The last chapter began with relationships of friendship and alliance that highlighted the equality, indeed equivalence, of pairs of persons. Such relationships imply a very simple structural form—the clique—and we followed analysts as they looked for this structure in everyday life. They found very, very few. In large part this had to do with size—the interactional demands of the clique grow exponentially with the size of the group, and hence cliques tend to be small. This in turn implies that we are unlikely to find cliques concatenating to form larger structures without some sort of change. But what sort?
We found the analysts needing to relax their expectation for cliques of mutual relationships and allow for asymmetric relations of “choices” of preferred interaction partner. Allowing for the nonreciprocation of choices tends to induce vertical differentiation among persons, as some receive more choices than others (the “popularity tournament”) or do not reciprocate the choices they are given (one person A “chooses” another B as a friend while B does not “choose” A as a friend). Adding many more such dyadic relations, we find that “friendship” can no longer be understood simply as a relationship of equivalence uniting equals. Instead, it is a relationship that induces inequality—B is more popular than A.
This was our first encounter with the problem of equality—that is, the problem that certain relationships by definition require equality between the participants but may induce inequality. Yet it is also important to remember that just because there is a relation of inequality between A and B does not mean that there is any particular relationship between A and B—indeed, it may be that because B does not reciprocate A’s choice, the two never interact. Thus the existence of a popularity tournament does not itself determine what the social structure of interaction will be. But let us now assume that inequality does affect relationships and leads to asymmetry. That is, we consider relationships in which actions are performed by A to or for B, but not necessarily vice versa.
In some ways, this “solves” the problem of equality, by changing the nature of the relationship to one that is more in harmony with the relation of potential inequality between the participants. But in many cases allowing for such asymmetry also leads to a structural problem that I shall treat as the problem of inequality. In many cases, the natural effects of the popularity tournament—the “Matthew effect” by which “to them that have, more shall be given” (Merton 1973)—leads to an inherent instability. We wish to examine what local structures may arise that contain this problem. Once again, we start with the most fundamental form of an asymmetric relationship, and using empirical cases, deduce form from content.
If the essential mutual relationship is alliance, the essential asymmetric one is probably donation or transfer, the action whereby A who possesses O relinquishes (alienates) this possession so that B may take charge of O. In many circumstances, this is considered a “gift” or, in the terminology of Mauss (1967 [1925]), a “prestation.” Let us assume that it is understood that receiving a gift incurs an obligation to render the giver support when it is needed (Schwimmer 1973: 48). It is therefore reasonable for people to give gifts to the more powerful, as a form of social insurance.
Such conditions will lead to the same sort of positive feedback we saw in the case of popularity tournaments. The only problem is that some sorts of nonrenewable gifts will all flow eventually to the highest-ranking members of some society, and stay there to stagnate, unless there is some sort of redistribution. The increasing inequality may thus be disastrous. Further, aggregating smaller structures will only increase the problem, by increasing the intensity of the feedback effect. Consequently, or luckily, many societies have worked out ritually required forms of such redistribution, whereby the “big man” (say) gives these gifts back to people and thus increases or maintains his prestige. In other cases, rather than allowing all the goods first to accumulate and then to be redistributed (which we can consider the “two-stroke” motor of redistribution), there may be a structure that continuously keeps transfers moving in such a way that no one becomes bankrupted.
Following the anthropological tradition, I will call these “exchange” structures. The essence of such structures is that they temper the tendencies toward inequality inherent in asymmetric actions by ensuring that the difference between inflow and outflow to any person or group is relatively small over the long run. Such exchange structures, it must be emphasized, are quite different from the more familiar ones of contemporary Western market exchange, where fundamentally different goods are exchanged (A gives O to B and B gives Q to A). Where a specific Q is associated with some O (for example, A always votes for B and B always recommends members of A’s family for jobs, and not vice versa) we do not have an asymmetric (but possibly reciprocated) relationship but an antisymmetric one; such structures will be examined in chapter 6.
Now it is not always the case that donation relationships must be structured if inequality is not to prove ruinous. For an example, let us take the gifts given by thirty-seven Pokot herdsmen of Kenya in response to a drought as studied by Bollig (1998: data on 149). These gifts, usually a goat or sheep, were a form of help to afflicted households, and because each of the thirty-seven herdsmen was the head of a household, these transfers represent a substantively important part of life for considerably more than thirty-seven people.
In this case, the redistributive imperative is complicated by two other considerations. The first is the preexisting differentiation of the households by wealth, which affected giving practices.1 The second is a general imperative of reciprocity that underlies much of the Pokot social structure. Put in terms of the schema introduced at the end of the previous chapter, we find that the tendency toward structure at the group level is pitted against the organization at the individual level (preexisting differentiation of persons) and organization at the dyadic level (reciprocity).
Both of these can be quantified using the model discussed in the previous chapter that breaks every asymmetric relationship between person A and person B into three parts, one having to do with characteristics of person A (in this case, does he tend to give a lot?), another having to do with characteristics of person B (does he tend to receive many gifts?), and a third having to do with the tendency of gifts to be reciprocated. (This is the Holland-Leinhardt [1981] p1 model.) The first two sets of parameters capture individual-level structure, and the third dyadic structure. More important, the organization of individual-level parameters tells us a great deal about the likely results of the set of transfers. If a pure “charity” logic operated, the first two parts would tend to be negatively associated (as rich people would give but not get, and poor people would get but not give), and there would be no reciprocity effect. If balance was achieved by reciprocity and was indifferent to wealth, the reciprocity parameter would be positive and the others randomly distributed and nearly equal.
We can display this set of relationships as a network as in figure 3.1. Each person is placed on two dimensions, the vertical being the extent to which he was likely to give, and the horizontal being the extent to which he was likely to get. The axes are at the means of each dimension, which divides the space into four quadrants. Those who are above the mean in giving but below in getting are termed “givers”; those with reversed values are “getters”; those low on both are termed “peripheral”; while those high on both are termed “central.” There is a moderately large tendency toward reciprocity—the parameter is 1.15, indicating that the reciprocity observed is probably not an artifact of person qualities—which is easiest to see among the central, though it is worth emphasizing that the parameters used to determine centrality are estimated controlling for this tendency toward reciprocity.2
Figure 3.1. Donations among herdsmen
Interestingly, there is no correlation between the two types of person parameters.3 If there was a negative correlation, we would have evidence of a deliberately redistributive system—there would be only givers and takers (those on the upper left and the lower right). If there was a positive correlation, we would have only central and peripheral players (those on the lower left and the upper right). Here we see a system that is likely to be de facto redistributive without being clearly organized in such a fashion. All must give (and the rich have more to give) but all must get as well. This allows the system to be both relatively redistributive in fact without violating the norm of reciprocity.4
The redistributive nature can be intuitively understood by reconstructing “chains” of transfers. These are paths in the graph that do not represent temporal connections but rather illustrate the overall flow of goats. Three randomly chosen chains are portrayed in figure 3.2.5 One (the double-lined) consists of a single transfer, and another (the dashed line) has six links. The third (the solid line) begins with one of the more “giving” of the central actors, who gives to an even more central actor whom we can term B. B gives to a peripheral person who gives to a more central “taker” who gives to a more central person who gives to another central person who gives to a more taking person who gives back to B who now gives to a peripheral person who gives to a more central person who gives to a sink—someone who only takes, and hence the chain ends there.
Overall, we expect goods to move from the upper left to the lower right—but many others will both give and get, and presumably get when they need and give when they don’t. The very vagueness of the structure can allow it to best meet the fluctuating needs of the herdsmen. But in cases where even a minor imbalance in accounts might be ruinous, there may be more pressure toward clarity of structure. Imagine, though it sounds foolish, that these herdsmen had the same level of capital, but herded elephants. Each lineage would be likely to have only one. While life may be tolerable if you have sixteen goats and your neighbor seventeen, it is quite another thing to be the family without an elephant. Inequality in such a situation is more likely to provoke extreme actions.
Still referring to figure 2.13 at the end of chapter 2, we may say that when the problem of inequality in donation arises—perhaps because the things being donated are nonsubstitutable goods—any movement toward structure can take us either toward the group-level organization (the lower right) or the dyadic (the lower left). Before treating such cases in depth, it helps to clarify what one means by exchange.
Figure 3.2. Possible chains
Let us for the moment consider the solution toward the lower left of figure 2.13, in which dyadic reciprocity is the basis for a structure. Our understanding of the structure of such dyadic exchange has been (somewhat ironically) seriously hampered by the obsessive interest with understanding social life in terms of exchange found in the social sciences. To make a long story short, there is something about capitalist society that leads many people to be easily convinced that exchange is the be all and end all of society. Consequently, there are recurrent waves of fanatical exchange theorizing, all foundering on the same ideological shoal. This is the dogma that all exchanges must be equal. To be fair, there is some analytic reason to wish for such an axiom: if it is true, it can be used to identify utilities not obvious at the start—plus, we can hope to always be able to talk our poorer neighbors out of killing us. Further, when social structures exist to make this true, social interaction is dramatically changed. However, the conviction that it is always true is perhaps the single least intelligent thing that can be said about exchange.6
The recurrent assumption that exchanges are always equal is particularly foolish since it does not even flow from the postulates of rational action (postulates that are indeed frequently useful, though the one thing we know about them is that they are not strictly true).7 These postulates do not even allow us to derive the often assumed conclusion (e.g., Landé 1977a: xxvii) that for any freely made exchange, the costs cannot outweigh the benefits for either party. The costs of exchanges very frequently do outweigh the benefits to one party in a rational interaction; they simply are less than the costs entailed in not making an exchange. This is generally the case for exchanges between unequal parties in the absence of a true market, and we will see the importance of this in our analysis of patronage structures below.
For example, let us consider the ideal typical case in which a serf “exchanges” corvee labor for protection on the part of a lord. Of course, the “protection” supposedly provided by the lord may never actually materialize, and the serf would gladly inhabit a world with no lords at all (cf. Roemer’s [1982] game theoretic analyses of different types of class relations). The “exchange” is only comprehensible when one understands that each serf must have some lord, and while we might imagine any serf trying to get the best lord he could “command”—itself a fanciful idea, though one that may have slight analytic value—this would simply be the best of a bad bargain.8
The fundamental inequality of such a relation is not a moral judgment but an important structural quality; the ability to identify such inequality is necessarily lost when analysts attempt to demonstrate that this is still a “fair” exchange, by including the absence of the cost incurred were the exchange not made as one of the benefits of the exchange. According to this logic, the most valuable security services are “provided” by mobsters who “protect” one only against themselves.9 There may be rational reasons to make an unequal exchange; this should not be assumed to make the exchange an equal one. One person may, for example, rationally give an object of greater value for one of lesser value if not doing so may have other consequences that may involve third parties (and not the exchange partner himself, as in the mobster scenario). For the case of marital exchange (either considered as exchange of women between groups or pairing on a mating “market”), not pairing may be equivalent to failure to reproduce; for the case of patronage relations or symbolic capital, not conducting financially ruinous exchanges may lead to a serious loss of prestige (we will see examples of this in chapter 6; also see Barth 1981: 50). To take all the situational reasons that would justify someone taking a bad bargain and to try to fold them in to the dyadic exchange itself is as ludicrous as formulating an optics of reflection that declared on axiomatic grounds that objects had to be “in the mirror.”
We cannot, then, simply assume that if an exchange is made, we are free to declare that it must be equal. But there are ways in which exchange relationships can be patterned that tend to produce this equality as a result. One sort of equality is likely to arise if social structures are fractured into bits. Let us follow White (1992) in considering the “forum” to be a set of individuals accessible to costless mutual observation (copresence is generally sufficient but not necessary for this). An exchange that takes place in the forum is not necessarily different from one that takes place in private, unless there are other possible exchange partners with whom A can make the same exchange. Such knowledge of alternatives is widely assumed to increase the equality of exchanges, and this seems substantively reasonable even though it does not directly follow. But if we add a few more conditions—the presence of many different goods, that the goods negotiated be divisible, that participants be free to decline any and all exchanges, and that prices be attached to goods (see Stigler 1968: 5–12) —we have the sort of market that is assumed by conventional economics, one that strongly tends to equate the marginal utilities of things exchanged for the exchangers. But even without these additional criteria, exchanges in a forum where there are alternative partners can induce regularities in the pattern of reciprocal action between A and B that can be said to be transdyadic in nature and indeed to constitute the benchmark of “fairness” (also see Barth 1981: 50, 55).
The market, or forum, is in some ways an “antistructure” in that the existence of obdurate social structures in the form of repeat transactions with the same parties is considered to be a sign of market imperfection or an indication that a true market has not yet emerged (see, e.g., McLean and Padgett 1997). But a contrary way of handling related interactions is to solidify the relationship between two interactants.10
In such a case, there is no reason to assume that any common metric emerges so that one may speak of mathematical equality in exchange, and no reason to think that where such a metric does emerge we find that exchanges are equal in these terms. Indeed, exchange may often magnify preexisting inequalities, for if the transfers always occur in one direction, they will tend to drain one party to the benefit of another, just as the larger of two twin stars may eventually suck up all the matter of the smaller, as each additional bit transferred only increases the gravitational field of the larger, as opposed to being “fair” and hence leading to equilibrium. One may, of course, consider this to be “fair” if gravity “should” be proportional to mass; indeed, Newton’s laws force us to see a form of equality, but this should not distract us from the important fact that at the end, one star is there and the other is not. Given this drain, it is reasonable to call this an unequal relationship, and similarly unequal relationships that occur among persons lead to a similar drain. If we adopt a framework that in principle makes it impossible to identify unequal exchanges, we fail to notice those that are potentially ruinous for some participants. We then are unable to understand the principles of those structures that are best understood as determined efforts to control the emergence of hierarchy.
In sum, persons may try to organize relationships of donation in a reciprocal fashion—the problem of inequality arises when imbalances in donations cannot be tolerated past a certain point, and in which free interaction is not guaranteed to equalize things. In these cases, rather than move toward the antistructure of a pure market, relationships may move toward an extremely clear social structure. Such structures have been explored most thoroughly in the anthropology of kinship understood as the exchange of women.
Who Really Exchanges Women?
We will begin with marriage as an example. In contemporary American society it is not surprising that marriage is often seen as an exchange. Yet such a statement as conventionally made has little analytic power for the investigation of structure, for once the “exchange” is made, the dyad leaves the forum and becomes a social structure of its own.11 While it may at times be reasonable to treat the marriage decision in exchange terms, this is largely to miss the fact that the marriage itself is the construction of a relatively stable social structure that may (or may not) facilitate transfers that need to be reciprocated.
There are, however, other ways of understanding marriage as exchange, most importantly between lineages. This is relevant in societies in which lineage matters (ascriptive as opposed to achieved status, they used to say), which is to say nearly all of them, except for the modern and urbanized first world. Instead of focusing on the husband-wife dyad, many anthropologists focused on the ceremonial prestations—ritually fixed scripts of a series of gifts and countergifts—that occur between the man’s family and woman’s family.
But Levi-Strauss (1969 [1949]: 115, 36) argued that really what is exchanged is the women themselves, between groups, not between a man and a woman. (Thus in the matrimonial vocabulary of Great Russia, the groom is called “merchant” and bride “merchandise.”) Any marriage is a net gain (+1 woman) for one lineage and a loss for the other (-1 woman). The trick in composing a stable social structure is to manage things so that no lineage runs out of women and becomes extinct. We must not, argued Levi-Strauss, be fooled by the universality of the incest taboo into thinking it is wholly unremarkable that lineages exchange women. It is structurally no different from two dogs exchanging bones (Adam Smith’s example of a senseless exchange)—and indeed, groups that exchange women frequently have parallel structures for the exchange of other goods, immortalized in the Arapesh saying, “Other people’s sisters . . . other people’s yams . . . you may eat; your own sister, . . . your own yams . . . you may not eat” (Mead 1940: 352; cf. Smith 1983: 75).12
This understanding of marriage as an exchange of women between patrilines (that is, patrilineal lineages) is indeed a good starting place not because it is the norm—rather, it is atypically simple and hence amenable to structural analysis. That is, many mid-twentieth-century anthropologists focused on marriage as an exchange of women, taking as paradigmatic the case in which some patriarchs made arrangements using women as chattel. This turned out to be problematic. In many applications, assuming the existence of such patriarchal logic and control was egregious and unnecessary to derive the marital patterns; in others some (male) informants may have used such heuristics to explain their philosophies of matrimony but there was considerable evidence that actual marriage was conducted differently. Patriarchal marriage exchange is the exception, in that in most cases, even those with nominally patrilineal descent, there is some degree of bilineality—for example, those descended from high-status women may well make sure that this is not forgotten (Sahlins 1968: 48). Further, contrary to the assumption that ego’s wife is “lost” to her patriline, ties of obligation remain and her family generally has a stake in the reproductive consequences of her marriage (here see Singer 1973, especially 89; Lee 1972: 350; also Bourdieu 1977; Barth 1981: 142).13
Because the pure case of men exchanging women is an exception (though one that does occur),14 the more anthropologists looked carefully at their cases, the more they found their results confounding the Levi-Straussian vision; as a result, there has been a tendency to ignore the results of this tradition, indeed to dismiss its outlook as patriarchal. This is probably both true and unhelpful, in that it leads to a paradox whereby identifying a patriarchal logic is itself patriarchal.15 That is, it is a polar case in which there are three structural simplifications that are compatible with patriarchy but also that imply clear heuristics of action. First, simply by assuming unilineal descent, we can treat any lineage as a bounded set of actors, each of whom has no complications of interest by virtue of belonging to multiple lineages. Second, by assuming patriarchal control, we simplify things further by identifying whose interests count—men who are assumed to want to reproduce their group. Finally, by assuming that men exchange women we have the key principle that an imbalance can be ruinous for the interests of the leaders of the lineage.16
This simplified perspective gives us one answer to the problem of inequality in asymmetric relationships, in part simply by assuming that one sex is fixed within the sib and the other is exchanged between lineages. The key is to remember that structurally, by “exchange” we really mean a directed, and possibly reciprocated, relationship, and not a “trade” or “purchase.” We may imagine that some persons are indeed traded or shipped about, but even if they are not, simply seeing marriage as “female marries into some kin group” satisfies the definition of a directed and possibly reciprocated relationship between lineages.17 Formally, it may seem to make no difference whether we imagine women exchanged or men exchanged,18 but it is harder to handle polygynous cases from an “exchange of men” perspective, and there are considerably more polygynous cases than polyandrous.19 Further, because of women’s greater reproductive scarcity, the problem of inequality gains importance when we consider men as fixed. If a patriarch who cared only about the continued production of a line of male descendents had his druthers, he would likely be more concerned with the balance of women entering and exiting his lineage than would a matriarch concerned with the production of a line of female descendents, since (if we assume polygyny) only one man is needed to sire many offspring.20
Let us consider the possible responses to this problem of inequality in terms of heuristics of interaction. We can make a distinction between principles that are architectonic—compatible with the preservation of a structure of interaction—and those that are not. For an example of the latter, “take take take” is a possible response to a situation of necessity that is not necessarily compatible with structure. That is, if lineage A lacks women it may find some lineage B from whom they may be wrested by force or at least without the consent of the patriarch. For example, Yanomami with greater access to highly desired Western goods would accumulate women while giving up very few of their own (see Ferguson 1992: 215), imperiling the long-term survival of other groups.21 Although there is no particular reason that lineage A should worry about the survival of lineage B, we still find that this heuristic is incompatible with that regularity of relations between particular persons that has here been termed social structure.
If we only consider architectonic heuristics that solve the problem of inequality, perhaps the most obvious would be the principle of reciprocity. Returning to figure 2.13 introduced at the end of chapter 2, such heuristics will lead to structures that emphasize dyadic level reciprocity (the left corner). But as we shall see, there are also structures corresponding to the right corner of the figure. We begin with the simpler dyadic case.
Let us, then, begin with the simplest case, namely the direct reciprocity that leads to what is called sister or daughter exchange: the males of lineage A exchange a nubile woman from their lineage for one of lineage B by having a male from A (AM) marry a female from B (BF) and some BM marry AF. If we imagine, for a moment, these lineages to simply consist of one set of parents and their children, this is equivalent to “sister exchange” or “daughter exchange” (the two names come from seeing things from the point of view of the older or younger males). This means that a male offspring of a AM–BF union (say, Y) is related to a female offspring of a BM–AF union (say, X) in two ways: Y is X’s father’s sister’s daughter (FZD), and X’s mother’s brother’s daughter (MBD).
If we assume unilineal descent, then one of these children will end up attached to one lineage and the other to the second. One way to ensure that these lineages always exchange their women is to require that such cousins marry each other. Thus we might find a rule that men should marry either their MBD or their FZD. Such rules are found where there are classes that regularly marry with one another, which we shall follow Levi-Strauss in calling “restricted exchange.”
Now consider a society neatly divided into two and only two exogamous marriage classes, called phratries or moieties, and with one’s placement in a moiety being either patrilineal or matrilineal.22 The difference between FZD marriage and MBD marriage is now academic, and indeed, in such societies there may not be a preference for one as opposed to the other. Although such organization is reasonably common (though see Levi-Strauss 1963, chapter 8) and ensures that a male ego’s MBD (and FZD) are in the opposite moiety and hence marry-able, this does not necessarily solve the problem of equality. That is, if each moiety is itself composed of a number of distinct patrilineages, and it makes a good deal of difference to the members of some patrilineage whether they give up more women than they receive, the presence of exogamous moieties is not wholly comforting.
At the level of the individual lineage, it may prove hard to accomplish an actual daughter exchange simply because lineage A may have a daughter of marriageable age but lineage B does not. As a result, the parties may allow for a delayed repayment, which also makes sure that the various lineages stay together even when they cannot accomplish a tit-for-tat exchange (see, e.g., Gouldner 1960; Bourdieu 1990 [1980]).23 It is possible that delayed reciprocity is handled by people remembering how many women any lineage is owed from any other, but this is not only a recipe for disagreement (for memories tend to differ in ways correlated with interest) but vulnerable to filibuster and threat. For example, stronger Yanomamö lineages may refuse an even exchange (see above), or they may also use delays to their advantage by exploiting the “float” that results in taking a nubile one and betrothing an immature woman in exchange.
A different way is to use individual heuristics for preferential marriage. Above we found that consistent daughter-exchange between two lineages might lead any ego to marry someone who was his FZD or his MBD. Now let us generalize to more than two patrilineal lineages exchanging women. Thinking from the perspective of a male from A about to be married, there is quite a difference between marrying a father’s sister’s daughter (FZD) as opposed to a mother’s brother’s daughter (MBD). The MBD is from the same lineage (B) that your mother is from—the same lineage that “gave” your patriline your mother. Your father’s sister, however, has married into some other lineage, C. Thus marriage with MBD takes a second woman from B to A, while marriage with FZD cancels out a debt, by taking a woman from the lineage who took your father’s sister.
Thus using the heuristic of “marry your FZD” is equivalent to a structure of reciprocity with a possible delay that does not require that people keep track of how many women have been transferred from one lineage to another (Levi-Strauss 1969 [1949]: 130f). Similarly, other heuristics are compatible with a longer delay in repayment. For example, consider the rule that male ego’s spouse is in the same class as his father’s father’s sister’s daughter’s daughter (FFZDD)—the Maring, Manga, and Wogeo of Highland New Guinea speak of this particular rule as a return made for a woman given two generations earlier (Tjon Sie Fat 1990: 139). (That is, since one marries one’s grandfather’s sister’s granddaughter, one has married a woman from a patrilineage to which one’s own patrilineage gave a woman, the grandfather’s sister.) Having several such rules can allow ego to choose a spouse from a lineage that is extremely likely to have given a woman to ego’s lineage relatively recently, without tying ego to one particular generation of spouse (who may not exist).
Many of the classic elementary structures enforce delayed repayment by complicating restricted exchange. Moieties are divided into smaller marriage classes, and membership in classes alternates across generations (thus men of class A may need to marry women of class B and their children will end up in class C who must marry from class D, etc.). If the marriage class is neither too big nor too small, it may be able to decently coordinate exchange so that no patriline is likely to be bankrupted of women: from the position of a male ego in some class A, there are enough patrilines in class B so that there are nubile women to “take” but not so many that other ways of determining who shall marry whom must spring up to coordinate transfers of women.
But this is not the only way of ensuring that the A who gives O to B does not go without O. We have found that the difficulties turn on whether B actually has an O that B is willing to alienate. It need not be B who makes this donation—it can be a third party, C. We go on to explore the resulting structures.
Such solutions to the problem of inequality—structures in which those who give get from someone other than those to whom they give—are usually called “generalized exchange,” or “group-generalized exchange” or “net generalized exchange.” I will reserve the term generalized exchange for the particular circular system as discussed by Levi-Strauss (sometimes called “chain-generalized” or “network-generalized” exchange), and term the broader case in which A will receive from some X (as opposed to particularly from a specified C), simply “spreading out,” since the essential thing is that either gains or losses (or both) are spread out among the group in some way—usually across persons and across time.24 It is with such general cases (and not the specific case of elementary kinship structures) that we begin. I will speak of the transfer here as a “donation,” since it is understood that it will not be reciprocated by the recipient, at least not immediately.
Of course, it is possible to have a structureless solution—that is, to have a norm in which someone gives when giving is likely to be needed (for example, blood donation)—but these fall outside the scope of the present work. When we consider structured solutions, we find two fundamentally different ways in which spreading out can be organized, one oriented around giving and one around getting. To discuss these, it is convenient to denote a donation from person A to person B as A → B, meaning that A ends up with less than before and B with more.
One way in which spreading out can be accomplished is by following B → C with A → B; this leads to A having less and C more than before the transfers took place. Person B has only suffered a temporary loss and has been recompensed by A. If we had a chain of four people, with their state at any time denoted as a vector, we might denote the first state [0,0,−,+]—the third person has given up and the fourth person gained. The second state would look like this: [0,−,0,+] and the third [−,0,0,+]. (Here see the analysis of Breiger and Roberts [1998: 247].) We can see the − sign as a pulse moving backward as time goes forward (an example here are chains of moka exchange in New Guinea [see Hage and Harary 1991: 68]). It may be difficult to understand why three people would do this, as opposed to A directly giving to C. But there are two reasons why this often makes a good deal of sense. First, it spreads the loss out among a large number of people, and may thereby efficiently allocate resources or at least lessen the pain of donation. This can be observed at a busy working meeting involving somewhat absentminded persons. One person will suddenly attempt to get to work writing and find that she has no pen, at which point she will turn and request one from a neighbor. The neighbor may soon realize the need for a pen, and ask for one from a different party, as the first is still busily working. The nonpen thus circulates around without actually preventing anyone from writing who has a mind to write.
Second, it is possible that the person making the current transfer is always the one who has the greatest surplus. In this case, the system is de facto redistributive without taking anything away from anyone else (permanently)—a remarkable accomplishment possible only because the system lives off the “float” involved.
The second way in which spreading out can be thus accomplished is by following A → B with B → C, etc. Using the same notation as before, we might see three states as [−,+,0,0], [−,0,+,0] and [−,0,0,+]. Here we can see the + sign as a temporary gain moving forward. Since A, however, ends up with a permanent loss, this is well suited for cases in which the cycle begins because of an unusual windfall for A. One important example of this system is discussed by Levi-Strauss (1969 [1949]: 466f, 471), namely the “marriage by purchase” found in parts of Africa. Far from being a system that individualizes the transactions (as would market purchase), the money given is not fungible and not consumed by the recipient—instead, it is immediately used to “buy” a wife (i.e., facilitate a marriage) for a brother or cousin. Thus the money circulates through the society accomplishing marriages like a Cupid.
Such a chain can be extremely efficient in redistributing surpluses in contexts in which people are separated and never get together in a forum for barter (e.g., the Tee exchange of New Guinea discussed further below; see Meggitt 1974: especially 181, 191, 195). Consider someone with a surplus of some good, which we call O1. Required to donate something, he chooses O1 to give to B. B similarly conducts an inventory and chooses the good of which he has the greatest surplus to donate. This good may or may not be O1—if it is, we can imagine O1 as a pulse that will travel until it reaches someone who lacks O1, at which point some new O2 takes off looking for someone in need of it (for an example, consider Smith 1983: 111, 117).25
We have so far investigated simple line structures, but small variations on the line can lead to dramatic concentrations of wealth, at least temporarily. We are familiar with pernicious versions of such structures such as the “chain letter” pyramid or Ponzi scheme. The essence is simple: produce a pyramidal structure in which an ever widening base sends resources upward—the constriction increases the material density, so that those at the top profit greatly. This is a zero sum system, and the universe surprisingly quickly turns to have run out of willing participants, at which point those at the bottom lose everything.
But it is possible for concentration to be a net good. For example, in one version of what are known as “revolving credit associations,” members all contribute some amount to a pot (say, $5.00 from 10 members) and each person gets the jackpot in turn. This makes sense even though the expected payoffs are exactly the same as the costs: imagine that all persons need $50 to purchase some piece of equipment. In the absence of the donation structure, all will need to wait 10 weeks (assuming all they can divert for savings is $5.00 a week) before making the purchase; with the lottery, only one of 10 must wait this long. There is a net benefit that would be lost, unless there are banks that pay interest for savings. Not surprisingly, revolving credit associations tend to arise where there are no such banks.
In between these two extremes are a variety of systems that involve temporary concentration and redistribution. Even a temporary concentration of wealth that is later wholly redistributed is a tremendous source of power, and it can frequently be harnessed by one person. The trick is to sit on top of the jackpot at a key point in the cycle; one need not even divert any of the flow to be elevated by it. We will explore some “big man” systems in chapter 6 that build on this logic; the Tee Exchange noted above also was used for this combination of redistribution and political entrepreneurship. The structure of relationships seems to have been a pyramidal spanning tree which was used to concentrate wealth, which would then be used to make matrimonial alliances which would in turn lead to material benefits, which could be used to repay those who had contributed. In essence, it allowed for the creation of giving relations between nonkin of a kind normally restricted to close kin.26 Those at key positions could amass political power by building allies who in turn would be compensated by a “pulse” of donation going the other way (Meggitt 1974: especially 189; Wiessner and Tumu 1998).
In sum, depending on how the interactions are arranged, pulse chains can facilitate complex transactions that benefit everyone who participates, though some more than others.27 While these structures can still be used to increase inequality—indeed, we shall examine this in another guise in chapter 6—they can also be used to prevent inequality. That is, a chain might pile up all the good things at one end, increasing inequality. The simplest structural solution that prevents inequality is to connect the chain into a circle. It is this solution that, following Levi-Strauss (1969 [1949]), we will term generalized exchange.
In a generalized exchange structure, each participant must make a donation to a specific other participant, as shown in figure 3.3 below. The relation of transfer cannot be reciprocated if the circle is not to be disrupted; at the same time, no member can refuse to make required transfers. But members can refuse, especially if they are more powerful than others (hence the importance of inequality that we will explore below). Accordingly, generalized exchange always involves an element of trust (Levi-Strauss 1969 [1949]: 265), yet in contrast to less-organized systems of spreading out, this trust is a reasonable one. That is, since everyone can determine precisely who is supposed to give in some situation, compliance can be assessed and noncompliance sanctioned; even in the absence of sanctions, the concentration of responsibility seems to encourage participation (see the results of Yamagishi and Cook 1993: 244).
This structure is clearly a reasonable one given the imperative on maintaining equality, but how could it arise? It cannot be due to simple urges toward reciprocity, as might be the case in restricted exchange. Let us then derive it for kinship structures. It is clear that a focus on marriage with MBD (mother’s brother’s daughter) is compatible with generalized exchange,28 for the men of lineage A all take women from the same lineage, but this is not in itself sufficient to produce a workable system. Is the system as a whole a consciously created architecture? If this were so, there should be evidence that participants are able to understand the overall construction, and hence have kinship terms to express the relevant relations (see Levi-Strauss [1969 (1949): 411, 419]). But recently, Bearman (1997) found a pattern of generalized exchange among Groote Eylandters who lacked descriptive labels for the implicit classes.
Clearly, in this case, the system could not have originated on the basis of conscious understanding of certain rules in terms of prescribed marriages between categories, even though the Groote Eylandters understood what was going on well enough to sanction those who violated these rules. Bearman (1997: 141 Iff) points out that once the system was given a jump start, one would reasonably expect it to continue on the basis of the same rational principles that Yamagishi and Cook (1993) demonstrated would keep generalized exchange circuits going among people who did not understand the whole cycle.29 The jump start might be the simple age difference between husbands and wives in a gerontocratie society. Following Hammel (1973), Bearman notes that the older husbands are than wives, the more likely they are to prefer marriage with MBD as opposed to FZD (father’s sister’s daughter). (This will be demonstrated shortly.)
Figure 3.3. Generalized exchange
We have already seen that marriage with MBD tends toward generalized exchange, as a patriline always takes women from the same lineage. Unless there are only two lineages, this either requires an infinite number of lineages or a circular system. Somehow people seem to have the foresight—at least in this case—to send the last lineage in the chain back to the first when it comes time to marry.30
In sum, it seems reasonable that “spreading out” can lead to the strong structural form of circular generalized exchange; while participants need not be able to visualize the circular structure, they often do. It may seem strange that a lineage prefers to keep taking women from one group and giving to another, as opposed to coming to a square deal once and for all, but there is a heuristic that runs in the opposite direction of the heuristic of reciprocity. In Levi-Strauss’s (1969 [1949]: 435) words: “One is the slave of one’s alliance, since it is established at the price of transferring irreplaceable, or almost irreplaceable, goods, viz. sisters and daughters. From the moment that one is bound by it everything must be done to maintain and develop it. . . . the gaining of a sister puts one in a privileged position to obtain the daughter also.”31
Thus generalized exchange is one structure that may arise to facilitate necessary asymmetric transfers while preventing a drain from one party to another. Such a situation occurs under lineages obeying some form of incest taboo. Generalized exchange is an answer based on the trust that comes from stability and equality, and a loss of either of these can shatter the system and lead to a reversion to restricted exchange, as people demand the security of immediate repayment (Levi-Strauss 1969 [1949]: 471).
The cheery scenario developed above suggests the robustness of generalized exchange—to make everything even, people tacitly agree to ties the ends of a chain together. Yet things are not always this simple. As Levi-Strauss (1969 [1949]: 266) says, confusion enters because “generalized exchange presupposed equality, and is a source of inequality.” In contrast to restricted exchange, which conserves the relation and equality between the parties, in generalized exchange one interactant is a giver and one a taker, a potential source of inequality.
This danger of inequality was most clearly discussed by Levi-Strauss in his speculative reconstruction of Indian exogamous marriage.32 If India began with a system of generalized exchange, this would break down with the development of feudalism, as the upper classes would refuse to exchange their women with lower classes, and instead shift toward restricted exchange (Levi-Strauss 1969 [1949]: 416f, 420). These upper classes would orient to hypergamy, taking but not giving women, and breaking the cycle of generalized exchange.
Further—and here I follow Levi-Strauss (1969 [1949]: 474) more in admiration of the logical consistency of his approach, which can serve as an exemplar for the current work, than in conviction that this is a defensible claim—there is a second-order solution to the stoppage of generalized exchange due to inequality, and this is to promote a select section of the lower castes to the status of worthy-to-accept-higher-caste-daughters; the Indian term for this is swayamvara marriage. Levi-Strauss argued that European (Germanic) marriage is the residue of a disintegrated generalized exchange structure turned toward swayamvara, something that would certainly explain the ubiquity of “boy-of-humble-birth-marrying-princess” fairy tales.33
While the exchange of women is traditionally seen from the standpoint of patriarchs—male elders authoritatively determining the marriages of their children—the exchange of women (here we still treat women as having no input although this simplification is increasingly problematic the more we turn to individual decisions) may also be seen as a relationship established between a young man and an old man. The former is the groom and the latter the bride’s father. Let us imagine that there are status differences between patrilines. If we assume men tend to increase in status as they age, then in a society in which “wife-taking” are generally superior to “wife-giving” patrilines,34 it will be seen that marriage with a MBD (but not a FZD) establishes a relationship between men who are rough equals.
In the diagram shown in figure 3.4, marriage relations are transformed to diagonal double lines indicating status differences between patrilines, while vertical lines are lines of descent, and horizontal ones lines of sibship. Again, we start with a male ego. Otherwise the conventions are the same as those used in the previous chapter. Woman 1 is ego’s MBD, and woman 2 is ego’s FZD. It can be seen that marriage with woman 1 establishes a rough equivalence between ego and his future father-in-law, while marriage with woman 2 does not.
This seems to be a more common response to inequality among lineages than the dual one whereby wife-givers are seen as superior to wife-takers, which would be compatible with FZD marriage, though there are examples of this,35 The rarity of female hypogamy may be partially explained by its poor fit with patriarchal principles. The former arrangement (wife-taking lineages are of higher status) is compatible with the “take take take” heuristic in which women are considered the objects—this is problematic only for the weaker lineages, and their extinction is not inherently worrisome to the more powerful.
Figure 3.4. Gerontocracy and cross-cousin marriage
For example, Padgett and Ansell (1993: 1294) argued that among the elite of renaissance Florence, it was understood that wife-giving families were of higher status than wife-accepting families (that is, that men married up).36 In this case, rather than unite rough status equals, the marriage was often intended to secure a “political lieutenant” for the higher-status and older man. Thus what Levi-Strauss saw as akin to the swayamvara marriage—the exception that completes an otherwise broken cycle that follows the rule of female hypergamy—may in fact be not so much the exception as the contrary rale—a tendency toward female hypogamy or son-in-law elevation. With the introduction of fixed capital that requires management, heads of elite households need not only heirs but assistants who can be treated as inferiors; the bride’s father looks for a worthy recipient of lesser status who will accept subordination and a bride as a package deal. Wife takers are thus of lower status than wife givers, and sons thus marry women of higher status than themselves.
What resulted, according to Padgett and Ansell, was a treelike structure down through which women trickled.37 Of course, this is no solution to the problem of inequality with which we began—in contrast to a system of generalized exchange, a “trickle down” structure means that some groups become bereft of women and hence extinct. In hypergamous systems it is men of the lowest ranks who may be forced to remain unmarried; women of the highest ranks may have difficulty marrying, although this is not necessarily the case in polygamous societies. But given that Florentine sons had to marry up, those of the most distinguished lineages were hard pressed to marry—there was no one good enough for the sons of the elite to marry. In this case, there was no elegant structural solution, but rather a cheat: the elite, argue Padgett and Ansell, snuck away to other neighborhoods to find women as opposed to effectively announcing to their neighbors that there was a family of higher status than themselves.
In sum, the pulses of donations that lie at the heart of the cycle of generalized exchange can redistribute a surplus and deal with the inequality introduced by a windfall or a shortfall. In the simplest case (marriages arranged by an oligarchy of imperious patriarchs, equal in power to one another, who only care about maximizing their number of male descendents) we can assume a simple relationship between heuristic and structure. As we turn to progressively more complex environments, there is room for greater slippage between structure and subjectivity. I close this chapter by exploring how people may internalize the logic of these structures, and how these structures may fit into a wider class of mating systems.
Starting from the perspective that women are valuable yet cannot be kept within any specific lineage, we have seen the development of a number of structural problems. There are in turn a number of solutions that imply local structure, most important the “exchange of women.” Because it is rarely the case that two lineages have women available for an actual exchange, this imperative can lead to rules of preferential marriage. These rules can be dually understood in terms of classes; such subjective comprehension in terms of classes—especially if they are given names—is frequently easier than thinking in terms of kinship preferences.38
But the existence of such classes is not necessary for the structural solutions. Most obviously, dual organization can be coordinated through cross-cousin marriage, without named moieties. For example, the Yanomamö prescribe bilateral cross-cousin marriage (that is, “wife” is placed in the same category as structurally equivalent with both father’s sister’s daughter and mother’s brother’s daughter). Not surprisingly, their villages tend to have two dominant lineages. “But while dual organization exists in a de facto sense, there is no overt ideology of dual organization. That is, the village does not have named halves, rules stipulating that half of the village should be the domain of one lineage and the other half the domain of the second, etc.” (Chagnon 1968a: 141, 143). Instead, dual organization arises naturally from the limited trust that prevents generalized exchange—“males stand a better chance of obtaining a wife if they give their sisters consistently to the same group, for by giving women one can therefore demand them in return” (ibid.: 144). That is, rather than attempt to manage many exchanges, each of which may be insufficiently strong to provide a source of women, they prefer to put all their eggs in one basket.
Even further, more complex structures may lack any simple duality between categorical analysis and strategic analysis (that is, analysis in terms of heuristics). Thus Tjon Sie Fat (1990: 113) points out that there are distinct structures—that is, sets of classes of equivalents—that have the same marriage rule (for example, that male ego’s spouse is in the same class as FFZDD). But the structure cannot be wholly derived from this heuristic alone; thus the heuristic is not correlative to a distinct structure.
Classically, it was assumed that complex structures involved the layering of multiple prescriptive systems (multiple elementary structures) or the progressive attenuation of their prescriptive force (cf. Levi-Strauss 1965: 20). But Tjon Sie Fat (1990: 226, 249) has questioned this, and instead proposes that, just as simple deterministic systems can lead to complex behavior when initial conditions are weighty, so much of complex behavior in kinship systems “may be the result of local interactions governed by simple rules.” In other words, both simple and complex structures may have subjective correlates that are simple heuristics—the difference lies in the initial conditions that actors face as they try to carry out these heuristics. Just as a generalized exchange structure might be understood as the combination of preferential MBD-marriage given a certain number of preexisting lineages as inexplicable initial conditions, so complex marriage structures may simply result from a different set of initial conditions.39
That is, if our question is “what structures arise given asymmetric relations?” we find that our answer has partly to do with the nature of the relationship and partly to do with other conditions. If we compare relationships to molecules and structures to crystals, we recognize that the initial conditions under which relationships begin to crystallize can make a great deal of difference to the resulting structure. Thus we cannot expect a general one-to-one mapping between relationship and structure, not even between heuristic and structure.
Evolution and Strategy
A second level of complication may arise when more than one heuristic is available to guide choice. The layering of multiple ways of understanding action can introduce exponential complexity into structure without introducing randomness. Boyd (1969) has suggested that the elaborate elementary structures found among Australians may arise as successive introductions of distinctions. Boyd examines the Arunta eight-class system, which can be seen as alternating four-class generalized exchange.40 This confusing system may be derived algebraically as the successive addition of less complex heuristics, to wit (in temporal order) first a division into matrilineal moieties,41 and then a superimposition of patrilineal moieties.42 If there is then a division within the restricted exchanging classes between “wife takers” and “wife givers,” one has the eight-class system.
Whether this particular derivation is historically accurate is beyond our ability to judge. But this approach links the complicated structures with a number of heuristics that can be intuitively understood, as they spring from an attempt to make distinctions—distinctions between one’s mother’s people and one’s father’s people, and distinctions between givers and takers. In contrast to the joking-avoidance systems, in which such distinctions lead to only two classes that are paradigmatically different for all persons, here we have sets of stable equivalence classes, which might seem much more constraining on the action of the individuals involved.
In this case, the multiple prescriptions are mutually reinforcing; in other cases, they appear as alternatives that obscure structure. For example, the Iatmul of New Guinea had a number of prescriptive rules of exogamous marriage: marriage with FMBSD (“a woman should climb the same ladder that her father’s father’s sister climbed”), with FZD (“the daughter goes as payment for the mother”) and with ZHZ (“women should be exchanged”) (Bateson 1958:88–91). Multiple rules increases the flexibility with which one can act.43 But even this flexibility was not always enough, and Bateson found some endogamous marriages. These “tabooed” unions were explained with a shrug: “She is a fine woman so they married her inside the clan lest some other clan take her.”
How to explain this combination of rule-bound and rule-breaking action? It is correct, but not enough, to point out that for every law, there are conditions under which it makes sense to bend or break it (see Levi Strauss 1953: 538; Chagnon 1990: 96; Hart and Pilling 1966: 27, 57), and that this may lead to an inability to understand the resulting actions in purely structural terms (cf. Bourdieu 1990 [1980]). It is that the presence of alternative prescriptions makes it easier for these heuristics to be unmoored from particular structures. Structure has passed into institution—the frustration of many anthropological fieldworkers at the dissociation between actual marriage patterns and the norms expressed by informants is the result of the informants bringing these regularities to the same sort of conscious explication sought by the fieldworkers.
But pursuing this theme requires a more complete overview of the sets of structures that develop (and forms the core of the final chapter). Let us return to the question of what structures emerge for the relation of marriage between lineages. We find that the choices facing persons as they navigate the relationships—the trade-offs they face—are closely related to those explored in the previous chapter. Different heuristics can be employed depending on how one wants to handle any particular problem; sets of responses that use reinforcing principles cohere as systems (in this case, marriage systems). I close by considering these.
We have been examining well-studied structures that allow a system of transfers to avoid the production or exaggeration of inequality, despite the lack of mutuality of the fundamental relationship in question. The strength of such a system of generalized exchange is, however, its weaknesses—it claims too much in terms of the equality of participants. A lineage B gaining in importance can reasonably expect to receive women from A without giving any to C. It is probably not accidental that such systems thrive in conditions in which the threat of inequality is relatively low in two ways. First of all, material differences in wealth are less than in most other societies, and second, polygamy allows for what inequality there is to affect the number of connections made, not their nature.
We have followed this logic for the case of mating, but it is worth pointing out that this is not the only way to handle these tendencies toward inequality in this relationship. The first, which was raised at the end of the last chapter, is to go toward hierarchy; indeed, to embrace it in a principled fashion via a popularity tournament. This is the position marked “preferential attachment” in the figure at the end of chapter 2. A classic example for mating structures is the “rating and dating” system analyzed by Waller (1937). Here the problem of inequality arises in the form of a substantive contradiction between the mutuality established by the relationship (pairing) and the competitive ranking of persons in which every relationship begun or finished changes the balances that define equality. This problem is hard to solve simply through a determination to police the equality of the relationship. As Sprecher (1998) has found, emphasizing exact reciprocity in romantic relations—the paradigmatically rational action of refusing to accept transactions in which the costs outweigh the benefits—actually decreases subjective utility, since (given the human folly of overestimating one’s own sacrifices and minimizing others’) the closer the attention to reciprocity, the less likely that one will actually reciprocate.
The second polar position is to move toward mutuality and equality: vertical differentiation is suppressed by adopting a spatial model of likenesses (as in chapter 2), which I shall call homophily (one likes—or at least chooses—those like one). In this case, the closer one person is to another in social space, the more one loves the other, and since distance is inherently a symmetric quantity, the more that one is loved in return. This must beg the question—if there is a vertical ranking of persons in terms of some preexisting inequality, then homophily solves the problem of inequality by making it the solution. That is, imagine people ranked vertically, all looking upward and wishing they had someone closer to the top. The homophilous solution is more or less to knock this tower on its side and make sure that people now look for those who are close to them—in what was previously vertical position—without changing the overall ranking or disturbing the tendency for those of similar rank to pair.
Further, this solution leads to a tendency toward fragmentation that is a parallel to the dyadic withdrawal discussed by Slater (1963). This is what lies behind Levi-Strauss’s reconstruction of Indian marriage, and the problem that faced some of the Florentine elite: if everyone insists on only marrying their equals, their society will cease to hold together as a solidary unit, but instead will shear off into separate layers. Marriage relations will not “spread out” and unify the group, which is accomplished by the generalized exchange structures that we have been discussing.
At the same time, the emphasis on likeness does solve the instability of preferential attachment. Because relationship formation is dependent on external considerations (as opposed to being wholly endogenous), we do not see the positive feedback of the popularity tournament. The logic of relationship formation may be unequal (all want to marry those from the richest family), but making a relationship does not increase the inequality (the wealthy do not get wealthier from marrying the poor).
These three possibilities may be schematized as follows (see figure 3.5 below). The parallel to the figure at the end of chapter 2 arises because there are similar trade-offs: between organizing relationships in terms of preferential attachment at the cost of true reciprocity or spreading out across the group, and so on. Classical anthropology has focused on cases in the bottom right, while analyses of American society based on college dating have generally focused on the upper corner. Analyses of marriage in the modern West have been more likely to accentuate the model given in the bottom left corner.
Of course, existing structures often involve a trade-off between these three imperatives, and it is possible to join an attempt to “spread out” with a spatial model of tie-formation. Thus in recent work, Bearman, Moody, and Stovel (2004) find dating structures in American high schools tend to form “spanning trees,” simple graphs that can be understood as arising in a number of ways but have the notable properties that they efficiently connect as many nodes as possible with as few redundant ties as possible. (Technically, a spanning tree is a graph that has N-1 lines connecting N nodes.) Using the terminology from the previous chapter, we may envision this structure as the result of tie formation that follows a spatial but antirelational logic: one wants to pair with those like one, but not those to whom one is already indirectly tied.44
Figure 3.5. Mating systems
Although this scheme is then oriented around pure cases, it may be of use in organizing the actual dispersion of mating systems, because these dimensions are likely to vary in importance in accord with well-understood structural attributes. I have argued that classic exchange structures arise when lineages exist that could conceivably splinter off of a larger social group. In such a case, it is crucial that the structure connect persons, and to the extent that stratification impedes this, stratification is a threat.
Where such lineages do not exist, yet mating decisions involve substantial capital investments (capital in the broadest sense), it seems that the degree of homophily becomes the most important thing in leading to successful pairings. In such cases, it is understood that the decision of whom to marry is not an automous one—one that neither refers to which partner is most attractive (preferential attachment) nor to the involute rules of marriage classes. Rather, the relationship formation is structured because it is dependent on other factors, most important, the wealth or status of the family of the prospetive partner.
In the periods in which mating is divorced from such decisions (such as in “dating”), endogenous stratification may emerge as the organizing principle of mate selection. In other words, the mere fact of selection can generate a popularity tournament, but it takes something more to turn this into a viable social structure. This “more” is the suppression of group interest. Both solutions at the bottom of the triangle are compatible with the preservation of a lineage’s acquired capital—to the left, this capital is material and cultural, and to the right, it is the women themselves.
“Group” interest, however, is an abstraction—we were able to use this idea nonproblematically when (for purposes of derivation) we assumed patriarchy, a particular combination of unilineal descent and despotic control. There are other conditions in which group interest may be a reasonable simplification, but in general, we should expect that as we move away from these conditions associated with patriarchy we allow for mating structures to move away from the bottom of the triangle, something that Collins (1971) discussed in terms of the emergence of sexual “markets” in mating.45
It is worth briefly noting that these dimensions have some correspondence to the three dimensions of organization discussed by Harrison White (1992), namely differentiation, dependence and involution. When organization arises because of the stratification of individuals, we may say that there is high differentiation of persons. When this organization relies on homophily, namely the existence of distinctions external to the mating structure, we may say that we see high dependence—that is, what takes place in this area is dependent on valuations made elsewhere. Finally, when the organization involves an orientation toward the group as a whole and involves the linking of relationships in a particular way, as in the “impluse to spread,” we see a tendency toward involution—that is, a particular form of nonindependence of relationships that makes reference only to the pattern of other relationships. In the previous chapter, we saw such organization as related to transitivity being itself a principle of organization. But just as there, here we see that this does not mean that other ways of leading to organization do not lead to transitivity.
Let us consider the nature of transitivity of relationships for each of the polar positions. In the “stratification” solution, attempted pairings are transitive but uninterestingly so—the transitivity of choices is a by-product of the more fundamental fact that individuals are rankable. There is no other pressure toward transitivity. Thus if the top ranked person A “mistakenly” chooses the bottom ranked Z who also chooses the mid ranked M, there is no increased tendency of A to choose M. In the “homophily” solution we see the limited transitivity of the spatial logics we examined in chapter 2—because the probability of tie formation decreases with distance, the impulse of sociation dies out after a few links. In the generalized exchange structure, relations are actually necessarily antitransitive. If lineage A gives women to B and B does to C, A will not give women to C. And yet precisely because of this nontransitivity, the whole is engaged and no part can be removed. In all cases, then, a successful solution to the problem of inequality is incompatible with transitivity—either the group can be linked with antitransitive relationships, or the transitivity of relationships must be localized.
Let us conclude by returning to the problem of inequality. In the solution at the top of this figure, isolated individuals who need not preserve a lineage’s balance vis-à-vis other lineages generate a hierachy via a popularity tournament. Because they are unconstrained by a structural imperative to preserve equality, they are free to develop a structure that maximizes inequality. And this, too, is a consistent way to handle the potential for inequality in asymmetric relationships—to systematize it, to make it clear and consistent.
In other words, instead of trying to ensure that transfers balance in general (as in generalized exchange), or by tying two transfers going in different directions (restricted exchange), or converting the relation to a mutual one (homophily), one may cast aside any attempt to preserve equality and convert the asymmetric relations to necessarily antisymmetric ones. One may turn, as Levi-Strauss (1953: 547) said, an intransitive and cyclical system into a transitive and acyclical one. The simplest arising structure is an order of statuses—it is akin to taking the results of a popularity tournament and elevating them to the status of social law. It is to such structures that we turn next.
1 The 27% comprising the richest group gave 44% of the gifts, while the 19% comprising the poorest gave proportionately little (9% of the gifts) and received proportionately more (28%). Yet as Bollig notes, the rich also received a fair amount of gifts (23% of all).
2 That is, there are more reciprocations than expected simply because some people both gave and received a great many gifts.
3 Because some people gave nothing and others received nothing, their parameter values are technically infinite. Depending on what was chosen to replace this infinite value, the overall correlation was affected, but outside of these cases, there was no relation.
4 Compare Hage and Harary’s (1983: 36) analysis of a taro exchange system in Melanesia, which also finds relative egalitarianism combined with more central positions of village leaders. Schwimmer (1973: 119, 126) in the original analysis of this Taro exchange similarly found that there was little evidence of a concern with exact balance.
5 Three edges (i,j) in the graph were chosen at random, with all edges getting equal weight. For each, starting with node j, an edge leaving j was chosen at random among all edges not already illustrated. The path stopped when that last j had no more new edges.
6 It is both fascinating and deeply saddening to realize that these same mistakes were made by the supposed archenemies of the (individualist) exchange theorists, namely the (collectivist) functionalist theorists. As Gouldner (1960) has argued, they had the same incentive to find creative functions for every institution no matter how dreadful, and hence extortion structures could be similarly valorized, only the invented utility went to the group, not the victim. As a further consequence, they were led, as Gouldner emphasizes, “to neglect the larger class of unequal exchanges.” Evidently, theoretical orientation is not as important as the desire to normalize when it comes to the direction of theorizing.
7 See Stinchcombe (1990: 300). Generally conclusions regarding equality in exchange require additional assumptions that goods are infinitesimally divisible or that utilities are perfectly transferable across the trading partners outside this particular exchange. That is, if I trade a wagon for your air rifle, and your air rifle is better than my wagon, I will make it up to you in some way. Refraining from making this assumption leads to a class of noncooperative game-theoretic approaches that do not imply equality of exchange.
8 For a pertinent example given the marriage exchanges we will explore below, Chagnon (1968a: 123) reports that weaker Yanomami groups that are forced to accept unequal exchange of women with some ally do have the option of “exit” but are reasonably afraid that their new neighbors will prove “even more exorbitant in their demands.”
9 I have shown how this undermines Coleman’s theory in Martin (2001a). Scott and Kerkvliet (1977: 449) are attentive to the problems that such extortion—quite common in actual social life—poses for equal exchange arguments. Furthermore, they point out that using the language of exchange fools nobody into thinking a protection racket is the same as hiring real protection. If an economic analysis cannot distinguish them, this speaks poorly of the analyst, not well of the racketeer.
10 Much of recent work in economic sociology has attempted to deemphasize this distinction between the rational antistructure of pure markets on the one hand and the (economically) irrational structure of premarket society on the other, an attempt that increases the verisimilitude of studies of concrete economic relations in market societies but also downplays the very real differences between market and nonmarket societies. In particular, the important findings that force recognition that even “pure” markets have a social structure that has observable consequences (Swedberg 1994; Lie 1997; for a classic example see Baker 1984) can impede attention to the structural forms of exchange that arise in the absence of a market. In other words, to say that all markets have (some) social structure does not mean that all exchange structures are markets.
11 Becker (1991: 130–34) famously uses a market approach to examine the joint utility of dyads, but this requires that utilities are perfectly transferable across persons, an assumption that is difficult to defend without generating paradox.
12 In a number of societies sharing is enforced by taboos against eating what you yourself have hunted; for the Guayaki of Paraguay, see Clastres (1972: 168ff).
13 As Barth (1981: 66f, 72) emphasizes, bilineality of inheritance generally undercuts the capacity of lineages to cohere as corporate bodies, but so do other disruptions pertaining to unequal transmission of inheritance in land.
14 An example might be the Tiwi of Australia, who made sure that all females (from birth if not before) are betrothed to some man; the details were in the hands of her mother’s present husband (Hart and Pilling 1966: 14–20, 52), who used this asset to make alliances, repay debts, and invest in others. (“Tiwi men valued women as political capital available for investment in gaining the goodwill of other men more than they were interested in them as sexual partners.”) Although widows escaped this control, and might have more say in their next marriages, they were also often under the thumbs of their brothers, or if older, those of their sons.
15 In essence, this problem may be compared to one of dirty people looking at each other through binoculars. Dirty people are likely to have dirty binoculars, which means that when they look at others, they are convinced that these others are very dirty. However, we cannot from this argue that all persons are clean—surely if there are so many dirty binoculars there must be some dirty people.
16 It is possible to develop a coherent structural approach to kinship as exchange starting from a bilineal system, as in the Leiden tradition. This approach is mathematically more general and leads in somewhat different directions. Most important, it blurs the distinction between generalized and restricted exchange. Thus a system of generalized exchange between four patrilines and four matrilines in which from one perspective, patrilines (or matrilines) exchange women (men) circularly, can also be seen as a system in which four groups are split into two sets of pairs taking part in restricted exchange, with children from any class being in a different class from their parents (e.g., Tjon Sie Fat 1990: 13, 21–22).
One important example forces a qualification of Levi-Strauss’s dim view of the possibility of restricted exchange to produce unified societies. Tjon Sie Fat (1990: 198, 209–11) follows Turner and others in showing how marriage with father’s father’s sister’s daughter’s child in a four-class system can lead to restricted exchange at any generation, but the exchange partners alternate over three generations, leading to an indivisible society. A similar six-class system can alternate over two generations (thus children from matriline A marry opposite sex partners from matriline B in every odd numbered generation, but marry from matriline F in every even generation, so the structure cannot be split into two independent components).
17 Adoption also has these structural characteristics, and it is significant that there are cases such as the Palauan in which adoption is used to tie lineages together, in that one family may request an infant from another family in order to create bonds of obligation. This may be a major source of social structure; more than half of the Palauan population studied by Smith (1983: 58, 184, 204f; also 207f, 223, 240, 244) had been adopted by another household.
18 Levi-Strauss did not deny that there are cases in which men are in fact exchanged; on the duality between matrilineal and patrilineal analyses, see Levi-Strauss (1969 [1949]: 385, 409).
19 Further, even in matrilineal cases it may actually be more accurate to understand action heuristics as men exchanging women. For example, among the Palauans, matrilineages are headed by men, who are in charge not only of the female descendents but other men who attach themselves as clients. These heads attempts to increase the standing of his matrilineage in part by facilitating marriages of women in the matrilineage with men of other matrilineages. These ties are understood setting up conduits through which certain goods will pass (Smith 1983: 54, 78).
20 Thus the exchange of women may indeed be central to patriarchy. Rubin’s (1985) emphasis on this was reasonable, but she wrongly extended this to European societies with different marriage systems.
21 Chagnon (1968a: 110) stressed the woman-stealing aspect of Yanomamö intervillage relations; recent evidence has cast doubts on Chagnon’s emphasis on the nature of Yanomamö conflict, but his work on marriages is considered reliable and will be used below.
22 Thus a man in moiety A (AM) must marry a woman in moiety B (BF), while a man in moiety B (BM) must marry a woman in moiety A (AF). We can accordingly see four classes, AM, BF, BM, and AF, where classes are paired off and men circulate among classes in that the son of a man is in a different class from his father (Levi-Strauss 1969 [1949]: 146). There are other possible forms of dual organization in marriages that can arise but are not considered here, such as the “sidedness” discussed by Houseman and White (1998a: especially 79, 83f), which cannot be represented as a set of classes under unilineal descent. Sides are more complex entities that can develop in a set of bilaterally structured roles that have to do first and foremost with relations to land.
23 It is important to note that this does not imply that the two lineages in question only have this relationship with each other—each may have a relationship of continuing exchange of women with a number of other lineages, just as businesspeople keep accounts with a number of others.
24 On these two types of generalized exchange, see Yamagishi and Cook (1993); for a clearly defined spreading out marriage heuristic see Smith (1983: 92f).
25 The Melanesian taro exchange studied by Schwimmer (1973: 130–36) demonstrates a similar principle of interaction with those geographically close, still linking an overall system together such that one object could in principle get from any one place to any other via intermediaries.
26 Importantly, these pseudo-kin relations were not transitive, although kinship normally is (Wiessner and Tumu 1998: 300). If it were, it would threaten to have an “ice nine” effect (the example given in chapter 2) and make too many people kin.
27 Even in the simple form of an endless cycle in which no exchanged goods are actually consumed, such as the archetypal kula ring of the Trobriand Islands, all individuals benefit simply from having their fifteen minutes of fame when they hold the ritual goods. See Hage and Harary (1991: 158, 167) for support for Malinowski’s (1922) original interpretation.
28 Tjon Sie Fat (1990: especially 128) shows that there are other preferential formulas compatible with generalized exchange.
29 In particular, a quest to preserve balance in the sense that equivalence relations are consistent (e.g., the person whom the person you call brother calls mother is someone whom you can call mother) leads to reinforcement of the system.
30 This example highlights the increasing conviction that classic models paid insufficient attention to age differences and their structural correlates, particularly the incompatibility of age bias and straight sister exchange or bilateral cross-cousin marriage (e.g., the simplest restricted exchange forms) (see Tjon Sie Fat 1990: 147f, 153ff, who formulates these as “spirals” in a cylindrical surface of generalized exchange that would lead to circles if there were no age bias). It is possible for the simplest heuristic of marriage with mother’s brother’s daughter to be compatible with an age spiral; if ego’s father married a woman x years younger than herself, chances are that her brother’s daughter will be around x years younger than her son. But other structures, based on marriage with sister’s daughter, are also possible given a severe age spiral.
31 This same logic can be seen in international capital flows, which often seem consciously intended and understood as “donations” intended to establish a lasting social relation and not as investment decisions determined on the basis of forecasted returns. While some debtors are “too big to fail,” and hence it is in the interest of creditors to extend new loans if there is a possibility that they will contribute to solvency, the same pattern of “sending good money after bad” is found where debtors are small enough to fail. There is evidently an understanding that a relationship has been established that allows the donor (creditor) to have a fair amount of avuncular authority and gives the recipient (debtor) moral claims to further aid.
32 Levi-Strauss (1969 [1949]: 419f) also suggests that in India a system of generalized exchange may have incorporated a group of external conquerors, but I will focus on the other possibility, namely the differentiation of statuses within an originally homogeneous society. Although the former may be historically closer to the truth, the latter may better express the tensions inherent in generalized exchange. Certainly many Indian subcultures combine patrilineal exogamy with hypergamy, in that the wife’s family must be lower ranking than the husband’s (e.g., the Rajput of Khalapur) (Tjon Sie Fat 1990: 280).
33 Unfortunately, there are also a number of “girl-of-humble-birth-marrying-prince” stories.
34 It is not necessary that these status relations be transitive—it is possible for a circular generalized exchange system to exist with all participants considering themselves superior to those who give them wives for the very reason that the latter are wife-givers.
35 Thus among the Tanimbar of Indonesia, others are divided into one’s patrilineal descent group (“Men brothers”), wife-givers (“masters”), and wife-takers (“Sister’s child”) who are regarded as inferior (Tjon Sie Fat 1990: 224f, 266).
36 Padgett and Ansell make the doubtful argument that this is linked to the general prestige that accrues to a donor—since this is not a usual pattern in the societies studied by the anthropologists to whom they refer, this is not convincing (also see Sahlins 1968: 57). It may perhaps be that in the European context in which land was scarcer than labor (in contrast especially to Africa), and hence bridegrooms generally “worth” more than brides (hence dowry as opposed to bride-price), a man from a low-ranking family was equivalent to a woman from a high-ranking one, and thus wife-givers would tend to be of higher status than their wife-takers.
37 Padgett and Ansell (1993: 1295) called this a “hierarchical linear tree” or “pecking order,” but actually drew nonlinear (that is, horizontally differentiated) trees. This form will be called a “triset” in chapter 5 and is a common social form of directed diffusion.
38 In the preface to the 2d edition of the Elementary Structures of Kinship, Levi-Strauss (1969 [1949]: xxxiv) seemed to move away from the emphasis on subjective understandings; in trying to clarify his position on the reality of the preferential rules that were related to each structure, he claimed that the test of a structure was precisely the degree to which spousal matches corresponded to categorical relations to ego; a “preference” in this understanding had nothing to do with ego’s subjective inclinations, but had more to do with statistical overrepresentation. Yet Levi-Strauss (1965: 16) also argued that the role of deliberate, reflective systemization of marriage rules on the part of “so-called primitives” should not be underestimated.
39 Tjon Sie Fat (1990: 252, 254) pursues a number of interesting structures that correspond to plausible rules (e.g., male ego takes a spouse from the same line into which his mother’s brother married in the previous generation by selecting MBWBD, which may be equivalent to FFZDD). He shows that given such rules, different initial conditions can lead to steady state or cyclical structures. Since there is generally more than one way of describing a potential spouse, which subjective system is used to understand existing structural arrangements may begin to turn an existing structure one way or another. When any ego can choose from more than one type of permitted spouse (and hence simple permutations that involve one-to-one mappings are inapplicable), the system may remain highly structured yet largely opaque to traditional methods of analysis. Further, there are many cases in which rules that have different structural implications (e.g., sister exchange and marriage by purchase) exist side by side (Tjon Sie Fat 1990: 257, 195).
40 In this system one may marry a person of the opposite sex from one’s father’s mother’s class, men are in the same class as their grandfather (which is implied by the former consideration), one’s grandmother’s grandmother is in one’s own class, and one’s father’s great-grandmother is in the same class as one’s mother’s father.
41 This establishes that one is in the same class as one’s mother and one’s grandfather, but not one’s father. It is also possible to derive the system from patrilineal moieties that are then divided.
42 This leads to a four-class system where one’s father’s father and one’s mother’s mother are from the same class as oneself; this is restricted marriage with alternating classes (that is, there are four classes, where class 1 marries class 2 and has children in class 3 if the father is from class 1, and children in class 4 if it is the mother who is from class 1; classes 3 and 4 similarly intermarry).
43 Indeed, Sahlins (1968: 59) suggests that the reason bilateral cross-cousin marriage is more common than either prescriptive MBD or FZD marriage is simply that it allows elders more room for strategic considerations without violating prescriptions.
44 Bearman, Moody, and Stovel (2004) suggest that the structures observed arise because of a tendency for the network to move away from cycles, as people follow the heuristic,“don’t date your ex’s ex’s ex.” But such structures are also produced if people are distributed in a space, and they try to establish ties to those of the other sex relatively near them. As they end relationships, they turn to others relatively near them. If they do not have too many partners, simulations demonstrate that spanning trees result.
45 The reader will note that there is no place where “restricted exchange” is located in this triangle, and this is because the fundamental idea is too vague. As Tjon Sie Fat (1990) emphasized, some systems called “restricted” can unify an entire society; but this terminology is also compatible with a complete atomization of choices and destabilization of a group.
