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Numerators and denominators

By Christopher W. Larimer, University of Northern Iowa Professor of Political Science.

In a recent New York Times column, John Paulos, a mathematician at Temple University, discussed the difficulty of assessing the threat from the coronavirus due to the “mystery of the denominator” (the number of people actually infected).

The “mystery of the denominator” concept is fundamental, in my opinion, to understanding the modern policymaking process and the constant battles we observe between elected officials and researchers.

Consider the following:

Last fall, when reporting on the evolution of the anti-vaccination movement, Jan Hoffman of the New York Times wrote, “People are flummoxed by numerical risk.” As Alison M. Buttenheim, a professor in the School of Nursing at the University of Pennsylvania who was interviewed by Hoffman, explained, “We pay more attention to numerators, such as ‘16 adverse events,’ than we do to denominators, such as ‘per million vaccine doses.”

In the policy world, considerable attention is given to the numerator (an existing problem). In fact, you will often hear legislators say that one of the reasons they introduced a certain piece of legislation is because they heard from a constituent about the problem. Policymaking thus becomes a competition over which numerator is most important. Elected officials are responsible to constituents, so their focus on the numerator is justifiable, so long as the denominator is not forgotten.

But, as Paulos explains, the modern media environment, in particular, the “breaking news” phenomena (see also Tom Patterson’s insightful book on this point), only exacerbates this tendency to neglect the denominator--breaking news is, by definition, an emphasis on the numerator.

The role of the researcher is to determine when the ratio of the numerator to the denominator is sufficient to warrant a response from policymakers that will result in an efficient use of resources. That is where we seem to be at the moment in terms of the discussion surrounding the response to the coronavirus outbreak.

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