We demonstrate that the commonly held conceptualization of the Friendship Paradox in a network results in a further paradox. We resolve this new paradox and make four primary contributions. First, we demonstrate that the friendship paradox is double-edged, exhibiting both local and global characteristics, each calculating a different mean number of friends of friends. Second, we prove the local mean is greater than or equal to the mean degree for any and all network structures. Third, we provide two distinct intervention strategies, a local strategy that takes advantage of the local mean and a global strategy that takes advantage of the global mean. Fourth, we develop a new network property, inversity, and demonstrate how the local and global means are formally related through this property. We also demonstrate how inversity allows us to determine whether a local or global strategy will be more effective in any given network. Finally, using a set of classic, real networks, we illustrate the implications for dramatic improvements in network interventions.
David Krackhardt is Professor of Organizations at the Heinz School of Public Policy and Management and the Graduate School of Industrial Administration, Carnegie Mellon University. Prior appointments include faculty positions at Cornell's Graduate School of Management, the University of Chicago's Graduate School of Business, INSEAD (France) and the Harvard Business School. He received a BS degree from the Massachusetts Institute of Technology and a PhD from the University of California, Irvine.
Over the past 15 years, his research has focused on how the theoretical insights and methodological innovations of network analysis can enhance our understanding of how organizations function. He pioneered the concept of "cognitive social structures", wherein individuals provide their perceptions of the entire network in which they are embedded. He empirically has related these perceived structures to turnover, reputations and power in organizations. Another interest of his has been in developing methodologies for better understanding networks and their implications. His contributions in this arena include adapting the quadratic assignment procedure to multiple regression analyses of network data. In addition, he has developed methods drawing from graph theory for studying the shape and structure of organizations as a whole.
His published works have appeared in a variety of journals in the fields of psychology, sociology, anthropology and management. His current research agenda includes developing models of diffusion of controversial innovations, exploring and testing visual representations of networks, identifying effective leverage points for organizational change, and exploring the roles of Simmelian (super-strong) ties in organizations. Prof. Krackhardt was born in 1950 in Massachusetts. He is married with three children.
