Is a horse bigger or smaller than a cow?

Ferenc Jánossy (1914-1997), an engineer-turned economist from a legendary Hungarian family (he was the step son of George Lukács (1885-1971), one of the founders of the philosophy of ”Western Marxism”), wrote a book in Hungarian with the title ”The measurability and a new measuring method of economic development level”, and it was a revelation at that time. Jánossy explained his approach clearly:

”The first issue is how qualitatively different objects can be compared quantitatively. Every child knows that an elephant is bigger than a sparrow. They would agree without the least doubt that the cow is smaller than the elephant, but bigger than the sparrow. Ranking animals according to size, they would place the cat between the cow and the sparrow without any hesitation. But suddenly the child is faced by the problem of the horse. Where should the horse go? Is it bigger or smaller than the cow? When comparing objects of different characteristics, ranking is no longer so simple because taking into consideration various features may lead to various ranking results. (The horse is taller, yet shorter than the cow.)..”

Generalizing the above game Jánossy finds that the greater the qualitative difference between two items the greater is the quantitative difference needed to make the ranking reliable according to size. Qualitative difference is limiting the quantitative comparability – this is what Jánossy calls the ’criterion of comparability’. Obviously, the critical limit depends on the features compared. (If ranking is only according to height, then the horse-cow dilemma does not even arise.) Ranking, however, is not the aim but only the means, therefore the basis of the comparison cannot be changed to make ranking easier. A clear definition of the organizing principle may lower the critical limit but cannot eliminate it.

The next question is how to move from ranking to measuring. How to make a quantitative statement, or rather under what conditions could be quantitatively described that Sweden is more advanced than Turkey. If any one feature is not additive or cannot be traced back to some additive feature, it cannot be measured. If a feature is measurable, then the comparison of two objects can be decomposed into two steps of “numerical measurements along a fixed scale”. Which means that the critical limit of measurability matches the given absolute scale and the limit of comparability of the object. If the examined feature of the objects can be measured along an absolute scale, the critical limit can be expressed numerically.

This is an example to gave the hint that ranking and rating needs appropriate methods, and the methods have limits! It is very vital to accept the existence of the limits of comparability!

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