In the coming weeks we will try to get a more ...



People are connected to others. Most people know about a 1000 others, although some might know less, and some might know many more. On the average, however, we are connected to about a 1000 people. If you think about the 1000 people any person you know knows, you can see that interpersonal networks stretch out a long ways.

When you go to a party and meet strangers, more often than not you will discover that you and a person you never saw before have an acquaintance or a friend in common. When we discover such an indirect tie to a stranger, we say 'it's such a small world!'

When you think of how many people the 1000 people you know might know, and then, one step further, of how many people are known by your friends' friends, you arrive at very large number of persons and it's not surprising that you meet them at parties. Of course, there is a lot of redundancy in these networks. A lot of the people your friends know are also directly connected to yourself.

 

Hence, the question of how small our worlds really are is sociologically very interesting. The amount of redundancy in a network and the possibility to reach out into the larger world from a small world is the so-called 'small world problem' and important for many sociological problems, as we will see. What is the probability of an indirect tie between any two persons? How many 'steps' are we away from other persons in the world?

 

Let's undertake a thought experiment: say we have two hermits in two different parts in the country. One lives on a mountain in Connecticut and the other in the Bad Lands in South Dakota. Both know only one other person, say, the storeowner. How many steps or small worlds might there be between these two hermits? Storeowners know their customers, of course, but these might be hermits themselves and prove to be 'blind alleys.' On the other hand, they have to know truck drivers and distributors. The truck drivers know regional managers, who, in turn, know state managers, who, in turn, know corporate managers, and so forth. The top managers in the hierarchy of the firm may know the president of the company, but they are also likely to know the congressperson. The company president is likely to know the state manager of another state, who in turn knows the regional manager and so forth. The congressperson of Connecticut is very likely to know the congressperson of South Dakota, who is likely to know the business people in the state...Hence, there a manyfold possibilities how the two hermits might be connected indirectly. Here, in our experiment, we find about 9-11 steps or small worlds between the two hermits who know only one other person.

 

Imagine a world with no redundancy in personal networks--person A knows 1000 people, each of which knows 1000 other people who don't know each other: 2 steps or ties away from A there are already 1 million persons, 3 steps away a billion. Thus, the theoretical boundaries of the number of small worlds between any two persons are from 3 in a world with no redundancy to 11 in our hermit example. But what is it empirically?

 

Stanley Milgram set up in experiment to find that out. He picked a population in Nebraska, selected randomly 200 persons and asked them to send an envelop to a Mr. G., a stockbroker in Massachusetts. He asked them not to use a directory or anything like that but to go only through people they knew. One possibility is to rely on locality. People sent the envelop to somebody they knew in Massachusetts. Another, usually faster way is go with occupation. Stock brokers know each other from school, from doing business, from professional organizations, and so forth. Generally, the higher up in the status hierarchy, the easier it gets to reach people--they are in tightly knit networks, know how to reach or mobilize each other, and monitor each other.

 

In the Milgram experiment, the average number of steps between a random sample of people living in Nebraska and the stock broker in a middle-sized town in Massachusetts was 5.6-7.4. It turned out that once the envelop got into the town, it landed at one person who knew everybody in town and forwarded it to Mr. G. So we might say that it takes around 6 steps to reach a male white professional. Blacks, women, and low status persons are on the average much harder to reach. Women, for example, are integrated in tightly knit local networks but are less likely to be connected to formal institutional structures. They also marry and change their names which makes it very hard to find them. It takes about 25% more steps to reach them, on the average. Thus, although women tend to have many more friends than men, they are in sense disconnected from the larger world.

 

Granovetter's concept of strong and weak ties accounts for this. Strong ties are multiplex ties. They connect persons by virtue of more than one social relations. Women's ties are likely to be their neighbors, their kin, the people they can ask for a loan, and the people they are friends with. Men, on the other hand, are more likely to have one set of friends, which isn't identical with sets of business partners, co-workers, advisors, and the people they play with. Weak, or uniplex ties, which 'contain' only one type of social relation, are better for instrumental ends, to reach out in the world, to get things done. Weak ties tend to bridge small worlds, and are therefore strong in the sense that through them new information and new ideas are transmitted between worlds. Granovetter showed that you are much more likely to hear about a job from acquaintances than from friends. Within a local, densely interconnected network, if somebody knows about a job, everybody else is also likely to know about it. Thus, a job or any other kind of new information, is easier to obtain from somebody not in your own small world.

 

Granovetter's work on strong and weak ties is really important to understand the intersection between networks and group or categorical properties. How do networks yield groups? Most people are somehow connected into small worlds. Granovetter asks what the value of these ties is for getting things done, to find a job, and so on. Weak ties are strong because they connect small worlds.

 

Now getting a job is easy, in a way, because jobs do not hide from you. They wait to be filled and employers go out of their way to make known that they exist. In a context where abortion is illegal, as up to the seventies in the United States, it will be much harder to find an abortionist because they tend to hide. Nancy Lee Howell wrote a book in which she traces how women managed to find an abortionist while abortion was still illegal. Abortionists had to constantly assess how well their identity was known--the more people knew about them, the more likely they are to move someplace else in order to severe ties and avoid legal prosecution. Thinking back at the small world problem, it becomes clear that as soon as about 1000 people know about the abortionist, almost everybody knows about him or her. On the other side, for women in search of an abortionist it is desirable to go through people not embedded in women's own small world. First, they are more likely to get 'new' information from somebody outside their own world; second, they don't want people in their own world to know or learn that they are about to break the law. Thus, women are forced to go out into the weak tie network, and ask, for example, a former college roommate.

 

What do we have know about an abortionist?

-safety, medical qualification, hygiene, emergency backup

-location

-cost

-confidentiality

-procedure

All these things are crucial in collecting information. The problem is that the quality of information declines the more away from one's own world one seeks information. Why?

 

The first problem might be called the '1.grade story problem': when you whisper a sentence in your neighbor's ear and he or she whispers it into the next persons ear, sooner or later lines will get distorted and at the end a completely different story emerges. Second, trust decays with distance from our own world. Others might evaluate abortions differently and have different notions about procedures and costs. Third, networks are redundant and, getting a couple of steps away from one's own world might reach persons who have ties back into my own world unknown to me. Hence, the fact that I am in search of an abortionist might come back into my own world to persons who I don't want to know about it. Finally, the more small worlds are between the abortionist and those who seek him or her out, the more people potentially know about the abortionist, and the more likely it is that he or she has already moved or given up the business.

 

Nancy Lee Howell found out that the most effective strategy is 'sampling': ask a number of acquaintances who belong to different small worlds. Chain strategies, where you ask an acquaintance to ask their acquaintances and so forth, yield much more information, but the quality is bad.

 

Thus, at the individual level, weak ties are strong in that they help to get things done.

 

Community level:

 

Granovetter shows that in communities, strong ties serve to resist penetration of the community from the outside, but are weak in that they don't help to mobilize beyond the level of the community.

 

Macro level:

 

Weak ties are what holds society together: they diffuse information, fashions, fads, values, ideas. All these things emerge within small worlds; weak ties help to diffuse them in larger society and thus create bonds between communities.

 

Thus, weak ties, the acquaintances which seem so trivial and unimportant to us, turn out to be critical in a lot of ways and on all levels of analysis.

 

Search for an abortionist II

 

You may remember that one of the questions we asked you in the survey was whether you personally knew somebody who had an abortion in the past year. Let's pretend for a moment that abortion was still illegal. One strategy to find an abortionist might be to look for a person who recently had an abortion. We analyzed the data from the survey and here is the best strategy: look for a female who knows many other people and engages in non-normative behavior. The most important thing is that she knows many other people. Socio-economic background, religiosity, and race have no impact on the probability to know somebody who had an abortion, and networks are better indicators than variables indicating group membership or categories, and behaviors such as political participation, drug use, and deviance.

 

 

2. Arithmetics

 

The Rytina & Morgan paper asks an important question: what makes a group a group? When does a 'group-in-itself' become a 'group-for-itself'? Can we find a structural property of groups which tells us where group identities flourish, which categories are salient for the formation of groups?

 

The answer is that in order to yield a group-for-itself, the number of in-ties (or ties within the population of persons characterized by some attribute,) must exceed out-ties (or ties with persons who don't have that attribute) by some margin. But what is that margin? One tie more is certainly not enough to yield a group.

 

Imagine two kinds of persons differentiated by eye color. We intuitively know that eye color is not a salient category. People don't organize their social life on the basis of eye color, at least not here and today. But there is a way to assess the salience of eye color or any other attribute empirically.

 

Let's look at our two categories. Say we have 10,000 persons with blue eyes and 90,000 people with brown eyes. What pattern of friendship ties can we expect if eye color is not a salient category for group formation? Table 1 shows this pattern assuming symmetry in relations and 500 ties per person.

 

Table 1:

| ties to |blue eyes |brown eyes |# of ties |

|from | | | |

|10,000 |50 |450 |500 |

|blue | | | |

|90,000 |50 |450 |500 |

|brown | | | |

|100,000 |  |  |  |

|sum | | | |

 

This is called a random table. It shows a population where blue-eyes are not more likely to associate with other blue-eyes than with brown-eyes. The math is really simple: 10% have blue eyes and 90% have brown eyes. If eye color is not a salient category, for each of the two kinds of persons, about 10% of friendship ties should go to blue-eyes and 90% to brown eyes. Thus, blue-eyes are not a 'group-for-itself.' They don't exist as group, so to speak, and are not interesting sociologically. This is Rytina and Morgan's baseline: departure from random tables of symmetric ties indicates groups-for-themselves.

 

Some people would be happy if this pattern of random association would govern race relations, too. If race ceases to be a salient category, we have true assimilation, and that is an ideal for some people. Most of us would probably prefer that religion in Northern Ireland, ethnicity in former Yugoslavia, class in friendship relations everywhere, were not salient for group formation. This is not always that clear, though. The conflicting ideal is to give every minority group the chance to sustain an independent culture. If social relations are formed randomly, minority groups will be always overwhelmed by majorities: the blue-eyes in our example can hardly sustain an independent culture and identity. Most people they know have brown eyes, brown-eye values and ideas, brown-eye practices. It is important to understand that these two ideals are really conflicting, one cannot have both at the same time. In the following we will see why that is.

 

Let's first look at a table which shows salience of a category. From the survey we know that African-Americans in this class are more likely to associate with other African-Americans. Of the 100 people you know enough to say high to, 75 are black on the average. Let's keep the numbers from table 1 for simplicity and see what cell frequency an in-group preference of 75% yields:

 

Table 2:

| ties to |blacks |whites |# of ties |

|from | | | |

|10,000 |375 |125 |500 |

|blacks | | | |

|90,000 |13.9 |486.1 |500 |

|whites | |  | |

|100,000 |  |  |  |

|sum | | | |

 

How did we get these numbers? First, remember that in a 2x2 table, there is one degree of freedom if we know the marginals. Thus, given a number of 500 ties per black person we arrive at 375 since 75% of ties have to go to other blacks, as we know from the survey. This number than yields 500-375=125 black-to-white ties per black person. Given 10,000 blacks and 90,000 whites in our population, we get a total number of white-to-black ties of 10,000x125=1,250,000 and, dividing by the number of whites 1,250,000%90,000=13.9 white-to-black ties per white person. Subtracting from 500 yields the last number of 486.1 white-to-white ties per white person.

 

From this example is it easy to see that, because blacks are a minority, whites' networks are much fuller of whites that blacks' networks with blacks: they are less often confronted with different ideas, cultures, values, and fashions than blacks are.

 

 

Last time we saw how comparing a random table of group ties with actually observed ties tells us something about the salience of attributes in group formation. We also said that given an asymmetry in group size, it is more difficult for the minority group to sustain an independent culture because members of minority groups have more 'out-group ties' in their personal networks than members of the majority group. Simple arithmetics have a lot to say about group live.

 

Today we will see how the proportion of minority in-group ties can be 'tipped' over by subtle changes in out-group ties. Say our white majority members decide that instead of 13.9 African-Americans, they want to know 16. The table of ties would then look like this:

 

Table 1:

| ties to |blacks |whites |# of ties |

|from | | | |

|10,000 |356 |144 |500 |

|blacks | | | |

|90,000 |16 |484 |500 |

|whites | |  | |

|100,000 |  |  |  |

|sum | | | |

 

Remember: the number in the upper right cell is computed like this: 16 times 90,000 divided by 10,000=144. Now, whites have still almost 97% of their social relations with other whites, but in the minority group, the proportion of in-group ties has declined from 75% to 71%. If whites had 5% of their ties with blacks--still only half of what is expected if they choose their friends at random--we would get the following numbers:

 

Table 2:

| ties to |blacks |whites |# of ties |

|from | | | |

|10,000 |275=>55% |225=>45% |500 |

|blacks | | | |

|90,000 |25=5% |475=>95% |500 |

|whites | |  | |

|100,000 |  |  |  |

|sum | | | |

 

Thus, very small changes in the network composition of majority groups can tip balance in the minority group and overwhelm the 'groupness' of the minority group, so to speak, namely the prevalence of in-group ties. There are many examples in American history were minority groups were assimilated into majority groups: Italian and Irish immigrants used to live in densely knit communities and segregated from other groups. Later, by virtue of residential and social mobility, out-group relations grew and today, the network composition of Irish Catholics, for example, approaches that in the random table. Jews used to be completely segregated and still are in some places, but more often than not they are as likely to have non-Jewish friends than Jewish friends. Hence, it becomes more difficult for them to sustain a Jewish culture.

 

The African-American upper middle-class, the so-called black bourgeoisie, is an example for how the salience of attributes can be changed. Given their class position, they are far more likely to interact with whites than with other blacks. Their politics look 'upper class,' not black; they are as likely as rich whites to vote Republican, to have a conservative outlook and conservative values. In sum, their reference group is different from that of poorer blacks: it is formed by class attributes instead of racial attributes.

 

Another example from the Rytina & Morgan paper is the tipping of adolescent subcultures. Let's look at a high school in a small town. There are about 2000 teens in the town, and about 48,000 adults. We also know that teens have less ties than adults: they simple know less people. Let's assume that each kid has 300 friends and 200 of them are other kids. That yields the following table:

 

Table 3:

| ties to |kids |adults |# of ties |

|from | | | |

|2,000 |200 |100 |300 |

|kids | | | |

|48,000 |4.16 |495.84 |500 |

|adults | |  | |

|50,000 |  |  |  |

|sum | | | |

 

Thus, adults know about 4 kids on the average. If adults try to increase their ties to kids, by activities in community centers, in clubs, tournaments, leagues, and so on, they can effectively block the emergence of adolescent subcultures: if each adult knows only 8 instead of 4 kids on the average, necessarily and by simple arithmetics, each kid has to know 192 adults instead of 100 adults, and has ties only to 108 kids. In the adolescent population, 'groupness' is thus reduced while adults still interact mainly with adults.

 

But, there is yet another important point in these arithmetics of social relations: Each adolescent in the population in table 3 has to choose 200 friends from among 2000 teens. He or she can reject as friends only 90% of all teens in the high school. One out of ten has to be a friend. Adults, in contrast, can reject far more other adults: they have to choose only one out of 97 adults in order to have 495.86 ties to adults. The density of social relations (i.e. the number of in-group ties relative to the size of the population) is far higher among minority group than among majority groups. The importance of density for minorities is that it forces the emergence of a 'master attribute' in friendship choices. Minority group members basically choose their friends on the basis of the attribute constituting the group--being a teenager, being black, and so on--much more than choosing friends along other dimensions, such as common interests, values, ideas, and so on. Conversely, for majority group members, density is low although the proportion of in-group ties is much higher. Actual friendship choices may be made on other dimensions. This precludes identity emerging from the majority group. Thus, for teenagers, age group membership is much more likely to emerge as a salient identity than for adults.

 

Thus, group identity is governed by the proportion of in-group ties and by in-group tie density. We saw how minorities can be simply overrun or tipped by subtle changes in the network composition of majority groups. This process is what we call assimilation, or the destruction of a category's salience.

 

There are two competing ideals in regard to intergroup relations: the first ideal is that a just society ignores categories. The second ideal is that we want minority groups to be able to sustain independent cultures. The arithmetics of social relations explain why it is so hard to realize both ideals at the same time and have salient minority identities but equality on other dimensions.

 

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