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I was fortunate enough to run across David Manley’s homepage today, which includes a list of very interesting papers. One paper in particular, A gradable approach to dispositions (with Ryan Wasserman), looks at explaining what it means for one glass to be more fragile than another.

The approach taken involves recognizing two distinct parts of a disposition – its triggers and its manifestations. Let’s say you enumerate all the ways a disposition can manifest, and call that the trigger-space for a disposition (my words, not theirs). You can then base a scale for measuring the magnitude of something’s disposition on the size of the part of the trigger-space that leads to this thing manifesting the disposition.

For example, let’s take a glass and assess its fragility. We might define its trigger space based on a range of heights from which we can drop it (e.g. 1 foot, 2 feet, 3 feet) and a set of surfaces (e.g. my pillow, my kitchen table, and the carpet in my living room). So we have a two-dimensional trigger space with nine possible combinations. If the glass would shatter from every height on my kitchen table, from 3 feet on my carpet, and never on my pillow, then the measurement would be based on the ratio 4/9 (depending on the choice of units).

This is a pretty cool idea that can be immediately applied to an analysis of retaliation. I enumerate the various ways that a retaliation can be triggered/provoked, and identify what the manifestation can look like (there’s a separate issue whether a disposition can manifest in different ways – I lean towards *yes*, but I’ll leave the discussion for another time).

Empirical testing for agentive dispositions like retaliation (i.e. dispositions whose manifestations depend on some conscious decision) are a little trickier than physical dispositions like fragility: you can’t depend on the same triggers leading to the same results every time. However, the core idea remains the same – by tallying the times that a trigger is followed by a manifestation, a measure of tendency for that can be established.

I’ve only read through the paper once, so I could very well be missing some key points. And I wonder about the ability to define dispositions that don’t have obvious triggers (e.g. the disposition to yawn, which at first glance seems to be a spontaneous event that happens more or less frequently). Heck, it seems that E.J. Lowe has reason to think that dispositions don’t even have triggers. Nevertheless, I think Manley and Wasserman’s paper is pretty damned interesting.

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.