Wednesday, August 20, 2008

The Power Law

The power law refers to polynomial relationships where scale invariance is evident. It involves the projected relationship between the magnitude of a physical stimulus and its perceived intensity. The power law is evident in social structures. In order to understand power laws in social structures, it is vital to determine the virtual location of a person within a social network by analysing its connections and relationships with surrounding entities. The two social network measures for this kind of analysis are known as ‘betweeness’ and ‘closeness’. It predominantly discloses the nodes beneficial or constrained location in a particular network. Both these measures are dependent upon the nodes existence within the fixed connection patterns involved in the network.

Betweeness is the measurement of a node’s control over what flows in the network, and closeness refers to the measurement of a node’s accessibility to available information via a network. When a node adopts higher levels of control and accessibility through its connections, they begin to gain the power to control other nodes within the network. There are networks with centralised power such as hierarchy and hub-and-spoke structures. This often consists of a collection of nodes with a vast amount of connections, and others with fewer connections. These types of network structures demonstrate the notion of unequal distribution of power. It is important to note that the distribution of power increases as the disconnection nodes begin to interact and connect with the other nodes in the network. This reflects the idea that diversity and freedom of choice tends to generate inequality; therefore the greater the diversity, the greater the extremity of inequality.

There are networks where individuals have the freedom to choose between various options. These types of systems promote uneven power law distributions where a small portion of the system experience an inequitable amount of traffic compared to other individuals involved in the system. This is not a reflection of moral weakness, selling out, or any other psychological explanation. Power law distribution is a result of the very act of freedom and choice. Freedom of choice has the potential to create unequal distributions. Because the curve is so heavily weighted towards the top performers, most elements in a power law system are below average (refer to diagram A for an illustration of a ‘Power Law Curve’). Despite the size of any network, freedom and diversity has the potential to create power law distributions.

Diagram A – Power Law Curve

Through Alberto-Laszlo Barabasi, Duncan Watts and Bernardo Huberband network theories, we recognise that power law distributions are inclined to take place in social systems where people have the freedom to express their preferences amongst a set of options. The theory proposes that the more preferential attachments and connections a node obtains, the higher their connectivity rate will become. The initial connectivity difference between two nodes may further increase as a network expands in size, therefore the longer the node exists in a network the higher their connectivity rate will be in comparison to the younger nodes of the network. This concept reflects a ‘rich-get-rich’ or the ‘winner-takes-all’ phenomenon. Vilfredo Pareto is an Economist that made the observations that wealth follows a “predictable imbalance”, with 20 percent of the population holding 80 percent of the wealth. In the last century, investigators have discovered power law distributions in human systems.



References:


Department of Physics, University of Notre Dame (2000).
Power-Law Distribution of the World Wide Web. SCIENCE (vol. 287)

Valdis Krebs (2004), Power in Networks

From
http://www.orgnet.com


Clay Shirky (2003),
Power Laws, Weblogs and Inequality,
From
http://www.shirky.com/writings/powerlaw_weblog.html

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