I do not understand the reference to Arrow's Paradox in a discussion of procurement policy (almost certainly related to my lack of knowledge). Can you elaborate?
Sure --- there's a neat paper by Franssen (2006) that demonstrates the formal equivalence between optimization problems and the social policy problems Arrow was concerned with. Basically, Arrow says that some constituents will always lose out under any social policy. Franssen showed that you can swap out "composite cost metric" for social policy and "components of the cost metric" for constituents, and the same arguments apply.
Here's the full citation. Turns out I misremembered the year (2005).
Franssen M (2005) Arrow’s theorem, multi-criteria decision problems and multi-attribute preferences in engineering design. Research in Engineering Design 16(1):42–56
Sure there is. Sadly you'll need humans for that part, though. You could get several humans who all get a sample of each supplyers chalk, and then ask them to rate the quality of each on one (or several) scales. The computer can then integrate this rating with the rest of its metrics.
I didn't mean to say that it wasn't possible, you probably don't need a subjective measure of quality. I think you could empirically discover some objective characteristics of good chalk that would do the trick. You could at least quickly reject the worst chalk which is too brittle and too hard. I meant to say that there was and is no way that is recognized sufficiently universally that enables one to specify a chalk with the desirable properties to a gov't purchasing agent such that s/he can buy the right stuff.
Specify bending strength, the chalk must not snap under specified force. Next define a writing pressure, angle and stroke speed and require fewer than x blank areas in the line. Require that the line width be within a specific tolerance, not too thick not too thin.
Maybe a spec like this doesn't exist now, but you could use the good chalk and write the spec based on how it did.
The trouble is that the places that sell chalk to universities don't rate chalk like this. Like I said in another post ITT, we derped around for a couple years before we just gave up and installed the damn whiteboards.
