I’ve been reading a few articles by Nancy Cartwright (not of Simpsons fame) on measurement lately. Her ideas differ from the ones I’ve been using recently by Brian Ellis, who stresses a focus on orderings when devising a measurement system. Cartwright instead focuses on the quantities driving those orderings, stressing three requirements for measurement: characterization of the quantity, appropriate metrical system, and rules for applying the system in practice.

First, we consider just what this quantity is that we’re talking about – what kinds of things can have the quantity, what values it can have, and how it relates or is influenced by other qualities and quantities. For example, the degree to which a player is acting like an enforcer may have multiple dimensions, each of which may lead to an indicator to look for.

Next, a numerical system for conveying the diagram is devised. This system’s mathematical properties should reflect the quantity’s own properties – if an enforcement measure of 10 is not twice as great as a measure of 5, then common multiplication shouldn’t be present in the numerical system. To put it another way, 10am is not twice as great as 5am – it’s only 5 hours greater, so addition can be defined in a numerical system for clock time, but not multiplication.

Finally, there needs to be a procedure for figuring out how to actually measure things to get these numbers, such as using a thermometer for temperature or a scale for weight.

An analysis following Cartwright’s requirements would subsequently lead to an interpretation of enforcement in a formal framework that is (more or less) popularly accepted in the scientific community. So we might first talk about enforcement in terms of retaliations. Next we search for a framework where something like retaliation has been studied – perhaps a particular game theoretic model for the tragedy of the commons. Then we interpret our theory of retaliation in terms of this game theoretic model. If we can derive the characteristics of retaliation inside the model, then we’ve both demonstrated the fit of the model and tied our theory of retaliation to a larger body of scientific work.

It’s an interesting idea, because a deeper understanding of retaliation may help find better instances of enforcement by refining the original definition. There’s no guarantee of a pay-off, of course, and your background view of the ontological status of quantities and measurement will color the expectation of profit. But I have time, so it probably pays off to try both ideas and see if the results differ. I’m guessing that the next step down Cartwright’s route will be towards her work in causation.

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