[[Note for bibliographic reference: Melberg, Hans O. (1998), Searching for the surprising and reliable truths: A review of Schelling, www.geocities.com/hmelberg/papers/980618.htm]
“…Close to my where I live there is a sub-way and when it arrives people simply cross the road without regard for the traffic. However, when people do not come in groups from the sub-way, they often wait before they dare cross the road. This suggests that there is a “critical mass” that is needed before the pedestrians dare to stop the traffic. The “critical mass” model can be used to describe a number of other phenomena. Of course, an atomic explosion fits a critical mass model (there has to be enough uranium so that the neutron released as a result of radioactivity decay, collides to produce more than one new neutron). Similarly smoking in non-smoking sections can be a critical mass phenomenon; One lone smoker breaking the rules may not be enough to induce the other smokers, but if many people smoke in the non-smoking section most smokers will probably disregard the rules. Lastly, a demonstration against an authoritarian government is a critical mass event. One demonstrator is not going to topple the government, a large number of demonstrators may. In all these examples there is a non-linearity. The event is “switched” on at some point, not gradually.
Two sub-models under the general class of “critical mass” are lemon models and tipping models. Lemon models exist when one person known more than the other, and as a result the market may either fail to exist of be inefficient in aggregate. Examples include the market for used cars, insurance and bank-loans. Tipping models describe, roughly, a situation in which people will do something if their neighbor also does the same think. Examples include people who are willing to stay in a neighborhood only if they expect that a certain percentage of people of the same ethnic background there; people who will join a demonstration only if enough other people do; or people who will only learn a new language if they think other people also will do so (David D. Laitin has written a book in which this kind of language tipping model is central to predict whether the Russians in Kazakhstan and Lativa will start to speak the native language or continue to speak Russian. See Identity in Formation, Columbia University Press, 1998)….”
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[Note for bibliographic reference: Melberg, Hans O. (1998), Searching for surprising and reliable truths: A review of Schelling, www.geocities.com/hmelberg/papers/980618.htm]
Searching for surprising and reliable truths
A review of Schelling
by Hans O. Melberg
Introduction
A good argument should be non-obvious, important, and reliable. If the author also writes well and provides many examples, we are close to a perfect book. Thomas Schelling's Micromotives and Macrobehaviour approaches this ideal.
Schelling's main idea is that to explain macro-features of society we should look at individual motivations and how the behavior resulting from these motivations interact. For instance, one macro-feature could be the ebb and flow of the occurrence of measles in an African country. One explanation for this pattern could be that people do not get vaccinated as long as only few people have measles. But if most people are motivated in this way, measles will slowly increase (since people are not vaccinated). As the number having measles increases there comes a point at which people will think that the risk is so great that it is profitable to be vaccinated. This will reduce the spread of the diseases so much that eventually people will stop getting vaccinated. Then the circle starts all over again.
Taken alone the interaction described above could be viewed as a good explanation of the macro-pattern (depending on the empirical truth of the statements). However, the story does not end here. First, there may be non-obvious conclusions that follow from interaction which do not depend on empirical observations. Second, we may find that there are a limited number of patterns that turn up in different phenomena. In other words, by knowing a few mechanisms we may explain very much.
Non-obvious analytic truths
It seems obviously true that to gain valuable knowledge about anything we need to do empirical research. The argument would be something like this: if something is true by definition, then it is so obvious that we should not spend time on it. For instance, to write a book in which you claim to have “discovered” that all bachelors are unmarried seems a waste of time. In short, to produce valuable knowledge you need to do empirical research.
Wrong, says Schelling. There are non-obvious analytic truths waiting to be discovered and it is important to discover these. A wonderful example is the following (adapted from p. 67). Imagine that you are standing in line at a ski lift. Someone says to you that he wished the chairs would go faster so the line would disappear. Intuitively we think this makes sense, but pure logic shows us that it is wrong. At any point in time you have to be in one of the following three places: Sitting in the lift going up, skiing downhill or waiting in line. Assume that you have a fixed amount of time you want to spend (say five hours). If the chairs go faster you will spend less time sitting in the lift. The time it takes going downhill stays the same, regardless of how fast the lift went up. Hence, if you spend less time in one place and the same time in another (and the time spend in all three places must add to five hours altogether), it is an unavoidable mathematical truth that you will spend more time in the third place (waiting in line) i.e. increasing the speed of the lift also increases the time you will spend waiting in line.
The measles example belongs to “an important class of statements: propositions that are true in the aggregate but not in detail, and true independently of how people behave” (p. 49). One reason why these statements are non-obvious, is that they “don't correspond to anything in the experience of the person …” (p. 55). For instance, in my experience when I stand up I get a better view and when I save more money my wealth increases. In aggregate, however, nobody gets a better view if everybody stands up, and my income and wealth may decrease if everybody saves more money (since they then must buy less of what I produce). Altogether this suggests that social scientists in principle can produce non-obvious knowledge; By exploring the aggregate consequences of interaction we gain knowledge that most people do not have.
Two more general examples should convince the reader about the value of such reasoning. First, there is what Schelling calls “the acceleration principle.” To illustrate this principle, imagine that the authorities decide to increase the number of houses by at least 25% in five years (see p. 62). Assume that the current construction industry is large enough to replenish 1% of the houses every year and support a growth of 2.5%. However, to produce a growth of more than 25% in five years we need the industry to be large enough to support almost 5% every year, in addition to the 1% replenishing. In other words the housing industry has to go from being large enough to produce 3.5% to about 6% i.e. the aim requires almost a doubling of the size of the construction industry. This line of reasoning suggests why prices may be very sensitive to changes in demand in some markets, as well as suggesting why planned economies in general often fail to achieve their targets. Moreover, the acceleration principle can be generalized. For instance, to double the number of soldiers in a short time, there has to be a very large increase in the number of the number of trainers. In short, one variable depends on the other and the relationship is such that an increase in the level of one variable requires a great increase in the other variable for some time.
Schelling discusses a second principle, under the title “positions in a distribution.” It is mathematically impossible for everybody to tip the waiter more than average. It is also mathematically impossible that most people are more skillful drivers than the average. These obvious truths have important implications. If many people have desires that are mathematically impossible to satisfy (like being taller than average), we may be better off if we collectively agree to some rules regulating the activity.
Generalization: Yes, but why?
Having finished the discussion of the non-obvious necessary truths, Schelling moves on to argue that social scientists should try to find general models that fit many different phenomena. An example is the already mentioned example of the measles. The same pattern found in that example can also be found in the cumulative growth of a child's vocabulary and the adoption of hybrid corn by Iowa farmers (see Schelling 1998). This suggests that we are dealing with a more general phenomenon. In this section, I first want to present some of the general models Schelling thinks exist. Next, I shall try to discuss the value of searching for these regularities.
Some general models
Close to my where I live there is a sub-way and when it arrives people simply cross the road without regard for the traffic. However, when people do not come in groups from the sub-way, they often wait before they dare cross the road. This suggests that there is a “critical mass” that is needed before the pedestrians dare to stop the traffic. The “critical mass” model can be used to describe a number of other phenomena. Of course, an atomic explosion fits a critical mass model (there has to be enough uranium so that the neutron released as a result of radioactivity decay, collides to produce more than one new neutron). Similarly smoking in non-smoking sections can be a critical mass phenomenon; One lone smoker breaking the rules may not be enough to induce the other smokers, but if many people smoke in the non-smoking section most smokers will probably disregard the rules. Lastly, a demonstration against an authoritarian government is a critical mass event. One demonstrator is not going to topple the government, a large number of demonstrators may. In all these examples there is a non-linearity. The event is “switched” on at some point, not gradually.
Two sub-models under the general class of “critical mass” are lemon models and tipping models. Lemon models exist when one person known more than the other, and as a result the market may either fail to exist of be inefficient in aggregate. Examples include the market for used cars, insurance and bank-loans. Tipping models describe, roughly, a situation in which people will do something if their neighbor also does the same think. Examples include people who are willing to stay in a neighborhood only if they expect that a certain percentage of people of the same ethnic background there; people who will join a demonstration only if enough other people do; or people who will only learn a new language if they think other people also will do so (David D. Laitin has written a book in which this kind of language tipping model is central to predict whether the Russians in Kazakhstan and Lativa will start to speak the native language or continue to speak Russian. See Identity in Formation, Columbia University Press, 1998).
Except for the critical mass models (with lemon and tipping as sub-classes), Schelling presents the well known tragedy of the commons (a model that can be used to explain pollution, failure of collective action and many other phenomena) and models of self-fulfilling expectations (e.g. if people fear that the bank will become insolvent this will cause actions that makes the bank insolvent). These are all general models that can be applied to a large number of social issues.
The value of finding models.
Let us pause for a moment and reflect on whether it is valuable to spend time thinking about the “models” above. First, there is the question of whether it is worth the effort to develop a model of one phenomenon. Second, there is the question of why we should think in terms of “families of models”; What is the point of discovering models behind the models?
A model, according to Schelling, can “mean either of two things. A model can be a precise and economical statement of a set of relationships that are sufficient to produce the phenomena in question. Or, a model can be an actual biological, mechanical, or social system that embodies the relationships in an especially transparent way, producing the phenomenon as an obvious consequence of these relationships” (p. 87). This gives one clue to the value of models: transparency. It also suggests that models are valuable in that they can be re-used to describe other phenomena than the one it was originally developed to account for. Schelling's example is the thermostat. As he writes: “Any variable x that increases or decreases according to the level of another variable, y, which increases or decreases according to whether still another variable, z, has a value of “on” or “off” (where the latter is on or off according to whether the value of x is above or below some target level), will behave like our heating system” (p. 88).
But, why is it useful to know this general representation? Schelling writes: “Whether or not that is any help depends, of course, on whether we can find other things that are both interesting and described by the model, and on whether we need the model – whether the model gives us a head start in recognizing phenomena and the mechanisms that generate them and in knowing what to look for in the explanation of interesting phenomena” (p. 88-89). A concrete example is the critical mass model which Schelling claims can be applied not only to nuclear fission, but in “epidemiology, fashion, survival and extinction of species, language systems, racial integration, jay-walking, panic behavior, and political movements” (p. 89). The eloquent question is then: So what?
I have to admit that I am unsure about this. First, the same macro-pattern can be generated by different mechanisms so I do not think we are simply searching for similar macro-patterns. Second, consider the following quotation by Jon Elster: “The mechanism provides an explanation because it is more general than the phenomenon that it subsumes” (Elster 1998, p. 49). Maybe this is the key: By trying to find models behind models (or general models), we find the few and simple “keys” that explain much. Maybe this is at least one (or the?) valuable aim of social science. (But, do these keys exist and do they really “explain”?)
Empirically speaking: Two case studies
In chapter four and five Schelling takes a more in-depth look at two phenomena: The sorting and mixing of race, sex, age and income. People often want to live want to live with a minimum of people from the same ethnic backgrounds, they also sometimes desire not to be in a minority (e.g. few females in a dormitory), or to be with people who all are older than you. By analyzing these micro motivations Schelling manages to come up with some surprising conclusions, such that increased tolerance does not necessarily make a stable mixed result more likely (see p. 163). He also comes up with a relatively convincing description of phenomena like “all-black” or “all-white” neighborhoods, as well as providing normative justification for regulation since this could sometimes create a result more in accord with the preferences of most people (“all-x” neighborhoods do not necessarily result from by all to live in an “all-x” neighborhood). Yet, to me these chapters were of limited interest.
A disappointing chapter
Chapter six, on “Choosing our children's genes” is the least interesting chapter in the book. Although today's technology makes this possible, so it certainly has some relevance, it failed to catch my interests. To some extent it made me think about the more general question of whether more choice (read: libertarianism) always is a good thing. Maybe the answers failed the “non-obvious” criterion or maybe I failed to appreciate the force of the arguments
A great chapter
If chapter six was disappointing, chapter seven made everything good again. This should be (and often is!) required reading for all social scientists. The main idea in the chapter is presented using what later has become known as Schelling diagrams. These diagrams are visual presentations of situations that are defined by the following characteristics:
1. n people have the choice between doing x or y (a binary choice)
2. the utility of each person depends on how many people choose x or y
3. the utility of doing x or y may depends on the number doing x or y
An example is the use of helmets when playing ice hockey. One reason why people do not wear helmets may be vanity: I would look like a coward to wear a helmet when few people wear helmets, but if most people wear helmets I would not look like a coward if I did so too. So, we have n individuals who have a choice between wearing helmets and not. Maybe they would all be better off it they all did so, but since the individual utility of wearing a helmet is low when few people are wearing helmets, they will never reach the situation in which helmets are worn. This may seem like a trivial example, but the same diagram can illustrate a host of other situations including the choice to become vaccinated, wearing tuxedos, wearing weapons, catching whales, daylight saving, the use of insecticides, the choice of communication systems, committee meetings, cleaning up after a party, and the decision to build a lighthouse.
The Schelling diagrams do not only provide a visual illustration of a situation. The diagrams also suggest explanations, solutions as well as normative implications. For instance, to explain successful collective action in one case and failure in another, we may point out that the Schelling diagrams show that the first case had a lower “critical level” before cooperation could get started. As a solution to the problem of collective action, the diagrams may sometimes suggest that a law/rule prescribing seat-belts/helmets/tuxedos may in fact benefit everybody. Normatively the diagrams imply that sometimes the “free market” may create socially inferior results compared to states with some kind of central intervention/coordination. (Needless to say, there are many other variables that also affect the costs/benefits of intervention so this argument does not represent an endorsement of large scale state intervention).
Criticism/Extension
Hovi (1984) argues that the Schelling diagram is a special case since it represents only situations when people are assumed to have symmetric and identical preferences. My criticism is related to this. The diagrams are meant to illustrate situation when people are influence by how many other people who engage in the activity. However, as I discovered when exploring the causes of ethnic violence the motivational structure may be much more complex than this.
To make the idea somewhat more rigorous, imagine a population of 20% fanatic, emotional and irrational nationalists; 30% who have nationalist preferences, but who are more rational about acting upon these preferences; 20% who are driven by a norm that tells them to cooperate if a majority does so; 20% who are selfish, rational and who seek only personal monetary gains; and finally 10% who will think it is morally wrong to use violence under any circumstances. I did not manage to illustrate this situation in a Schelling diagram, but I found an alternative presentation in Kuran (1991) which I think represents a more general form of analysis.
Building on Kuran we may say that corresponding to the different motivations there is a threshold level beyond which each group will take part in violent protests. If we simplify and assume that we are facing a population of 10 individuals we may have the following threshold sequence:
A = {0, 0, 20, 20, 20, 50, 50, 70, 70, 100}
In this structure the different motivations interact in a way that makes violence a possible outcome. The two fanatics will start and when the three rational nationalists realize that 20% are fighting, they will join in. This brings the total participation up to 50% at which point the two conformists also will join, making the total 70% which is beyond the level required before the careerist will find it profitable to join. At 90% involvement the process will stop and assuming this is beyond the critical level required to make violence happen we now have mass scale violence. Using this type of analysis we are able to illustrate a richer set of motivations than the original Schelling diagrams, as well as capturing the ideas of multiple equilbria, critical mass and socially inferior optima.
Even more generally, I sometimes speculate whether we might learn more if we used computer programs to model the micro-macro interaction that Schelling tries to capture. He himself presents a model that is perfectly suited for computer modeling (the self-forming neighborhood model, p. 147ff). I think this may represent one way forward for the social sciences; to make computer programs allowing us to specify individual motivations and characteristics and examine the macro-situations that develop after interaction.
Conclusion
Regardless of theoretical orientation one cannot help but be impressed and stimulated by Schelling's ideas and examples. Of course, if you believe that finding micro-macro links is impossible, not likely to have useful results and/or “premature reductionism”, than studies at the pure macro level, this book will not impress you that much. However, if you as me believe this is interesting and useful, your only complaint will be that Schelling has not produced a more integrated argument (the book is a collection of essays). In any case, it is a book I strongly recommend.
References
Elster, Jon (1998): A Plea for Mechanisms, kap. 3 in Peter Hedström and Richard Swedberg (eds.): Social Mechanisms . Cambridge: Cambridge University Press.
Hovi, Jon (1984): “Om bruk av spillteoretiske modeller med variable preferanser i studiet av internasjonal politikk,” Internasjonal Politikk 3:81-119
Kuran, Timur (1991): “Now Out of Never: The Element of Surprise in the East European Revolutions of 1989,” World Politics 44:7-48.
Laitin, David (1998): Identity in Formation: The Russian-Speaking Populations in the Near Abroad . Ithaca and London: Cornell University Press (forthcoming, my argument is based on the uncorrected proof version).
Schelling, Thomas C. (1998): “Social mechanisms and social dynamics,” ch. 2 in Peter Hedström and Richard Swedberg (eds.): Social Mechanisms. Cambridge: Cambridge University Press.
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