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Article Excerpt
The crudeness of our everyday language can sometimes seriously distort our pictures of reality. Many people seem to classify alcohol consumers into a few discrete types, labeled as "normal drinkers", "abusers", "drunks", and "alcoholics". The same phenomenon can also be observed in relation to other types of behavior, including crime (e.g. "criminals" vs. "law-abiding citizens"). However, more systematic observation uncovers a plurality of types and grades, whether the object of study is drinking or other behavioral dimensions. The population typically turns out to be distributed more or less smoothly along continuous consumption scales, whatever the commodity may be, and norm-violation of one sort or another is no exception to this rule (Allport (1934) for an early demonstration, and Gabor, (1994) for a wider range of examples.) It is simply not true that people are easily sorted into a few neat categories. Moreover, people's behavior is less stable over time than common wisdom would have it. "Alcoholics" may be "moderate drinkers" during prolonged periods and eventually end up as "normal drinkers" (Polich, Armor & Braiker 1981). Many young people with high criminal activity early in life, may have a much smaller criminal burden later in life--or none at all (Sampson & Laub 1993). And other people move in the opposite direction, with higher consumption levels or criminal activity levels later in life.
Alcohol consumption, measured, say, in liters of pure alcohol consumed per year, is obviously a continuous variable. Nevertheless, in the Anglo-Saxon world a dichotomy between "alcoholics" and "normal drinkers" seems to have been dominant even among many scholars until the 1960s (Jellinek, 1962). The French demographer Sully Ledermann appears to have been the first to conduct systematic, empirical studies of the distribution of alcohol consumers along the consumption scale. Others, for example Jellinek (1955), may also have touched upon the distribution problems, but Ledermann was certainly the first who sought a nondiscrete and general distribution function, which should be valid for a broad range of different populations.
In his search for a continuous distribution function, as opposed to discrete categories, Ledermann may have been guided by the French zeitgeist, which was very opposed to the Anglo-Saxon point of view. The latter postulated a prealcoholic maladjustment, for instance a biological disposition towards "alcoholism", in a certain fraction of the population. But according to Jellinek (1962, p. 385), "[N]othing can provoke greater dissent on the part of French physicians and others interested in alcoholism than the contention that prealcoholic maladjustments lead to the heavy use of alcoholic beverages." In Ledermann's academic context, and in a culture with alcoholic beverages strongly integrated into daily life, it probably came more natural to see alcohol consumption as a continuous phenomenon.
However, Ledermann went further than this and proposed a theory according to which alcohol consumption should follow a strict one-parametric distribution "law" (Ledermann 1956). In other words, his theory postulates that populations with the same average consumption shall also have identical distributions, and thereby that the proportion of the population consuming above a certain level should be the same. Furthermore, cultures with highly different overall consumption levels should have highly different prevalence rates of heavy drinking, according to this theory.
This bold hypothesis was not founded on comprehensive empirical documentation, and thus cannot be understood as an inductive generalization. On the contrary, Ledermann possessed rather limited documentation when the distribution theory was developed, and it is therefore most correct to understand it as a bold hypothesis inspired by the results that Ledermann had reached in other areas. Furthermore, it was not derived from well established social mechanisms, but some rather peculiar statistical arguments of doubtful validity, to say the least.
Ledermann's distribution theory has two main components. First, Ledermann proposed that alcohol consumption must follow a lognormal distribution. Causal mechanisms supporting this hypothesis, at least as a first approximation, can be found. Secondly, he found reason to believe that the two parameters in the lognormal distribution function (mean and standard deviation) should co-vary according to a certain pattern, so that only one of the parameters could vary freely. Ledermann's argument for the latter hypothesis was, however, rather weak, and the presentation of his distribution theory must be characterized as very brief and in important respects only fragmentary.
One may wonder why Ledermann came to believe that strong regularities should exist in the first place. For instance, the theory predicts a convex (curved upwards) relationship between the average level of consumption in society and the prevalence of heavy drinking, a rather counterintuitive prediction at that time--at least from an Anglo-Saxon perspective. However, if Ledermann's entire scientific production is seen together, it becomes easier to understand how he may have arrived at his hypotheses. As we shall see, the last one is in all probability an artifice in order to support certain results that Ledermann (1946, 1948, 1952a,b,c, 1953) had arrived at through his earlier epidemiological studies. The lognormal hypothesis is also to a certain degree inspired by these studies.
In the remainder of this article an attempt will be made to trace the intellectual history of Ledermann's theory. In the next section a brief description of the theory, mainly based on Ledermann's book from 1956. To obtain a closer understanding of the background for the theory, his hypotheses in the following section in the light of earlier works from Ledermann's hand. Finally, assessments of Ledermann's empirical testing of the theory. The article concludes with a brief summary of later empirical studies of the distribution of alcohol consumption.
Ledermann's basic hypotheses
As already noted, Ledermann suggested that alcohol consumption had to follow a lognormal distribution function (1956, p.125) within homogenous populations. His reasoning for this hypothesis was short and rather cryptic. Ledermann took as his point of departure that the consumption of individuals is largely determined by social forces and he maintained that the habits of consumption to a large degree are developed according to a contagion or snowball-like mechanism. Under these conditions there is, according to Ledermann, reason to expect that the logarithm of the consumption variable, rather than the consumption variable itself, should follow the normal distribution.
The shape of the lognormal distribution is strongly dependent upon the dispersion parameter, i.e. the standard deviation of logarithmically transformed consumption, which we will denote [sigma]. If [sigma] is very small, the distribution is approximately symmetric, while large values of [sigma] give rise to strongly right-skewed distributions. This is demonstrated in figure 1, which shows different lognormal distributions for the same total amount of alcohol.
As can be inferred from figure 1, the number of people with high levels of consumption will vary strongly with the dispersion parameter. In a population where the average consumption per drinker is 15 liters of pure alcohol annually, the proportion of the population whose consumption exceeds 15 centiliters of pure alcohol daily (that is 54.75 liters annually) will be 0.2% when [sigma] = 0.5. It will be 3.7% when [sigma] = 1.0, and 2.7% when [sigma] = 3.0. The highest number of such consumers will be reached when [sigma] = 1.6, when the proportion above 15 centiliters daily will become 5.4%. We observe here that the proportion of heavy consumers increases with [sigma] up to a certain point, and thereafter declines. It can be shown that this applies quite generally for lognormal distributions.
[FIGURE 1 OMITTED]
Now it is perfectly clear that the real proportion of the population with a consumption of more than, say, 150 liters annually is negligibly small, since most consumers would rapidly die off if their consumption were of this order. This implies that if the factual distribution of the consumption shall be approximated by a lognormal distribution with a satisfactory degree of accuracy, then the dispersion parameter of this function must be fairly small or quite large. Intermediate values would result in unrealistically large proportions...
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