Choosing parameters for the Less Wrong Metric (LWM)
January 29, 2016
You’ll remember that in the last installment (before Matt got distracted and wrote about archosaur urine), I proposed a general schema for aggregating scores in several metrics, terming the result an LWM or Less Wrong Metric. Given a set of n metrics that we have scores for, we introduce a set of n exponents ei which determine how we scale each kind of score as it increases, and a set of n factors ki which determine how heavily we weight each scaled score. Then we sum the scaled results:
LWM = k1·x1e1 + k2·x2e2 + … + kn·xnen
“That’s all very well”, you may ask, “But how do we choose the parameters?”
Here’s what I proposed in the paper:
One approach would be to start with subjective assessments of the scores of a body of researchers – perhaps derived from the faculty of a university confidentially assessing each other. Given a good-sized set of such assessments, together with the known values of the metrics x1, x2 … xn for each researcher, techniques such as simulated annealing can be used to derive the values of the parameters k1, k2 … kn and e1, e2 … en that yield an LWM formula best matching the subjective assessments.
Where the results of such an exercise yield a formula whose results seem subjectively wrong, this might flag a need to add new metrics to the LWM formula: for example, a researcher might be more highly regarded than her LWM score indicates because of her fine record of supervising doctoral students who go on to do well, indicating that some measure of this quality should be included in the LWM calculation.
I think as a general approach that is OK: start with a corpus of well understood researchers, or papers, whose value we’ve already judged a priori by some means; then pick the parameters that best approximate that judgement; and let those parameters control future automated judgements.
The problem, really, is how we make that initial judgement. In the scenario I originally proposed, where say the 50 members of a department each assign a confidential numeric score to all the others, you can rely to some degree on the wisdom of crowds to give a reasonable judgement. But I don’t know how politically difficult it would be to conduct such an exercise. Even if the individual scorers were anonymised, the person collating the data would know the total scores awarded to each person, and it’s not hard to imagine that data being abused. In fact, it’s hard to imagine it not being abused.
In other situations, the value of the subjective judgement may be close to zero anyway. Suppose we wanted to come up with an LWM that indicates how good a given piece of research is. We choose LWM parameters based on the scores that a panel of experts assign to a corpus of existing papers, and derive our parameters from that. But we know that experts are really bad at assessing the quality of research. So what would our carefully parameterised LWM be approximating? Only the flawed judgement of flawed experts.
Perhaps this points to an even more fundamental problem: do we even know what “good research” looks like?
It’s a serious question. We all know that “research published in high-Impact Factor journals” is not the same thing as good research. We know that “research with a lot of citations” is not the same thing as good research. For that matter, “research that results in a medical breakthrough” is not necessarily the same thing as good research. As the new paper points out:
If two researchers run equally replicable tests of similar rigour and statistical power on two sets of compounds, but one of them happens to have in her batch a compound that turns out to have useful properties, should her work be credited more highly than the similar work of her colleague?
What, then? Are we left only with completely objective measurements, such as statistical power, adherance to the COPE code of conduct, open-access status, or indeed correctness of spelling?
If we accept that (and I am not arguing that we should, at least not yet), then I suppose we don’t even need an LWM for research papers. We can just count these objective measures and call it done.
I really don’t know what my conclusions are here. Can anyone help me out?