Bekhap’s Law asserts that brains times beauty equals a constant. Can this be true? Are intellect and beauty quantifiable? Is beauty a property of the subject of investigation, or a quality of the mind of the beholder? Are any other relevant variables (attributes) intimately tied to brains or beauty? Assuming brains and beauty both are desirable, Backhap’s Law implies an optimization exercise – picking a point on the reciprocal function representing the best compromise between brains and beauty. Presumably, this point differs for all evaluators. It raises questions about the marginal utility of brains and beauty. Is it possible that too much brain or too much beauty could be a liability? (Engineers would call this an edge-case check of Beckhap’s validity.) Is Beckhap’s Law of any use without a cost axis? Other axes? In practice, if taken seriously, Backhap’s Law might be merely one constraint in a multi-attribute decision process for selecting a spouse. It also sheds light on the problems of Air Force procurement of the components of a weapons system and a lot of other decisions. I’ll explain why.
I’ll start with an overview of how the Air Force oversees contract awards for aircraft subsystems – at least how it worked through most of USAF history, before recent changes in procurement methods. Historically, after awarding a contract to an aircraft maker, the aircraft maker’s engineers wrote specs for its systems. Vendors bid on the systems by creating designs described in proposals submitted for competition. The engineers who wrote the specs also created a list of a few dozen criteria, with weightings for each, on which they graded the vendors’ proposals. The USAF approved this criteria list and their weightings before vendors submitted their proposals to ensure the fairness deserved by taxpayers. Pricing and life-cycle cost were similarly scored by the aircraft maker. The bidder with the best total score got the contract.
A while back I headed a team of four engineers, all single men, designing and spec’ing out systems for a military jet. It took most of a year to write these specs. Six months later we received proposals hundreds of pages long. We graded the proposals according to our pre-determined list of criteria. After computing the weighted sums (sums of score times weight for each criteria) I asked the engineers if the results agreed with their subjective judgments. That is, did the scores agree with the subjective judgment of best bidder made by these engineers independent of the scoring process. Only about half of them were. I asked the team why they thought the score results differed from their subjective judgments.
They proposed several theories. A systems engineer, viewing the system from the perspective of its interactions and interfaces with the entire aircraft may not be familiar with all the internal details of the system while writings specs. You learn a lot of these details by reading the vendors’ proposals. So you’re better suited to create the criteria list after reading proposals. But the criteria and their weightings are fixed at that point because of the fairness concern. Anonymized proposals might preserve fairness and allow better criteria lists, one engineer offered.
But there was more to the disconnect between their subjective judgments of “best candidate” and the computed results. Someone immediately cited the problem of normalization. Converting weight in pounds, for example, to a dimensionless score (e.g., a grade of 0 to 100) was problematic. If minimum product weight is the goal, how you do you convert three vendors’ product weights into grades on the 100 scale. Giving the lowest weight 100 points and subtracting the percentage weight delta of the others feels arbitrary – because it is. Doing so compresses the scores excessively – making you want to assign a higher weighting to product-weight to compensate for the clustering of the product-weight scores. Since you’re not allowed to do that, you invent some other ad hoc means of increasing the difference between scores. In other words, you work around the weighted-sum concept to try to comply with the spirit of the rules without actually breaking the rules. But you still end up with a method in which you’re not terribly confident.
A bright young engineer named Hui then hit on a major problem of the weighted-sum scoring approach. He offered that the criteria in our lists were not truly independent; they interacted with each other. Further, he noted, it would be impossible to create a list of criteria that were truly independent. Nature, physics and engineering design just don’t work like that. On that thought, another engineer said that even if the criteria represented truly independent attributes of the vendors’ proposed systems, they might not be independent in a mental model of quality judgment. For example, there may be a logical quality composed of a nonlinear relationship between reliability, spares cost, support equipment, and maintainability. Engineering meets philosophy.
We spent lunch critiquing and philosophizing about multi-attribute decision-making. Where else is this relevant, I asked. Hui said, “Hmmm, everywhere?” “Dating!” said Eric. “Dating, or marriage?”, I asked. They agreed that while their immediate dating interests might suggest otherwise, all four were in fact interested in finding a spouse at some point. I suggested we test multi-attribute decision matrices on this particular decision. They accepted the challenge. Each agreed to make a list of past and potential future candidates to wed, without regard for the likelihood of any mutual interest the candidate might have. Each also would independently prepare a list of criteria on which they would rate the candidates. To clarify, each engineer would develop their own criteria, weightings, and scores for their own candidates only. No multi-party (participatory) decisions were involved; these involve other complex issues beyond our scope here (e.g., differing degrees of over/under-confidence in participants, doctrinal paradox, etc.). Sharing the list would be optional.
Nevertheless, on completing their criteria lists, everyone was happy to share criteria and weightings. There were quite a few non-independent attributes related to appearance, grooming and dress, even within a single engineer’s list. Likewise with intelligence. Then there was sense of humor, quirkiness, religious compatibility, moral virtues, education, type A/B personality, all the characteristics of Myers-Briggs, Eysenck, MMPI, and assorted personality tests. Each engineer rated a handful of candidates and calculated the weighted sum for each.
I asked everyone if their winning candidate matched their subjective judgment of who the winner should have been. A resounding no, across the board.
Some adherents of rigid multi-attribute decision processes address such disconnects between intuition and weighted-sum decision scores by suggesting that in this case we merely adjust the weightings. For example, MindTools suggests:
“If your intuition tells you that the top scoring option isn’t the best one, then reflect on the scores and weightings that you’ve applied. This may be a sign that certain factors are more important to you than you initially thought.”
To some, this sounds like an admission that subjective judgment is more reliable than the results of the numerical exercise. Regardless, no amount of adjusting scores and weights left the engineers confident that the method worked. No adjustment to the weight coefficients seemed to properly express tradeoffs between some of the attributes. I.e., no tweaking of the system ordered the candidates (from high to low) in a way that made sense to each evaluator. This meant the redesigned formula still wasn’t trustworthy. Again, the matter of complex interactions of non-independent criteria came up. The relative importance of attributes seems to change as one contemplates different aspects of a thing. A philosopher’s perspective would be that normative statements cannot be made descriptive by decomposition. Analytic methods don’t answer normative questions.
Interestingly, all the engineers felt that listing criteria and scoring them helped them make better judgments about the ideal spouse, but not the judgments resulting directly from the weighted-sum analysis.
Fact is, picking which supplier should get the contract and picking the best spouse candidate are normative, subjective decisions. No amount of dividing a subjective decision into components makes it objective. Nor does any amount of ranking or scoring. A quantified opinion is still an opinion. This doesn’t mean we shouldn’t use decision matrices or quantify our sentiments, but it does mean we should not hide behind such quantifications.
From the perspective of psychology, decomposing the decision into parts seems to make sense. Expert opinion is known to be sometimes marvelous, sometimes terribly flawed. Daniel Kahneman writes extensively on associative coherence, finding that our natural, untrained tendency is to reach conclusions first, and justify them second. Kahneman and Gary Klein looked in detail at expert opinions in “Conditions for Intuitive Expertise: a Failure to Disagree” (American Psychologist, 2009). They found that short-answer expert opinion can be very poor. But they found that the subjective judgments of experts forced to examine details and contemplate alternatives – particularly when they have sufficient experience to close the intuition feedback loop – are greatly improved.
Their findings seem to support the aircraft engineers’ views of the weight-sum analysis process. Despite the risk of confusing reasons with causes, enumerating the evaluation criteria and formally assessing them aids the subjective decision process. Doing so left them more confident about their decisions, for spouse and for aircraft system, though those decision differed from the ones produced by weighted sums. In the case of the aircraft systems, the engineers had to live with the results of the weighted-sum scoring.
I was one of the engineers who disagreed with the results of the aircraft system decisions. The weighted-sum process awarded a very large contract to the firm whose design I judged inferior. Ten years later, service problems were severe enough that the Air Force agreed to switch to the vendor I had subjectively judged best. As for the engineer-spouse decisions, those of my old engineering team are all successful so far. It may not be a coincidence that the divorce rates of engineers are among the lowest of all professions.
Hedy Lamarr was granted a patent for spread-spectrum communication technology, paving the way for modern wireless networking.