The long waves of alcohol consumption: A social network perspective on cultural change

Social Networks 8 (1986) 1-32 North-Holland

1

THE LONG WAVES OF ALCOHOL CONSUMPTION: A SOCIAL NETWORK PERSPECTIVE ON CULTURAL CHANGE

Ole-Jorgen SKOG * T

National h)stitute for Alcohol Research **

Official records of alcohol consumption, as well as other historical sources, tell a story of variations which are both long-term and large-scale. In the first part of this paper the nature of these variations is discussed; also, the trends in alcohol consumption in Norway during the period 1851-1982 are analysed, in both the time domain and the frequency domain (spectral analysis). On the basis of the results, the question is raised whether the observed wave-like variations are suggesting the existence of a cyclical, recurrent process, or if they are the result of a less systematic and persistent mechanism, ln the second part of this paper a theoretical argument for the latter hypothesis is outlined, which links the problem to the alleged collective nature of the drinking culture. The argument is based on a model of dynamic processes of behavior modification in social networks, which links macro-level changes to micro-level mechanisms. It is argued that pseudo-cyclical patterns, very similar to those observed for alcohol consumption, can be produced by processes which operate without a persistent direction, and have their roots in these micro-level mechanisms.

1. Introduction

Since World War II, alcohol consumption has been increasing in most of the industrialized world. However, the 1970s brought a halt to this trend in many countries, and during the last few years the consumption level has even shown signs of a downward trend in some countries. These changes have created a renewed interest in the long historical trends in drinking cultures, with respect to consumption patterns, consequences of drinking, and political control measures. By studying the experiences of the past, one hopes to attain a better understanding of contemporary shifts in consumption trends and moral climate. * I thank Carole Giunta for correcting my spelling errors, and Lie Skog for drawing the diagrams. ** Dannevigsveien 10, Oslo 4, Norway. 0378-8733/86/$3.50 © 1986, Elsevier Science Publishers B.V. (North-Holland)

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O.-J, Skog / Alcohol consumption

Alcohol consumption apparently was very high in many cultures during the first decades of the 19th century. Towards the middle of the century, consumption seems to have declined in many countries. This new trend lasted for several decades into our own century. As several scholars have pointed out, the explanatory variables normally referred to in relation to the strong increase in alcohol consumption after World War II (e.g. increasing leisure time, higher incomes, urbanization, etc.), do not seem to explain the downward trend in the last century. It has been suggested, therefore, that such factors may have only a limited impact on the drinking culture. Some writers have suggested that the long downward trend in the 19th century may be related to the birth of industrial capitalism (e.g. M~ikel~i 1983). Extensive alcohol abuse may affect the productivity of the workers, and create a need for disciplining the working class. The problem with this explanation is that the decline in consumption seems to have started too early for the industrial revolution to offer a convincing explanation, at least in some countries. Another difficulty with this explanation is the fact that consumption seems to have gone down in rural as well as urban areas. In Norway, this occurred both among land workers and land owners, according to the sociologist Eilert Sundt's unique empirical study of inebriety in Norway in the 1850s (Sundt 1859). Furthermore, the productivity of workers must have been a problem in feudal economies as well, and waves of declining consumption might not be a unique phenomenon related to the new modes of production. There has been some speculation that the latter argument might be extended further into a hypothesis that long waves of increasing and decreasing consumption may have been recurrent phenomena throughout history. During long periods with high consumption levels, a growing concern for the harmful effects of drinking, such as those on morality and public order, productivity, the use of scarce resources (production of food versus alcohol), and so forth, may typically have given the beverage alcohol a bad reputation. Declining consumption may have been a likely outcome in many cultures, and it may have taken considerable time (perhaps several generations) before a new growth in consumption could take place. On the other hand, there is difficulty with this hypothesis in that the negative consequences mentioned above, which drive this hypothesized system, may be operative primarily in cultures where excessive intoxication is a typical mode of

O.-J. Skog / Alcohol consumption

3

behavior. It is also possible that this hypothesis is only relevant to the drinking of distilled beverages, and distillation is a fairly recent invention. Hence, a hypothesis of recurrent cycles may be valid only for some cultures, and only for the most recent centuries. The empirical support for such hypotheses is of course scarce, since reliable consumption data are available only from the middle of the 19th century in most countries. Furthermore, the data which are available on consumption trends during the last 100-150 years have not been analysed properly, and no one seems to have attempted to uncover the structure of the processes of change in any great detail. Such an analysis might give valuable hints about the dynamics underlying these trends. One central question is whether the trends are in fact the result of persistent and systematic forces operating over prolonged periods of time, or if they are the result of a less systematic mechanism. The argument regarding the industrial revolution seems to s u p p o r t the former mechanism, while the hypothesis of recurrent cycles might support either mechanism. A version of the latter hypothesis where the social control is executed by the state, probably supports the former mechanism, while a version with informal social control as the basic principle may be representative of the latter type of mechanism (see below). The first aim of the present study is to approach the long waves of alcohol consumption with modern analytical tools, in an attempt to shed some light on the mechanisms generating these waves. In particular, the problem of persistent versus nonpersistent patterns of change will be put into focus. Univariate time series analysis will be used in an attempt to uncover the series' internal structure, rather than its relationships to other measurable phenomena, such as economic development. The latter approach will be taken up elsewhere (Skog 1984a). The second aim is to formulate a theoretical argument regarding the developmental dynamics of drinking .cultures. The intention is to give an outline of the dynamics of informal social control, rather than the formal social control. This does not imply that I consider formal social control, or even factors exogenous to the drinking culture such as economics, politics and so forth, to be unimportant. It simply implies that I prefer to investigate this particular mechanism in more detail than there would be room for in a broad perspective article. The theoretical argument formulated here is an extention of a line of

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0.4, Skog /Alcohol consmnption

thought developed elsewhere (Skog 1977, 1979, 1980a, 1985). The general perspective is that of large-scale social networks, which are conceived as structural entities, of paramount importance for understanding the dynamics of cultural change. The result of the empirical analysis in the first part of this paper will be used as a point of departure. At the risk of overstating the obvious, I should stress at the outset that the nature of this dynamic cannot be logically deduced from the data. The deductions go in the opposite direction. From presumed mechanisms one can deduce certain structural features. When present, these empirical facts may be said to support the proposed mechanisms, but since it will always (or nearly always) be possible to find other mechanisms with similar consequences, support is not the same as proof.

2. An analysis of the Norwegian experience 1851-1982 2.1. Data and methods

Changes in the taxation laws for distilled beverages in the late 1840s, coupled with new production technology for beer, which led to centralized production and rapid growth of the beer industry during the same period, made it possible to construct reasonable accurate statistics for alcohol consumption in Norway from 1851 onward. Statistics for beer, wine, and distilled beverages are available. However, the present analysis was restricted to consumption in terms of pure alcohol per capita, 15 years and older. Univariate time series can be analysed both in the frequency domain and in the time domain. These two methods complement each other, as they each bring different aspects of the variations into focus. Therefore, both methods have been used here. Analysis in the frequency domain is known as spectral analysis, or applied Fourier analysis. This approach is especially suited for uncovering cyclical or periodic patterns. Through the use of this method, sinusoidal curves are fitted to the data and to see how much of the variation can be statistically "explained" by curves of different wavelength, or equivalently, different frequencies. (The frequency, measured by the number of cycles per time unit is inversely proportional to the wavelength.)

O..,L Skog /Alcohol consmnption

5

By fitting many sinusoidal curves simultaneously to the data, one can obtain an accurate description of the series. In fact, one can decompose any univariate time series into a set of sinusoidal curves. By choosing the wavelengths (frequencies) of these curves in a suitable way, the total variance of the observed series can be decomposed addifively. Each wavelength can, in effect, be ascribed a certain percentage-wise proportion of the total variance, which the corresponding sinusoidal component "explains". This is a result of the analysis, and is called the spectrum of the series. If truly cyclical patterns exist in the data, certain wavelengths would explain a disproportionate fraction of the variance, that is the spectrum would have a peak at certain wavelengths. The spectrum can be estimated in many different ways (cf. Chatfield 1975; Jenkins and Watts 1968). Since there are reasons to expect a fairly smooth spectrum, I have applied a so-called Tukey window in order to suppress erratic fluctuations, due to estimation errors. I have also estimated the spectrum by parametric methods, with the aid of autoregressive models. The main tool for an analysis in the time domain is the autocorrelation function, also called the correlogram. An autocorrelation is simply a p r o d u c t - m o m e n t correlation between observations at a certain distance apart, that is at a certain time lag. Given N observations X(1) . . . . . X(N) on a discrete time series, we can form ( N - 1) pairs of observations with one unit of time lag, namely [X(1), X(2)] . . . . . [X(N - 1 ) , X(N)]. Regarding the first observation in each pair as one variable, and the second observation as a second variable, ' the correlation coefficient can be calculated. This would be the autocorrelation at lag one. In a similar way, we can find correlations between observations two lags apart, three lags apart and so forth. These correlations seen as a function of the time lag, are called the autocorrelation function. The shape of the autocorrelatios function tells a good deal about the structure of the series. One can also estimate partial autocorrelations at different lags. These tell us to what extent links at certain lags exist, which are not simply mirroring indirect links via intermediate years. The analysis in the time domain can be brought o n e step further by fitting parametric models to the data. Thus, we can investigate to what extent future consumption levels can be predicted on the basis of present and past consumption levels. We shall do this by fitting

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O,-J. Skog / Alcohol consumption

autoregressive models to the data, by solving the Yule-Walker equations (Box and Jenkins 1976: 54-56). 2.2. Results

The general trend in alcohol consumption in Norway declined during the second half of the last century (Figure 1). Superimposed on this general trend are shorter periods of rapid increase and decrease in consumption. It is notable that the highest consumption level during the last 132 years was reached during a short period in the middle of the 1870s, in spite of the fact that the trend was generally declining. The consumption of alcohol reached its lowest level during the first years of prohibition, which in Norway lasted from 1916 to 1927. As in many other western societies, the trend took a new direction after World War II, and consumption of alcoholic beverages grew steadily until the middle of the 1970s. Reliable statistics for alcohol consumption during the first half of the 19th century are not available. However, other historical sources indicate that the declining trend may have started in the late 1830s or early 1840s. The first decades of that century seem to have been a. period with increasing consumption (Fuglum 1972). The estimated spectrum for the Norwegian consumption series is

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shown in Figure 2. It has been estimated by using a Tukey window with truncation point at lag 40. One observes that a very large fraction of the variance is accounted for by very long waves. In fact, a single wave completing only one cycle during the 132 years of observation, "explains" one third of the variance. Another third is accounted for by waves completing two and three cycles, and altogether 90 percent of the variance is "explained" by waves completing less than 13 cycles during the period of observation, that is by waves which are longer than 10 years. Essentially the same result applies when the spectrum is estimated by fitting autoregressive processes to the data. This result confirms the notion of very long waves of consumption of alcoholic beverages. The fact that the longest wave which can be fitted to the data explains so large a fraction of the variance suggests that even considerably longer waves might have been found, had the data series been long enough. Analysis of data from countries with longer historical records than Norway might shed additional light on the problem. The estimated autocorrelation function for the series is shown in Figure 3. The autocorrelation at lag one is equal to 0.92, meaning that the consumption level in a given year can be predicted fairly reliably from the consumption level the preceeding year. As the distance

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increases, it becomes increasingly difficult to predict consumption. Less than 25 percent of the variance can be predicted 10 years ahead (r = 0.48). These difficulties occur in spite of the extremely long waves of consumption. The partial autocorrelations shed more light on this phenomenon. As can be seen from Figure 3, the partial autocorrelations are significantly different from zero only at lags one and two. This suggests that in order to predict future consumption one needs to know the consumption in the two preceeding years; additional information about the past does not improve the prediction any further. Autoregressive models of successively increasing order have been fitted to the data. Models of the type

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where we tried to predict future consumption X(t + 1) from knowledge about present and past consumption levels X(t) . . . . . X ( t - s ) were used. The variable W(t + 1) denotes the unexplained residual, or the "innovation" in the process of change. This component changes unsystematically over time, and is, in effect, unpredictable from the consumption series itself. It was found, as can be seen from Table 1, that only 13.5 percent of the variance is unexplained when the prediction is based on only one year. However, in this case the residual exhibits structure, suggesting that one can improved the prediction by including more information about the past. A second order autoregressive process leaves 13.0 percent of the variation unexplained, with the residual exhibiting no significant structure. Bringing in even more information about the past, does not improve the forecast significantly. The unexplained variance does not fail below 12.4 percent even in autoregressive processes of a very high order. This result indicates that the consumption series behaves like a cumulative process. Each change brings the population to a new level, which is the starting point for a new change, which does not seem to depend very much on the previous history of the system. As a matter of fact, the structure of the Norwegian consumption series closely resembles a Markov process, of the type called a random walk. Therefore, it may be useful to analyze the series of changes in consumption, as opposed to the series of consumption levels. Hence we shall pose the following question: Are there strong trends in the series of changes, so that increase tends to follow increase and decrease tends to follow decrease? A plot of the series of annual changes (i.e. first differences) in consumption is shown in Figure 4. Substantial trends do not seem to

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exist. Increases and decreases in consumption seem to follow each other in a highly unsystematic pattern. Furthermore, the mean annual change in consumption is not significantly different from zero (t = -0.12, p = 0.90). The original series has in effect no systematic drift in either direction. The spectrum of this series has been estimated using the same procedure as above, and the result is shown in Figure 5. A similar result is obtained by fitting an autoregressive model of order 4 to the series. We observe that practically all wavelengths contribute significantly to the variance of this series. The estimated spectrum has a small peak at wavelengths of about 10 years, suggesting that changes in consumption tend to become somewhat larger than average roughly every 10th year. These cycles explain a very modest part of the variance, however, and the most striking result is that the series of changes is a mixture of long, intermediate, and short waves in roughly equal proportions. This fact accounts for the highly irregular behavior of the series. The autocorrelation function and the partial autocorrelation function are shown in Figure 6. We observe that there is nearly no autocorrelation structure at all in the series of annual changes in consumption. In fact, a second order autoregressive process explains only 4.0 percent of the variance, and the residuals in this model show

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no signs of structure (Q = 13.0, df = 8, p > 0.10). It is, therefore, nearly impossible to predict future directions of change from the knowledge ot~" present and past changes. In effect no substantial tendency exists for increase to be followed by new increase, and decrease to be followed by new decrease.

2.3 Discussion of results and possible interpretations How does the observation of long waves of consumption fit together with the observation that changes in consumption vary more or less erratically? At first, this might seem like a contradiction, since intuitively one probably would expect that long trends require a persistent tendency for increase to follow increase, and decrease to follow decrease. We should not trust our shaky intuition. From the theory of stochastic processes it is known that long-term trends actually are a very likely outcome when change occur at random (e.g. Feller 1968). Consider as an example, the random walk. Here, the system at each step "decides" whether to increase or to decrease and each "decision" is independent of previous "decisions", as in a coin tossing game where the player either wins or loses a coin on each round. Since the "decisions" are independent, the law of large numbers guarantees that in the long run gains and losses will balance. But due the cumulative nature of the game, the runs may be extremely long. As an illustration I have made some Monte Carlo simultations of random walks. The results are shown in Figure 7. We observe that the general structure of the series is remarkably similar to the real consumption series. Long waves of increasing or decreasing "consumption", with shorter fluctuations superimposed, are typical characteristics. Furthermore, the autocorrelation function, as well as the spectrum, for these random walks are very similar to what was found for the Norwegian data. In effect there is no contradiction between long term trends and highly unsystematic patterns of change. Thus we may conclude that the analysis in the preceding section confirms that very long waves of alcohol consumption exist, but does not necessarily support the idea that these waves are the result of systematic and long-term processes with a persistent direction. The results obtained in the time domain could even be taken to suggest that something resembling a random mechanism is at work.

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The fact that the sequence of changes follows a random pattern does not, of course, necessarily imply that these changes have no external cause. Theoretically, a cause which completely determines the consumption level may exist, possessing the temporal structure of a random walk. However, it is difficult to see what kind of factor this should be. Alternatively, there may exist a whole series of causal factors operating successively, more or less independently of each other. In the present case, this seems to be at least part of the explanation. For example, during the second half of the 19th century, periods of prosper-

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O.-jr. Skog / Alcohol consumption

ity and depression had a strong impact on alcohol consumption, and contributed to the fluctuations in consumption (Skog 1984a). Furthermore, the two World Wars caused reduction in consumption, as did the strikes at the Norwegian state alcohol monopoly in 1978 and 1982. I shall argue, however, that more or less independent exogenous factors of this type provide only part of the explanation for the random-looking pattern. In fact, 1 shall argue that the term "random'" might be taken more literally. Many scholars will probably refute the notion that the historical development of cultures can be conceived of as a stochastic process. God doesn't play dice, Einstein said, and neither do people, many scholars would add. In the next few pages I shall try to show that the notion of '" random" changes is not necessarily a bad idea. This requires a definition of what I mean by the term " r a n d o m " in the present context. I shall avoid entering into a philosophical discussion of the concept of randomness; rather, I will approach the subject by outlining a process presumed to be generating the entity 1 call "'randomness".

3. A social network theory o f cultural change 3.1. Outline of a "'random" mechanism

When trying to explain macro-level changes over time or differences between societies, we are normally looking for macrolevel explanatory factors. Changes in per capita alcohol consumption are thus typically discussed in terms of changes in technology of production, prices and disposable income, urbanization, leisure time, control policies, and so forth. If one favors an individualistic terminology, one may prefer to state that an aggregate level change is the result of numerous individual changes, and thus proceed to try to identify explanations for the individual changes. One nearly always tries to find a common explanation, that is, a single factor or a small set of factors, which are assumed to have influenced everyone, or practically everyone. No one would dream of trying to explain aggregate change by identifying causes of change for each individual actor, without proceeding on the assumption that a commonality existed. Of course we do not - it would be a nightmare, even if one thought it would be the proper thing to do.

O. oJ. Skog / Alcohol consumption

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Apart from being intractable, the latter ultra-individualistic approach would be refuted on statistical grounds. Admittedly, large fluctuations exist in individual drinking from one year to the next (Skog 1979), and only a small fraction of these changes can be expected to have a common set of causes across all individuals. Individual changes very often occur because one gets a new job, or some new friends, because of changes in the family, because one decides to change lifestyle and reallocate resources, or due to diseases and so forth. However, the law of large numbers should guarantee that these individual fluctuations would cancel each other out and therefore have no significant effect in the form of variations in per capita consumption. Only when the individual changes are harmonized by an external force would one expect changes in per capita consumption, but in that case we are no longer talking about "individual" fluctiations. Therefore, unless the law of large numbers is abolished, the "sociological dogma" that macrolevel changes should have macro-level (i.e. common) causes, ought to be valid. I propose, however, that the law of large numbers may in fact break down "for many social phenomena, and in c a s u for drinking behavior. This proposition is not primarily motivated by an affinity for unusual hypotheses. It is a consequence of a theory of the distribution of alcohol consumption (Skog 1985). For our purpose, the most important aspect of this theory consists of the following propositions. First, each individual person's drinking behavior is strongly influenced by his co-actors' drinking behavior. This proposition is supported by numerous experimental and observational studies, and by surveys of self-reported drinking practises (see Skog 1980a, for an overview). At the level of social groups, one should therefore expect individual consumption to be synchronized, to the effect that group members move more or less in concert up and down the consumption scale. Assuming that interpersonal ties are not too weak, the theory states that this argument can be extended to society at large, or at least to very large segments of society. A society can be conceived of as an enormous social network - that is, a system of actors tied together by different types of social relations which tend to coordinate their behavior. Each actor is influenced by a fairly small number of co-actors, but he is indirectly tied to a very large number of others (possibly all members of society) by mutual friends, friends of friends and so forth. In effect, one can argue that each actor is

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influenced by practically every other member of his culture. From the study of mathematical models of such interactive systems, it is known that these indirect connections may in fact be fairly strong, provided that the interpersonal ties exceed a certain minimum value and that the network has certain structural characteristics (see below). We shall call this hypothesis the principle of long-range indirect ties. If practically everyone influences, and is influences by most m e m bers of society, then one should expect drinking to be a collective phenomenon. Not in the sense that everyone drinks the same amount, but in the sense that the whole population should slide up and down the consumption scale, more or less in concert, when per capita consumption changes. This is, in fact, confirmed by the data presently available, which were derived from 21 general population surveys in 9 different countries (Skog 1985). The effect is illustrated in Figure 8, showing how the consumption level among different types of drinkers covaries with the general consumption level in their culture. A breakdown in the law of large numbers is another consequence of (indirect) mutual influences between practically all members of society. This can be shown by the following argument. Let Xi(t ) denote the

O.-J. Skog / Alcohol consumption

17

consumption level of the i th member of society at time T = t. Since individual consumption fluctuates over time, an uncertainty exists in his consumtion level prior to the event. These fluctuations or uncertainties can be measured by the standard deviation of each Xi(t ), which we denote ai(t ). Furthermore, due to social interaction, covariation may exist between the fluctuations of individual actors, which can be measured with the coefficient of covariance. Let au(t ) denote the covariance between the fluctuation of the ith and the j t h actor. Per capita consumption, C(t), is the arithmetic average of individual consumption levels. Since uncertainties exist in each element of this average, uncertainties may also exist in this average itself. The variance of this average will measure this uncertainty and tell us whether individual uncertainties will have any effect on per capita consumption or not. Letting N denote the size of the population, we obtain the following relationship between uncertainties at the micro- and macrolevels:

02(t) = N-2Eai2(t) + N - 2 E Eoij(t) We shall call this the micro-macro uncertainty relationship. The first term on the righthand side is an aggregate measure of intra-individual uncertainties or fluctuations, while the second is an aggregate measure of inter-individual covariations in these fluctuations, that is, the degree of coordination. If no one influences anyone else, then there is no coordination, and the second term on the right hand side is equal to zero. Granted that individual fluctuations are finite, ac2(t) will be of the order 1/N, and hence practically zero in large populations. In this case, individual fluctuations will have no effect on per capita consumption. The law of large numbers is valid. However, if practically everyone influences everyone else to a significant extent, then nearly all covariances will be positive. In this case, ac2(t) will be approximately equal to the average of all covariances, and hence positive. In effect, the law of large numbers breaks down. Individual fluctuations will have observable effects at the population level, and the "sociological dogma" is no longer valid. No macro-level, or common causes, for such fluctuations in per capita alcohol consumption exist. They are the result of individual fluctuations, which are coordinated at the micro-level.

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O.-J. Skog / Alcohol consumption

For the sake of argument, let us presume that we have a social system where the direct mutual influences between actors are strong enough, and the structure of the network allows effective and rapid diffusion of influences, so that the coordination criterion in the micromacro uncertainty relationship is fulfilled. Since individual fluctuations have multiple causes (which essentially must be of a social nature, having their roots in human interaction), the same must be true for the corresponding fluctuations in per capita consumption. Therefore, these changes in per capita consumption will typically have an enormous number of causes. This is what is normally meant by the word " r a n d o m " - a phenomenon with a causal structure so complex and multi-faceted that it is beyond precise description. The kind of changes in per capita consumption implied by the principle of long-range indirect ties, may therefore rightfully deserve the name "random". To decide whether these changes are truly random in any deeper sense, is beyond my competence. Since the "fuel" of this process of change is an enormous number of micro-level impulses, which have their roots in trivial and significant, and large and small life events, the total outcome at each step is difficult to predict. Furthermore, one can hardly expect that successive changes, as a rule, run in the same direction. Such a system would therefore, as a rule, behave somewhat erratically, without persistent tendencies in one direction or the other. As previously mentioned, this does not exclude long-term trends, however. The model of micro-level interactions does have room for the " b a d reputation" mechanism mentioned in the introduction. At high levels of consumption a general tendency towards reducing consumption may exist, while the opposite could be the case when per capita consumption is low. However, since the bad reputation mechanism would necessarily be of a probabilistic, rather than deterministic nature, in this context it would not produce persistent changes over time to any significant extent, and systematic recurrent cycles would not be observed. Only long-term trends of a more indeterminate nature would follow, and the outcome would not appear very different from the simple random walks described above.

3.2. The effects of synchronized micro-level changes The perspective outlined above creates a picture of the drinking culture which is well described by the metaphor of a "boiling pot". We "see"

O.-J. Skog / Alcohol consumption

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an enormously complex system of actors - o r perhaps inter-actors is a better term - whose behavior is constantly modified by the behavior of "neighbors" in the topological space of the social network. Sociometrically local changes may remain local, or they may tend to travel through the network with the semblance of spreading waves, which mix, fortify and counteract each other. Sometimes they create aggregate changes in one direction, sometimes in the other, and sometimes there are no aggregate changes at all. Through the interactions between members, the system gains a potential for spontaneous and autonomous change. The drinking culture is not only passively reponding to exogenous pressure, but also lives a life of its own, developing according to its own rules. This does not mean, of course, that such exogenous factors are unimportant. But it means that they have only a partial effect, and that the drinking culture may sometimes develop in the same, and sometimes in the opposite direction, compared to what one would expect. In other words, the drinking culture is certainly affected by other sectors of social and economic life, as well as by the material conditions of living, but it is not completely enslaved by these factors. Another common metaphor in the social network literature, is that of a fishing net blowing in the wind. This picture effectively captures the interconnectedness of the actors in the social system, and their coordinated and collective response to an external force (the wind). However, it does not capture the potential for autonomous change inherent in such interactive systems. The role of being a genuine generative mechanism for cultural change is perhaps the most exciting attribute of the social network perspective. Not only actual drinking behavior, but also attitudes, opinions, social norms, social meanings and the more symbolic aspects of the drinking culture are shaped and reshaped in the process of social interaction. In general, similar conclusions should hold for these aspects of social life. However, attitudes and opinions sometimes crystalize into ideologies, which add a new dimension to the picture. These ideologies, as well as other symbolic factors, may effectively and rapidly diffuse over large sociometric and geographic distances. While mutual influence through encounters in concrete drinking situations may be highly effective in some respects, such a mechanism may by itself be too weak to explain collective changes across geographic boundaries (see below). After all, geographical distance is an important

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regulating factor for everyday social interaction. The diffusion of ideologies and so forth are less restrained by geographic boundaries, and may thus contribute to large-scale harmonization. Ideologies about temperance and moderation, about the legitimacy or illegitimacy of restrictions and state control of availability of alcohol, may be presumed to have more persistent effects on the drinking culture's course of development. However, even though the ideologies themselves may be reasonably stable structures, their popular support and actual influence on drinking behavior may be much more volatile. One is reminded of the following puzzle. Four frogs are sitting on a leaf. Three decide to j u m p off. How many are left on the leaf? It is difficult to know. The frogs decided, to jump, yet nothing was said about their actual behavior. Opinions, ideas, and decisions are one thing, behavior is another; they do not always correspond to each other. This does not amount to a refutation of the view that cognitive factors influence behavior. Rather, the point is that sometimes they do, and sometimes they do not. It is difficult to predict, particularly in advance. With an argument analogous to that formulated above, one could expect that it is difficult to predict the course of development even for public opinions and ideological commitments. Fluctuations might be typical, and in the long run large-scale changes should result. At this point we should remind ourselves that the model is designed to explain irregularities in the pattern of change. We do not argue that the present state of the system is irrelevant for future states, for obvious reasons. As mentioned several times already, the changes in average levels generated by long-range indirect ties originate with the individuals and their interaction. In relation to such averages, Durkheim (1964: 8) has argued: "Since each of these figures contains all the individual cases indiscriminantly, the individual circumstances which may have had a share in the production of the phenomenon are neutralized and, consequently, do not contribute to its determination. The average, then, expresses a certain state of the group mind (l'?~me collective)." In his perspective, the culture exists above and beyond the individuals, and exerts "external coercive power" over them. The alleged breakdown in the law of large numbers allows a somewhat different conception of culture and social facts. The individual circumstances are no longer completely neutralized, and the individuals are allowed to have an effect through micro-level interaction. In this perspective, the coercive

O..J. Skog / Alcohol consumption

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power is not located above and beyond the individuals, but between them. Individuals are influenced by their culture only through their contact with representatives of the culture, these being either persons or cultural objects. Intuitively, it may seem paradoxical that the same mechanism which produces collective behavior, namely the principle of long-range indirect ties, also has the effect of making micro-level, or individual, fluctuations a significant macro-level phenomenon. In fact, it is easily demonstr~ited that this is the case. If fluctuations in per capita consumption actually remain, then the collective's coercive power over the ith individual, that is his tendency to follow the main stream, which we denote d~(t), can be measured by the covariance between his consumption level and the per capita consumption level. Simple algebra gives

di(t)=o[Xi(t),

C(t)]

=N-'Eo,j(t). J Comparing this with the micro-macro uncertainty relationship, one immediately sees that the average index of coercive power is equal to the uncertainty in the per capita consumption level,

N-'Y'.di(t ) =

o2(t).

i

Since the latter is presumed to be significantly larger than zero, it follows that the actors, on the average, have a significant tendency to follow the main stream, that is that nearly everyone tends to move in concert up and down the scale of consumption. Apparently we have another example of how misguided our intuition can be. Rather than being contradictory, the two phenomena can be generated by the same fundamental principle. If micro-level interactions generate collectivity in a network through long-range indirect ties, then micro-level fluctuations will produce fluctuations and trends in per capita consumption of an essentially indeterminate nature. Therefore, it may be true that our intuitive distinction between the concepts collective and indioidualistic may be more problematic than we usually think. The social network perspective represents a very promising approach for shedding light on this distinction and linking the microlevel to the macro-level of sociological analysis.

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3.3. The principle of long.range indirect ties The fundamental assumption underlying the model outlined above is that everyday social interaction between ordinary people is an i m portant element in the development of large-scale cultural phenomena. The principle of long-range indirect ties is a formalization of this assumption. This principle is admittedly speculative, since no direct empirical proof exists indicating that the structure of social networks actually allow micro-level interactions to create chains of indirect influence which extend over sufficiently large distances. In this section I shall briefly discuss the credibility of this assumption, by giving two theoretical examples of how it may come into existence. The first example concerns a situation where two equally attractive alternative behaviors exist, and each actor "chooses" one of them under the influence of his co-actors in the social network. We label the two behaviors + 1 a n d - 1, respectively, and we let Xi denote the the choice of the i th actor. Since the two alternatives are equally attractive, each individual has a probability of 1/2 of choosing either one of them in the absence of pressure from co-actors. In a dyad where one actor has already made his choice, the second actor will in general be apt to make the same choice, and we denote this probability as p. Assuming that both individuals influence each other equally, we can easily find the probability distribution of possible outcomes in this dyadic choice process. Furthermore, from one very simple additional assumtion, to be described elsewhere (Skog 1984b), one finds, via mathematical induction, the probability distribution in an arbitrary network. Let M be a symmetric matrix where element (i, j ) is one or zero, depending on whether actors i and j influence each other or not. Letting X be the vector of individual choices and X' its transpose, we can then write Pr(X) = K ( M , b) exp(bX'MX). The parameter b is related to the measure of interdependence, p, as follows, 2b -- log(p/(1 - p )).

K(M, b) secures that the probabilities sum to unity, and is independent of the actual outcome X.

0..3. Skog / AIcoholconsumption

23

-0----0--0----0-

Figure 9. Examples of networks of dimension one (top) and two (bottom).

In a large network where the actors choose independently of each other, the law of large numbers guarantees that about equal proportions of the population will choose one alternative or the other. Hence there is no dominance of one alternative over the other. The same will be true if the interdependence is very weak. When the interdependence parameter reaches a certain value, however, something dramatic happens, granted that the network fulfills certain minimum structural requirements. Under these circumstances nearly everyone will tend to choose the same alternative, signalling a breakdown in the law of large numbers. The structural requirement is essentially that the network is at least two-dimensional (see Figure 9). In one-dimensional chains, like long queues, long-range order cannot occur spontaneously. Except in very special social systems, we can probably safely assume that this dimensionality-criterion is fulfilled. The critical value for the interdependence parameter depends on the structure of the network. In particular, it depends on the dimensionality of the network, and how many direct co-actors each actor has. For instance, in a two-dimensional regular square network where each actor has four co-actors, the parameter p would have to exceed 0.707, while in a triangular network with six co-actors, the critical value is 0.634 (Skog 1984b). The degree of interdependence needed to produce a breakdown in the law of large numbers is in effect not very large. In an isolated dyad, these numbers correspond to correlations between the choices of the two actors of 0.41 and 0.27 respectively.

(9.-J. Skog / AIcohol consumption

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This very simple interactive structure thus allows long-range indirect ties, provided that interdependence is not too weak. As a matter of fact( these indirect ties may extend over infinite distances. Therefore, it is not necessary to postulate strong exogenous forces influencing every member of society in order to explain large-scale uniformities in behavior. It is also unnecessary to presume the existence of a few sociometric stars, or dominant normsenders. Of course, external forces and powerful normsenders often exist, but their existence is not critical for the genesis of holo-cultural uniformities in behavior. In the case of drinking, the category of behavior is not dichotomous, but continuous. Much less is known about continuous systems, which may be of several different types. If the system is linear, indirect ties over infinite distances are impossible, unless strong asymmetries exist in the social ties, that is very influential individuals (Skog 1979). The mathematical theory of non-linear systems is still imperfect, and although systems with infinitely long-range order are known, general knowledge of what is required to secure such order is still missing. However, infinite long-range indirect ties are not necessarily required in populations of finite size. In a linear interactive system, significant correlations may be present at distances large enough to secure observable fluctuations in the per capita consumption level, granted that the population is not too large. Some numerical examples can illustrate this point. From both cross sectional and longitudinal data it is known that drinking behavior roughly obeys the law of proportional effects (Skog 1979, 1985). We may therefore presume that individual fluctuations in consumption level are relative, rather than absolute. The standard deviations measuring individual uncertainties in future consumption level will therefore vary across individuals in proportion to the individual's typical consum.ption level. This means that the coefficients of variation ought to be fairly stable across individuals, and we denote this constant a. Multiplied by 100 this gives the typical individual fluctuations in percent. After some simple algebra, we find that the average individual uncertainty can be written i

N-l~'oi 2 = a2(V 2 + l)C 2 i

For simplicity, and without loss of generality, we have ignored the possible time dependence of the parameters. As before, C denotes per

O.'J. Skog / Alcohol consumption

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capita consumption. The parameter V is the coefficient of variation in the distribution of individuals along the scale of consumption. This distribution is known to be very skewed, often resembling a lognormal distribution (Ledermann 1956; M~tkel~i 1969; Skog 1971, 1980b, 1985), and the coefficient of variation is typically larger than unity except in cultures with an extremely high consumption level. Letting ~z denote the average individual uncertainty defined above, while r denotes the coefficient of correlation, we introduce the approximation

Z Eo,j-- o2Z E,,j. i j

i j

Letting r.i, i = 1. . . . . N, denote the correlations for a typical actor in the population, we obtain from the micro-macro uncertainty relationship (Tc2//C2=a2(V2-t -

1)(l +~r.,)/N.

From this we obtain estimates of the relative annual fluctuations in per capita consumption due to micro-level fluctuations. Consider a population where the coefficient of variation is V = 1.5, and the individual fluctuations per year are 25 percent (a =0.25). These values ought to be realistic in many populations. We shall determine under which circumstances one can expect to observe annual fluctuations of 5 and 1 percent, respectively in per capita consumption. Note that fluctuations of this order of magnitude are sufficient to produce large-scale variations over time, provided that a strong autocorrelation structure exists. In fact, during the highly unstable period 1851-1914, the fluctuations in annual changes in per capita consumption in Norway were 8 percent, and during the more stable period following World War II the fluctuations were 3 percent. Since our hypothesis allows for the fact that part of these fluctuations are generated by macro-level factors, micro-level mechanisms could not be expected to generate aggregate fluctuations of more than 5 percent. On the other hand, microlevel generated fluctuations well below 1 percent could not constitute a significant mechanism for cultural change. From the formula above one finds that the average correlation t

O.J. Skog / Alcoholconsumption

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must lie between 0.012 and 0.0005, in order to produce aggregate fluctuations of between 5 and 1 percent. In effect, the average correlations needed to produce observable and significant fluctuations in the aggregate consumtion level are not very large. If no micro-level coordination exist, that is if all correlations are zero, macro-level fluctuations of these magnitudes will be present only in very small populations, N = 80 and N = 2000, respectively. If the typical drinker is directly influenced by, say, 20 co-actors and r = 0.5 in these relationships, then this direct coordination alone increase the limits to about N = 900 and N = 22,000, respectively. Indirect links may increase these limits considerably, granted that indirect influence does not die out too rapidly with increasing distance. This will depend on the nature of the interactions and the structure of the network - in particular its dimensionality. Consider, as an example, a finite and regular d-dimensional network where each actor has f direct co-actors, or 1-step ties. Let A ( s ) denote the number of actors which can be reached from an arbitrary starting point in exactly s steps, discounting loops. We shall assume that this reachability function increases as

A(s) until about half of the population has been reached, and then declines so as to make this teachability function symmetric. Furthermore, we assume that the correlation die out exponentially as a function of sociometric distance, r(s)--- bc ~-1

0 < b , c < 1.

The correlation between actors in direct contact is in effect b, and the correlations between indirectly linked actors are reduced by 100(1 - c) percent for each sociometric step separating them. Since obviously

Er,,=EA(s)r(s) i

s

we can now estimate the resulting fluctuations in per capita consumption in populations of different sizes. In particular, we can estimate how large a population can be, and still allow micro-level fluctuations to produce fluctuations in per capita consumtion of 5 and 1 percent, respectively.

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Table 2 Size of a population which will allow 5 and 1 percent fluctuations in per capita consumption, as a function of range of ties and dimensionality of network Range

Dimension

5% fluctuations Size of population

1% fluctuations Population diameter

Size of population

Population diameter

Short

2 3

2700 10,000

32 50

65,000 250,000

160 144

Medium

2 3

11,000 94,000

64 104

250,000 2,200,000

314 300

Long

2 3

42,000 800,000

128 212

1,000,000 19,000,000

632 610

In the calculations we have assumed that each individual has !0 co-actors, and that the correlations in these direct ties are r = 0.5. If these parameters are changed, the fluctuations change proportionally. We have made the calculations for two- and three-dimensional networks, and for three levels of indirect ties. When c = 0.6, the indirect correlations die out quickly, and only short-range ties exists. At a distance of four steps the correlation is less than 0.1. When c = 0.8, medium-range ties can be said to exist, since at least eight steps are required to produce a correlation below 0.1. And when c--0.9, longrange ties exist, and 16 steps are required to bring the correlation below this level. The results of the calculations are shown in Table 2. Initially, we note that the dimensionality of the network is of vital importance for the efficiency of the diffusion process. The dimensionality of real social networks is a much ignored topic in the network literature; this topic obviously deserves more attention in the future. When only short-range indirect ties exist, large fluctuations (over 5 percent) cannot occur in populations exceeding 10,000, unless the network is more than three-dimensional. Small fluctuations (1 percent) can occur in populations up to a few hundred thousand, that is medium size cities. When indirect ties extend over medium large distances, moderately large fluctuations will be present in such cities, while small fluctuations could be present in populations counting a few million, provided that the network is at least three-dimensional. And if the

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O.J. Skog / Alcohol consumption

indirect ties should extend over large distances, according to our definition, then moderately large fluctuations would be present in populations with millions of inhabitants. Theoretically, it is therefore quite possible to have significant macro-level fluctuations in very large populations, even in the absence of an asymptotic breakdown in the law of large numbers. The two cases described above ought to convince us that the so-called principle of long-range indirect ties is not as wild an idea as one might have thought initially. They do not, of course, prove that coordination of sufficient strength will necessarily follow from micro-level interactions. They signify, however, that this theoretical possibility cannot be ignored; hence the "sociological dogma" may not always be true. One difficulty with these examples, is that both tacitly presume what may be called a "smooth" network structure. Real networks may typically have a more "granulated" structure, with subgroups of closely connected actors and a much lower number of ties between subgroups. Large geographic regions, containing several population centers are obvious candidates for this pattern, as are regions which house more or less segregated substrata, such as different ethnic groups. Furthermore, it is frequently assumed in the sociometric and network literature that even relatively homogeneous population groups tend to have this structure, and a series of analytical techniques have been designed to identify such dusters within larger networks. The fact that attention has been focused so much on this subject may have contributed to a bias concerning its importance, but it is nevertheless clear that real networks are not at all "smooth" and homogeneous. It is an open question whether ties between clusters are strong enough to produce significant coordination even at this level. On the one hand it is clear that subcultures exist (at different levels of social organization) with very different drinking habits. This signifies that coordination at this level is only partial. On the other hand, different substrata of the population and different geographic regions (even different countries), often - but not always - seem to follow similar lines of development. This may indicate that a significant degree of coordination exists even at this level, although it may also be interpreted as resulting from common external forces. Without denying the importance of the latter mechanism, one could at this point underline the importance of the more symbolic aspects of the drinking culture (and culture in general) mentioned in the preceding section. Ideologies

O..J. Skog / Alcohol consumption

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and so forth are easily transported across social and geographic boundaries, and may contribute significantly to coordination at the levels in question. Before we can seriously assess the possibility of significant large-scale coordination via micro-level processes, our knowledge about real-life social network processes needs to be greatly improved. As was mentioned above, we also need a better theoretical understanding of interactive systems with continuous state variables. And last, but not least, we need to known more about the topology of social networks.

4. Summary and concluding remarks Analysis of official statistics on alcohol sales in Norway for the years 1851-1982 confirms that very long waves of consumption exist. However, the results do not support the notion that these waves are the result of a persistent and systematic process of change, since the sequence of annual changes in consumption forms a highly unsystematic pattern. This absence of significant structure is not unique to Norway. Very similar results were found in British data for the period 1902-1975 (Skog 1984c). These irregularities result, to some extent, from a series of more or less independent external "disturbances", such as economic prosperity and depression, wars, strikes, and so forth. However, such factors seem to give only part of the explanation; there are reasons to believe that a highly significant explanatory factor is to be found within the drinking culture itself. The drinking culture seems to develop according to its own inner rules. In this paper I have tried to identify these "inner rules" which derive from processes of interaction in everyday life at the micro-level of social organization. I have argued that long-range indirect ties may create sufficient integration in very large populations to produce a breakdown in the law of large numbers. This would give the drinking culture a potential for autonomous and spontaneous change, and would create erratic, rather than persistent patterns of change in the aggregate consumption level. At each stage, the future course of development is difficult to predict, since its direction is determined by an enormous number of factors at the micro-level, and these are generally not stable over time. Since this process is a cumulative one, very long wave-like temporal structures would result.

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Whether such changes should be called "random" processes, as I have done, is mostly a matter of taste. The important point is that social processes have been identified, that tend to produce patterns of change which closdy resembles random processes, and that the outcome of this process of change would, to a large extent, be unpredictible on the basis of conventional theories of socio-cultural change. It is a typical feature of socio-cultural inquiry, that the ability to explain cultural evolution in retrospect is not matched by an equally impressive ability to predict future trends of development. Perhaps the term "random" could serve as a reminder of this asymmetry. The basic premise of this argument, namely the principle of longrange indirect ties, may be valid or invalid in the context of drinking cultures. It will be a difficult task to settle this question. Assuming that it is correct, however, it becomes clear that one cannot hope to find the full explanation for the long-term trends in alcohol consumption at the macro-level. The consumption trends are of course related to other macro-level processes such as economic and technological development and so forth, but only within certain limits. It is symptomatic that economic development and increasing buying power across all social classes could not prevent a declining trend in alcohol consumption during the second half of the 19th century, in spite of the fact that economic development had a significant positive impact on consumption in this period (Skog 1984a). Other factors, pulling in the opposite direction, more than neutralized the effects of increasing buying power. The formal model outlined above is based on the assumption that the historical transformation of the drinking culture must, at least to some extent, be understood as a dynamic process within the drinking culture itself, and that this perspective is at least as important as an analysis in terms of independently measurable "factors" and "variables" with a known history. When consumption of alcoholic beverages goes up, for example because people start to drink wine, rather than water with meals, or because people begin to take beer as a thirst quencher on ordinary week days, these changes should be understood in terms of the actions and interactions of the people who actually do the drinking, and not only in terms of external influences. What actually happens, is that real human beings start to drink alcoholic beverages in situations which used to be the "domain" of other beverages, and this habit spreads by way of social interaction between people. Sometimes such transformations may be triggered by exoge-

O.-J. Skog / Alcohol consumption

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nous changes, such as increased availability of alcohol or increased buying power, but this need not be the case. New habits can be born, and old habits can die out for no apparent reason, as is well known from other sectors of social life (e.g. fashions). The fact that we can see no apparent reasons is not necessarily a sign of ignorance and failure to identify the true causes. The arguments outlined above suggest that external reasons may not always exist. Cultural change in drinking patterns is clearly the outcome of a highly complex process involving different levels of social organization and different sectors of social and economic life. One can describe and analyse these changes from many different perspectives. The approach chosen here represents a kind of methodological individualism. It is based on the regulative idea that it should be possible to describe and understand wholes in terms of dynamic interactions between the elements of a social structure. This idea does not imply psychological reductionism in the sense that these elements are presumed independent of, and prior to, the whole. On the contrary, the elements (i.e. individuals) are shaped and reshaped in the process of interaction, and they are therefore products of social life as well as building blocks of social life. However, individuals are observationally distinct "objects", and from a methodological point of view they may serve as units of observation in the study of cultural phenomena. Cultural change may therefore be described in terms of interaction between these building blocks, without presuming that they are "atoms" with fixed properties.

References Box, G.E.P. and G,M. Jenkins 1976 Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day. Chatfield, C. 1975 The Analysis of Time Series. Theory and Practice. London: Chapman and Hail. Durkheim, E. 1964 The Rules of Sociological Method. New York: Free Press. Feller, W. 1968 An Introduction to Probability Theory and its Applications. Vol. 1 New York: Wiley. Fuglum, P. 1972 Kampen om alkoholen i Norse 1816-1904. Oslo: Universitetsforlaget. Jenkins, G.M. and D.G. Watts 1968 Spectral Analysis and its Applications. Oakland, CA: Holden-Day. Ledermann, S. 1956 Alcool, Alcoolisme, AIcoolisation. Paris: Presses Universitaires de France.

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Mitkel~l, K. 1969 Alkoholinkuluktuksenjakautuma. Mimeo. Helsinki: Social Research Institute of Alcohol Studies. 1983 "Alkoholkonsumtionens v[grorelser och alkoholfr[gans historiska former". Sociologisk Forskning 20: 11-19. Skog, O.-l. 1971 Alkoholkonsumetsfordeling i befolkningen. Mimeo. Oslo: National Institute for Alcohol Research. 1977 "On the distribution of alcohol consumption", in The Ledermann Curve. Report of a Symposium. London: Alcohol Education Centre. 1979 Modeller for drikkeatferd. SIFA-mimeo no. 32. Oslo: National Institute for Alcohol Research. 1980a "Social interaction and the distribution of alcohol consumption". Journal of Drug Issues 10: 71-92. 1980b"Is alcohol consumption IognormaUy distributed?" British Journal of Addiction 73: 169-173. 1984a An Analysis of Divergent Trends in Alcohol Consumption and Economic Development. SIFA-mimeo no. 84. Oslo: National Institute for Alcohol Research. 1984b "A social network perspective on large-scale cultural phenomena". Manuscript. 1984c "The risk function for liver cirrhosis from lifetime alcohol consumption". Journal of Studies on Alcohol 45: 199-208. 1985 "The collectivity of drinking cultures: A theory of the distribution of alcohol consumption". British Journal of Addiction 80: 83-99. Sundt, E. 1859 Om Edruelighetstilstanden i Norge. (New edition 1976) Oslo: Gyldendal Norsk Forlag.