Institutional Stars: Gravity and Network Externalities
Mauricio Zachrisson Girón
We are just an advanced breed of monkeys on a minor planet of a very average star. But we can understand the Universe. That makes us something very special.
-Stephen Hawking
The study of stars and institutions are the greatest marvels of the human intellect. Both have existed for a long time, and it hasn’t been until recently that they have become of importance for understanding this complex world. A number of stars and institutions have been born and perished into oblivion, before we could even think of grasping our attention to them. Is there something in common between these two wonders that could help us understand them better? There seems to be one force that governs the formation and life of both, and it may be in different ways, but the very essence of this force can give us an insight on how institutions are born, how they grow, or simply disappear. This powerful force is called gravity. It explains why mass attracts mass, and it may give us an important understanding of how people can attract people.
Defining what institutions are is a great challenge, since they are abstract and new in the semantics area, but there have been some pioneers who have given a very precise definition, including the Nobel Prize winner Douglas North. According to North, “institutions are the humanly devised constraints that structure political, economic and social interaction.” He adds that institutions can either be, “informal constraints (sanctions, taboos, customs, traditions, and codes of conduct), [or] formal rules (constitutions, laws, property rights).”1 This essay will consist of informal institutions, which I define as social mechanisms of cooperation that govern the behavior of a group of individuals and are not enforced by an authority. As North puts it, these can vary from codes of conduct to customs and traditions2. For an institution to exist, it has to provide a benefit for those participating that cover the costs. There are different benefits, some varying from institution to institution, but there is one that prevails in all of them, and it is that they create network externalities.
Robert Melancton Metcalfe, the creator of the Ethernet, was the person who established the term network externality, which was originally called the network effect. Metcalfe believed that the value of a network depends on the number of people in it. The more people used a certain network, the more possible connections existed for an individual, which increases its value. This is what is now called Metcalfe’s Law. For example, if only two people used the telephone for communication, there would only be two possible connections, but if there were five people using the telephone, there would be twenty possible connections. Therefore the value of the telephone network is proportional to the number of nodes made possible by the number of phone users. The number of nodes is equal to
An example is the institution of money, and in this case gold. This institution gives the benefit of means of exchange between numerous individuals. The value of gold as a mean of exchange depends on the number of people who use gold for this purpose. Suppose there are only ten people using gold, there would be 90 nodes, which are 90 different potential ways of exchange between the groups of people that use gold. Now, if an additional individual started to use gold with the same purpose, he would increase the value of the institution by 20, and if another individual was incorporated into the institution he would bring its value up to 132. That is a relatively low value for the institution at the time compared to what it could have been in 1971. Suppose that before the gold standard was eradicated by Richard Nixon, approximately 2 billion people (53.45% of the 1971 population4) used it as means of exchange, this indicates that the value of the institution, using Metcalfe’s Law, was 
Now suppose there are two different institutions of money, gold standard and silver standard, and it is the year 1971, just before Nixon eliminated the gold standard. Both goods have the same characteristics as money; they are equally homogeneous, divisible, durable and fungible. Now suppose there were only 10 people using silver as means of exchange, while there were 2 billion for gold. What would be more attractive to the marginal individual, to use silver or gold as means of exchange? An institutional value of
Institutions therefore have what I call a Force of Institutional Gravitation (FIG). The FIG of an institution is generated due to its network externalities, and since its network externalities depend on the institutional mass, so does the FIG. A greater institutional mass leads to a greater FIG. The institutional mass has its limitations, which depend on many things, including the kind of institution. Suppose there is an island off the coast of Asia, and due to its political situation it is practically impossible for its people to get out of, and also for outsiders to join the island. The people in this island over the centuries developed, in a spontaneous way, a code of conduct called Bushidō. What is the growth limit for this institution? In this case the limitation is merely geographical, since there are no possibilities for more people to join the institution beside the individuals in the island. Geography is just one possible limitation, although it isn’t necessarily always the case. Other limitations may include sex, ethnicity, age, socioeconomic status, language, etc. The potential members of an institution (the number of people who are able to join it) are what I will now call the social nebula. A nebula is a cloud of dust and gases, where, due to the gravitational forces of the masses, stars are born. In the same way, social nebulas are a cloud of potential members where institutional stars are born, and just like in a stellar nebula, there are different kinds of institutional stars that may emerge. The formation of these different institutional stars depends on their FIG. Before getting into the different institutional stars, it will be of a great help to see what exactly determines the force of institutional gravitation.
It has already been said that the FIG depends on the network externalities created by the institutional mass, but only in a Metcalfean way. Another great contributor to the study of network externalities has been David P. Reed. This MIT computer scientist developed what he called Group-Formation Networks (GFN). According to Reed, the value of a network grows at a faster pace than what Metcalfe proposes. Instead of deriving the value of a network according to the possible nodes, he believes it depends on the potential sub-groups that can be created in a network. As Reed puts it, “a GFN has functionality that directly enables and supports affiliations (such as interest groups, clubs, meetings, communities) among subsets of its customers.”5 In institutional terms, a GFN enables the possibility of the creation of multiple groups within the institution.
Taking the institution of language can give a clear view of the power of Group-Formation Networks. When the number of people speaking a same language increases, the possibilities of sub-group creation also increase. As Silvana Dalmazzone puts it, “knowing a widely spoken language enables the individual to communicate with a larger number of persons and widens the set of possible interactions (employment, investment and trade opportunities, exchange of information, cultural activities, etc.) available to them.”6 Dalmazzone has clearly laid out some of the possible sub-groups that may emerge from this institution. The number of sub-groups in a network is equal to
Consider a phone that can call only 911. A customer for such a phone buys it because of a low probability future need to call for emergency help; in fact, the customer probably takes other steps never to need to use the phone. But the existence of a lucrative market for such phones indicates that customers can value potential connectivity to a single point, even though the connection is never used. Potential connectivity to many points should have value proportionally larger, since it is not necessary to use the connection to find value in its availability.
Now that the basic concepts of network externalities and institutions have been set, it is possible to propose a model for the Force of Institutional Gravitation. This force is what attracts the individuals in the social nebulas that are not involved in the institution to participate in it. Therefore, since the number of nodes (Metcalfe’s Law) and the number of sub-groups (Reed’s Law) is what creates the network externalities in an institutional star, and the force affects the non-participants in the social nebula, the equation for the FIG will be like so:
As
Figure 1
The higher the percentage of participating individuals, the higher the force of institutional gravitation will be on the non-participating. Following Reed’s interpretation of the GFN, the FIG depends on the potential nodes and sub-groups, not the existing, which does not mean it will be weaker. It is worth noting that the force of institutional gravitation, contrary to the force of stellar gravity, does not imply that individuals will necessarily incorporate themselves in the institution, since the FIG simply exposes the benefits of the participation, not the costs. Assuming that individuals make their choices based on a cost/benefit analysis, it may be possible that even if the FIG is large, it may not have the consequence of additional incorporation of non-participants, due to bigger costs than benefits. The costs of incorporation are normally opportunity costs, the sacrificing of others things to be part of the institution.
There is still some information left out of this equation. The FIG does not only depend on Metcalfe’s and Reed’s Law, but it also depends on variables that are exogenous to the network externalities effects. Bringing back the gold and silver example, one important assumption was that both institutions had the same characteristics (money wise), but this is not necessary true. It has been proven through the workings of the markets throughout history that gold has proven itself to have better characteristics of money than silver, and these kinds of differences can be found in every institution. A constant needs to multiply the network externalities effects in able not to make the mistake of excluding these exogenous variables. The equation is now
being the sum of the exogenous variables that have an effect on the FIG.
In the example, the institution of gold as means of exchange will have a higher than silver. Assuming that both gold and silver belong to the same social nebula and have the same number of participating individuals, gold will have a higher force of institutional gravitation of the non-participating than silver. For the sake of the argument and noticing only the effect of Metcalfe’s Law and Reed’s Law on the FIG, we will assume a ceteris paribus condition, and will be the same for every institution in a common social nebula.
There is still another characteristic that stars and institutions share, and this is what some astronomers, including Hideyuki Kamaya, call critical mass. Before a molecular cloud (the beginning of star formation) reaches a certain level of mass, called critical mass, its marginal gravity due to additional particles will not be as strong as after it has reached this mass level. Institutions also have a critical mass. The critical level of institutional mass varies among institutions, mostly due to the size of the social nebula it belongs to. What distinguishes this phenomenon is that below the critical mass, there are no increasing marginal returns, and when it is reached, the increasing marginal returns begin. This fits perfectly into the FIG model.
Its first derivative is always positive, but it decreases until it reaches a certain level, and then starts increasing (See Figure 2). As said before, the critical institutional mass level varies, but it is always relatively small.
Critical Mass Level Figure 2
We now have a clear view of what the force of institutional gravitation depends on and its tendency, and we can analyze the different institutional stars that can be formed in the social nebula. All stars start in the same way, but gradually turn into different kinds. The most interesting resulting of a star, in my opinion, are black holes. Stephen Hawking, in his book A Brief History of Time, gives an excellent description of what black holes are. These are concentration of masses, which are so intense that their gravity is incredibly strong. Due to this immense force, any particle, gas and even light, in its proximity is attracted to the huge mass, with no possibility of escape.8 Another kind of star is the white dwarf. These stars are masses that have existed for a relatively long time, and due to their low mass level, are very unstable. These stars can be absorbed by a larger and more stable mass when it comes to their proximity. The last case to be analyzed is when a star ends due to gravitational collapse. This kind of collapse is a consequence of the inability of the mass to maintain itself, and therefore collapses due to its own gravity. As we shall see, there are institutions that share the same characteristics with the stars described above.
The institutional black holes are those that, due to their high level of institutional mass, have a FIG so powerful that every individual in the social nebula will be attracted to it, with no possibility of getting out. The prisoner’s code that existed in many prisons in the United States during the twentieth century is an example of an institutional black hole. Every prisoner followed this unwritten code, which governed their behavior in many ways, including the relationships with the guards, the management of the information about possible escapes, the sexual relationships between inmates, etc.9 Any prisoner who disobeyed the prisoner’s code was punished by his fellow inmates in many ways. When new prisoners arrived, or fish as they called them, they were immediately drawn to the institution, with no possibility of getting out due to the high costs of doing so. The participants were all of the potential members in the social nebula, so
This fits perfectly in the description of the black hole, since any particle (individual) in its proximity (social nebula) was attracted with the greatest possible force to the mass (institutional star).
The institutional white dwarfs are another type of institutional stars that may exist in a social nebula. These institutions, just as stellar white dwarfs, are those that have existed for a long time, and due to their relatively low institutional mass, the individuals in them may be attracted to a bigger institutional star with a greater FIG in its presence. A great example of this institution is the measurement of time in Japan. Before the sixteenth century, Japan had lived in what was called Sakoku, a period in which Japan was isolated from the rest of the world. During this period, the Japanese used to measure time in a different way than how must of us do in the twenty-first century. Their measurement consisted on dividing the day into six equal units of time, and the night in another six10. The institution of measurement of time in Japan had worked well within its geographically limited social nebula. In 1550 the Portuguese Jesuit Francis Xavier introduced the mechanical clock in Japan, which consisted of the occidental measurement of time in hours, minutes and seconds. At first the new institution was rejected due to the fact that the FIG of the old institution of measurement was strong. After a few years, when the period of Sakoku ended, the Japanese social nebula was incorporated to a larger, international social nebula, increasing
Both institutions (Japanese measurement of time and occidental measurement of time) now shared the same social nebula,
Using the FIG equation can be a good illustration of the effect caused by a strong institutional star on an institutional white dwarf. The occidental measurement of time will be institution 
Before Japan opened its frontiers, these two forces did not interfered with each other, since they belonged to separate social nebular. As mentioned before, alter the end of the Sakoku period; the Japanese social nebula became part of the occidental one, which resulted in a new social nebula that consisted of 
Now that both institutions belong to the same social nebula, their forces do interfere with each other, and since institution 
The last case of institutional star to analyze is the gravitational collapse of an institutional star. This idea can be easily illustrated with an institution that prevailed in societies such as New Guinea and the Caraïbes in the Caribbean islands. This was the institution of cannibalism, which purpose was to acquire the wisdom of the dead by eating parts of them. In the case of New Guinea, there was a virus called Kuru that was transmitted by indigestion of the brains, and if it weren’t for the Australian establishment in 1959 that prohibited cannibalism, the society would have collapsed.11 In other cases, such as in the Caraïbes, cannibalism was a well-practiced custom among the living. This lead to a decrease in the number of active participants as the amount of new participants grew. The more people began to practice cannibalism, the more people from the institution died. In some cases, this would have lead to a constant decrease in
When this happened, the FIG of the cannibalism institution fell to zero as well, this would have ended the institution, as well as its members. The case of this custom is similar to the stars that collapse due to their gravity; the institution could not support a strong gravity, and collapse due to it.
Network externalities are not only an important tool for analyzing technology and networks, but also give an insight on how institutions are formed. This effect creates large benefits for the incorporation of an additional individual for both the active participants, and the marginal. The analogy with the different stars takes the analysis further and gives a better understanding of why some institutions include large proportions of societies and last so long while others perish under the presence of other institutions. I am sure there are many more institutional stars in the mysterious universe of human kind, and of various types. Some may be black holes or white dwarfs, others maybe even institutional galaxies or supernovas. Science and the human mind are far from understanding the stars and institutions in a complete way. Astronomy however, has given us another useful tool for the comprehension of how institutions work. The stars for hundreds of years were used by sailors as their guides, and led them to great adventures and discoveries. Similarly, institutions are our compass, guiding us to new discoveries through this great adventure called life.
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1 North, Douglass C. Institutions. Journal of Economic Perspectives. Volume 5, Number 1. Winter 1991. Page 97.
2 For the sake of the argument, I will refer to informal institutions generally as institutions.
3
4 For more data on the 1971 population go to http://www.nationmaster.com/graph/peo_pop-people-population&date=1971
5 Reed, David P. The Sneaky Exponential: Beyond Metcalfe’s Law to the Power of Community Building. http://www.reed.com/Papers/GFN/reedslaw.html. 1999.
6 Dalmazzone, Silvana. The Economics of Language: A Network Externalities Approach. Department of Enviromental Economics. University of York, United Kingdom. 2000.
7 Reed, David P. The Sneaky Exponential: Beyond Metcalfe’s Law to the Power of Community Building. http://www.reed.com/Papers/GFN/reedslaw.html. 1999.
8 This is still a controversial issue, since some astronomers believe that mass attracted to a black hole may escape through other means, but for the sake of the argument lets assume this is impossible.
9 Caldwell, Morris G. Group Dynamics in the Prison Community. The Journal of Criminal Law, Criminology, and Police Science. Vol. 46, No.5. (Jan. – Feb., 1956), pp. 648 – 657.
10 Cipolla, Carlos M. Clocks and Culture 1300-1700. W.W. Norton & Company, Inc. 2003.pp 106.
11 Diamond, Jared. Guns, Germs and Steel: The fates of human societies. Norton Paperback. 1999.
