Single Distribution Theory of Consumption

The single distribution theory (also often called the Ledermann theory in alcohol studies) is a misunderstanding of a statistical concept. It is interpreted to justify measures to restrict consumption or other behaviors considered hazardous or otherwise undesirable.

The theory was originally developed in relation to the consumption of alcohol in a homogeneous population and held that consumption was distributed lognormally with a fixed proportion of the population drinking more than the beverage equivalent of one liter of pure alcohol per day. As a result the proportion of “excessive drinkers” (variously defined) could be determined by the average consumption of the population. Although taken seriously enough by [Page 727]some to result in the production of tables giving the proportions of excessive drinkers corresponding to various levels of mean consumption, it soon became apparent that in this form the theory was flawed. Statistical distributions are in general merely convenient models applied for the purpose of statistical analysis, and cannot be expected to hold exactly, particularly at extreme values.

As a result, contemporary use of the term often implies no more than that the proportions in the extremes of the distributions are related to the mean of the distribution. In this formulation the theory has been applied more generally to other forms of consumption/behavior/health risks such as gambling, drug-taking, hypertension, and others. The great attraction of the theory in its original form is that it appears to imply that any action that affects the average value of the phenomenon in the population will automatically affect the proportions exhibiting high levels of the phenomenon, and is thus used to justify attempts to reduce average values, particularly of alcohol consumption.

As the flaws in the formal statistical aspects of the theory were recognized, a number of revisions took place. In the alcohol field the distributional assertion became simply that the distribution of alcohol consumption in a homogeneous population was “continuous, unimodal and skew.” The assumption that natural populations are homogeneous was unquestioned, indeed usually the term homogeneous was undefined, while continuity of the distribution is a mathematical approximation, not a real property, and researchers did not seek or test multimodality of such empirical distribution data as existed. The (assumed) regularity in distribution was assumed to be the result of collective social change. It was difficult to see that much remained of the theory, and the so-called “preventive paradox” approach threw out the distributional argument altogether.

Nevertheless some writers still take the view that the correlation between the mean and the proportion over a particular threshold continues to justify the aspect of the theory that emphasizes the importance of the average. But this correlational evidence for the theory may simply be an overinterpretation of a tautology—other things being equal an increase in the proportion of high-level consumers will result in an increase in the mean, hence it will often be found that the mean is related to the proportion of high-level consumers. This does not afford a basis for predicting the results of a change in mean. There is no plausible mechanism that requires that the redistribution of consumers following such a change will satisfy the theory.

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