5.1.B. Equipotentiality vs. the Power Law

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5.1.B. Equipotentiality vs. the Power Law

One of the most interesting findings of social network analysis is the existence of a power law. A power law says that for any x increase in the number of links per node (or specific characteristic per node, such as acreage per square kilometer for a river basin), the number of nodes having that characteristic will decline by a fixed factor. In economics this gives us the famous Pareto principle, i.e. 20% of the people having 80% of the wealth. Or 20% of the books in a bookstore generating 80% of the sales or profits. But the power law is nearly everywhere, suggesting a natural form of concentration and even monopolization as almost inevitable. In fact, it seems that whenever we have many choices and many distributed agents making these choices, inequality of choice is created . It seems to be the natural result of any 'economy of attention'. But that is the point, such distribution is not forced, as in a oligopoly or monopoly, but arises naturally from the freedom of choice, and can be considered a 'fair' result, provided no coercion is used. Networks where such a power law operates are called 'scale-free', because at whatever scale, the same relation between variables (i.e. distribution pattern) applies.

In terms of a normative P2P ethos, it is important to note that it should not necessarily and systematically favor egalitarian networks. The Internet and the web are both aristocratic networks; the blogosphere is characterized by a power law distribution. The key questions are: 1) is the network efficient; 2) does it enable participation; 3) is the emergence of an aristocratic structure non-coercive and eventually reversible. Focusing on this reversibility is probably one of the tasks of peer governance. Granted that a power law may be in operation, that does not mean we must acquiesce in social processes that re-inforce such inequalities, but rather, that we then look for human and technical/algorhythmic solutions that renders the structure fluid enough so that it may be reversed if need be. But in many cases, we have to admit that some form of centralization, is necessary and efficient. We all prefer one standard for our operating systems for example.

The power law can possibly mitigated by the development of algorhythms, that can highlight important information and connections from nodes that may not come up 'naturally', but this discipline, though still in its infancy at the moment, is making rapid strides and is the core competence of new internet companies like Google, Technorati and others. But the power law is also counteracted by what some network economists have called the 'Long Tail'. This is the phenomena whereby minority groups are not excluded from the distribution of knowledge and exchange, and markets, but are on the contrary enable to organize micro-communities. In the market for cultural products, this has the effect of radically enhancing the supply and demand for products. Instead of the 80/20 distribution of products, i.e. 20% of the products being responsible for 80% of the sales and profits, we get something more akin to a 50/50 distribution. Online stores like Amazon and eBay are instrumentalising the phenomenon by using affinity matching schemes, which have resulted in the creation of many thousands of previously not existing mini-markets. Books, CD's and films which would be destroyed for lack of interest in the mass media system, now have a second and third and perhaps infinitely extendable lease of life, through the continued attention given to them by self-organizing minority interests, which can perpetuate across generations. This is an important guarantee for a vibrant cultural life, which does not destroy difference and cultural heterogeneity.

One of the keys to avoiding the power law may therefore be to keep sub-networks small. One of the recurring debates within cooperation studies indeed concerns a discussion on the optimal size of online groups. Dunbar, an anthropologist at the University College of London, has posited a link between brain size and our maximum number of close social ties , a claim supported by many animal, especially primate, and anthropological studies. He predicts that 147.8 is the "mean group size" for humans and this number has also been applied to online cooperation. But such a number would require a large time of social grooming so in reality it is much less. This discussion is important because other researchers, such as Valerie Krebs, have shown that in smaller groups, the power law does not operate and that they function as egalitarian networks . The key therefore is to organize online collaboration in such a way so that it is divided in appropriate subgroups, and this seems pretty much the way software peer production teams seem to operate.

There will be a lot to learn from this emergent field of cooperation studies , as it weanes us from wishful thinking into a more systematic understanding of what it takes to make cooperative projects work.

One of the most important works have been those of Axelrod, in his Evolution of Cooperation (Axelrod, 1984). He reconceived Game Theory, which had originally been seen as undermining altruism, by grounding the experiments in the real conditions of social life, instead of abstracting it in unrealistic laboratory or thought experiments. Game theory is important because it models human intentionality as it wavers between altruistic and selfish strategies. His study of the classic Prisoner's Dilemma has yielded three important rules for cooperation to occur : 1) communities must promote ongoing interaction; 2) individuals must be able to identify each other; 3) individuals must have information about the past behaviour of others. Many of these insights have been incorporated in the social software tools being developed, and are the reason of the success of reputation systems such as exists in eBay etc… According to the findings of Howard Rheingold and his cooperation studies group, the Prisoner's Dilemma game, which undermines cooperation and operates in an information-poor environment, may well be superseded by new forms of the Assurance Game . A Prisoner's Game will operate when no information about the partner is available, as distrust will prevail, but the social accounting technologies generate information about the trustworthy of a potential partner, and in such an environment, the Assurance Game will prevail.

Another important milestone in cooperation studies did not focus on interperson interaction (as does Game Theory) but on group behaviour in real physical communities involved in the use and management of communal resources. It can be found in Elinor Ostrom's Governing the Commons (Ostrom, 1990). Amongst the principles applied in successful communities are: 1) boundaries must be clearly defined so that there is a clear sense of who may use collective resources; 2) the rules of usage must match local conditions; 3) affected individuals must be able to participate in the adaptation of these rules; 4) control mechanisms of user behaviour must exist, as well as a system of graduated sanctions. Her survey concluded that this was done better through self-regulation than through external authorities; 5) finally, the community must have access to low-cost conflict resolution mechanisms.

It must be stressed however that her study about physical Commons dealing with scarce rival goods, cannot be applied without adaptation to the digital commons dealing witn non-rival goods, where a Tragedy of the Commons, i.e. an abuse of these scarce goods for personal gain, cannot occur, though some of her conclusions on group behaviour and its regulation do apply. But the totality of her conclusions are certainly of interest to defenders of our very important physical Commons and show that well regulated Commons have found ways to deal with abuse and overuse.

The shift in 'business models' characteristics of the new networks is explained by David Reed, who has summarized the different mathematical laws inherent in the value created by networks. First, we focus on the individuals. If a network has N-members and memberships grows, then one can see a linear growth in audience, i.e. N+1, N+2, etc.. i.e. a proportional growth in value. This formula was already at play in broadcast media and in such an environment, 'content is king', and publishers vie for the attention of the users of the network. This explains the role of portal sites such as Yahoo, who re-intermediate the economy of attention that we discussed before. If we now focus on the 'interaction between individuals', we see that the network enables transactions, but that these grow by a 'square value'. This characteristic is called Metcalfe's Law. A network of 2 allows for 2 transactions (back and forth buying and selling), a network of 3 allows for 8 transactions, a network of 4 allows for 16 transactions. This aspect of the network creates transactional platforms such as eBay. Finally, we focus on community. Networks have the ability to enable the formation of subgroups, they are 'Group Forming Networks'. But value growth here is 'exponential'. It is this characteristic that is called Reed's Law . Every affinity group creates and 'consumes' its own content, and it is here that the true peer to peer processes emerge, characterized by infinite content creation . The economy of attention becomes moot, because what is happening is not limited content competing for the same audience, but infinite content competing for infinite combinations of affinity groups. You are then creating content, not for an audience, but as a means of creating interconnectedness between a group of people sharing an interest or common goal.

To conclude: the discovery of the theory of networks in the physical sphere, has therefore a corollary in seeing it in social life, and in particular, in the area of organizational life, including business. The finds its expression in the emerging discipline of social network analysis and cooperation studies generally, and also the business process applied "coordination theory", as pioneered by Thomas Malone . All these studies are important because they act as a corrective to misplaced idealism and provide lessons from scientific studies and objective experience with true cooperation.