency distribution by component size will show a right-tailed distribution of components. Average board size is related to the size of the components.
j. The metaphor of the glass ceiling is incorrect, the metaphor of a glass network is more appropriate for gendered director networks as some women are found in all director networks. A small proportion of diversity, approximately following the Pareto ratio of 80/20, is found in all director networks. Its role is to permit the adaptation of the network as environmental circumstances change, perpetuating the network (Andriani & Passionate, 2004). This accounts for the presence of 5- 15% of women in director networks where no affirmative action has taken place. In a stable director network only a few women will have board appointments, but those women who do become connector directors in the network will have the same network structures as male connector directors.
k. A characteristic of power laws is the ‘rich get richer’ effect, also known as the Matthew effect, Zipf’s law or ‘accumulated advantage’. This explains why a few directors get more board appointments than their peers, becoming connector directors, with a few of these directors becoming trophy and super-trophy directors (Branson, 2007a). This effect is also the result of certain directors possessing enablers that allow them through a filter or ‘glass net’, despite barriers such as race or gender. These may be family connections, celebrity status or another attribute that creates an advantage over equally well qualified and experienced peers.
105 The metaphor of a glass net is also used to describe the filtering rule or underlying power law that permits a few directors to become connector directors in a local network, a smaller number to become the linking directors in a national network and finally a select few to become the connector directors in a global director network. Women directors are subject to the same power law effects and also become connector directors, in proportion to their presence in mixed gender director networks.
l. Power laws create the illusion of glass nets which determine the seat spreads that have regularly been observed in director networks. A theoretical model is presented, based on a non-symmetrical generating function that derives the numbers of male and female directors at each level in the seat spread. This is a good fit with actual seat spreads, especially in networks where there has been little governance or affirmative action pressure. Gendered networks where women constitute a big enough grouping in the network, will also conform well to this model. This generating function will also permit a ‘world of gender equity’ to be modelled, allowing seat spreads to be predicted if a gender quota is imposed on a network.
m. Director networks are embedded in companies that have physical locations. As city size and company size follow a power law, so do director networks through component size and seat spreads. These are likely to be related phenomena, but the nature of this relationship is unknown. It may be a function of larger companies with larger boards being found in larger cities.
n. Finally, Glass Network theory accounts for three findings in the WOB literature, namely the ‘glass cliff’ phenomenon, the ‘queen bee’ syndrome and the positive correlation of performance and board diversity.
i. Boards prefer women directors in time of financial crisis. As there are few board positions for women available and competition for these is high, aspiring women directors choose to accept risky board positions to get
106 board experience or become connector directors and increase the likelihood of further board appointments.
ii. Connector directors of both genders display different behaviour patterns to single seat directors. Being a chairman enhances this behaviour. In female directors these behaviours are seen as violating the norms of feminine behaviour and are couched in derogatory terms as the ‘queen bee’ syndrome, whereas these are normative behaviours associated with male leadership.
iii. Larger companies tend to be found in the largest component because these companies may have larger boards with more connector directors of similar degree. These companies are financially more successful. Larger companies tend to have a token woman director and a critical few appoint more than one. More women directors are therefore found in the largest component of a director network and the presence of women directors correlates positively with financial performance.