Making an Index: How is Inequality Like Nutrition?

In one of my working papers, I expand on the axiomatic framework used in constructing measures of inequality to measure the inequality of the distribution of hungry people across the world. Assumptions that make good sense when talking about money distributed among people or countries don't when talking about people distributed among countries.

Parke Wilde's recent post on good policies for measuring nutrition put me in mind of this research. He complains about the lack of transparency and seeming 'ad hockery' of current nutrition labels. He proposes three properties that a good index of nutrition should possess in order to improve consistency:

1 - The nutrition score should be independent of serving size. This sounds a lot like the axiom that a measure of inequality should not depend on the size of the population.

2 - "The score should rate mixed foods in a consistent way." In other words, the nutrition score should be linearly decomposable. What in inequality measures is merely a useful if debatable device to break inequality down into component parts is here a practical - but not necessarily obvious - understanding that otherwise the score will unfairly promote or attack "mixed" foods more than its component ingredients. A ham sandwich should not be worse or better than eating the individual ingredients.

3 - "The score should rate each good and bad nutrient independently." That is, adding more salt to a food should do the same thing regardless of what other ingredients are already there. Really, this is just another argument for point 2 of making the score linearly decomposable.

Unfortunately, it also undermines the second point because it is rather suspect. Some nutrients interact in the body. Consumption of one may affect absorption of others. This would lead to a non-linear effect from mixing interacting ingredients.

There's another problem with his second axiom, and that's the method of cooking. Baking, boiling, and other cooking methods change the nutrient content of many foods and how our body processes them, and do so to different extents for different foods. It is healthier to eat raw vegetables than baked or boiled, for instance. The final fat content of meat depends on how it was cooked. Thus cooking processes will change that linearity.

Neither of these factors matter much for ham sandwiches. The interactions are close enough to linear as to make no difference. For more complex ready-to-eat meals, however, the difference can be nutritionally important and ought to be reflected in a consistent way in a good nutrition label.

UPDATE: Wilde responds that some nonlinearities might be justified, but to do so you would have to know how much people are consuming. Lacking that knowledge was what prompted him to propose the first axiom.