The Mathematics of Undervaluing and Overvaluing Job Candidates
Then there’s the opposite scenario: When, because of comparably flawed math, you’re overexcited by your incomplete or flawed understanding of the candidate(s) “wow!-factor” or the job market.
The two chief mathematical lapses fall into two categories:
- Confusing proportions and absolute numbers: confusing absolute numbers with relative proportions (to be explained below)
- Confusing payoffs and probabilities: failing to keep payoffs and their probabilities emotionally and cognitively separate (also explained below).
Consider the case of ill-advised under-excitement: Five years ago, you interviewed a spectacular candidate —a “10” and were dazzled by some credential, e.g., a Wharton MBA or internship at a big corporate player. Hypothetically speaking and to make a mathematical point, let’s say the proportion of such 10s in the general population of candidates (which is a sub-population of the general population) was, according to the data available at that time, about 25%.
But, over time, as their number and demand for them, but not their proportion in that sub-population, has increased—again, hypothetically speaking, your encounters with and overall exposure and familiarization, including through media, to these 10s have likewise increased, and you find yourself less impressed, as you would with anything trendy that has become cliched, even though the small proportion of them in the candidate population remains constant, within an unaltered bell curve and despite the demand keeping up with their increased numbers.
So, this invites the question: Why would you or anyone become less impressed with an “impressive” candidate, when the number of others who are exactly the same has increased (increasing the probability of encountering, interviewing or hearing, reading, etc., about them), but when the proportion of them in the candidate population hasn’t?—especially when demand for them and the total number of interviews with them has at least kept up with their increased numbers).
Is that logical or rational?
Or does the increased demand for them and interviews cut both ways: The 10s are valued because they are in demand; but psychologically trivial because of increased exposure to them created by that same demand?
Or is your cooling to them defensible in terms of some absolute numbers concept of scarcity and “scarcity value”, as opposed to a relative (static) proportion concept of scarcity and scarcity value? (This is a useful question, even though some forms of “excellence” have, in fact, historically increased proportions as well as absolute numbers, e.g., B.A.s.)
The Mathematics of Becoming Blasé
To focus the analysis, imagine a pool of five candidates, one of whom is a “10”, the other four being “5”s. Now, imagine maintaining the candidate population’s 1-to-4 proportion, but increasing the absolute numbers to 1,000 and 4,000, respectively. So now there are 1,000 “10”s and 4,000 “5”s. The percentage of 10s has not changed; it is still 25%.
Hence, you’d think that in terms of “scarcity value”, as a function of proportion of the population, the market value of being a 10 would be unchanged—since the “supply”, as a proportion, has not increased, despite the increase in numbers. (Again, assume supply/demand ratios or differences are unaltered, or that total demand exceeds total supply.)
A “10” should presumably be as exciting as before, given it’s relative rarity and high “score”. But, given the increased numbers, your market demand for and media coverage of the 10s, your “exposure” to them has increased. Hence, if you are operating with a numbers-based concept of supply and scarcity, you will be less impressed than previously by any individual 10, in comparison with all the other 10s and the now larger total number of them. On the proportion-based perception, that should not happen and you should remain as impressed as ever, rather than blasé.
That’s because, in terms of “mathematical expectation” or “expected gain”, the average payoff to your company in interviewing the entire candidate general population will not change as the population increases from 5 individuals to 5,000, if the proportions do not change. That is to say, (10 x 0.25) + (5 x 0.75) = 6.25 expresses the (weighted) average wow!-denominated payoff to a company or economy that hires the entire candidate pool, irrespective of how big that pool is, given the proportions do not change with size. (Here, 10 and 5 are the utility values; 0.25 and 0.75, the probabilities.)
Despite the fact that the proportion, and therefore the payoff, is unchanged, you nonetheless apparently have become less impressed with the 10s, because of your increased exposure and their increased numbers, much as you are now unlikely to be impressed with someone who has a cell phone (but with the crucial difference being that cell phones have vastly increased in proportion as well as in numbers since their debut).
Is that a mistake?
The Case of Increasing Numbers, Not Proportions
Consider the following: The rankings (on the 0-to-10 scale, for example) should not change as only the number of individuals of each type, but not the proportion, increases. For example, an IQ test score’s percentile rank, e.g., about 99.9% for an IQ of 170, will not change just because the total tested population size increases. (So, should your ranking of that rank, i.e., the utility to you of that percentile rank, change? For constant proportion MBAs, if not for constant proportion IQs?)
Moreover, even if the proportions in the population did change, the rankings shouldn’t. That’s because the “utilities” (the value of the credential) and “probabilities” (of finding it in the reference population) are presumably independent of each other. This means that the “wow!” factor of being a 10 should not be impacted by there suddenly being immensely more 10s in the candidate pool, but in constant proportion, i.e., 1-to-4, relative to the 5s, and on the additional assumption of demand strong enough to absorb the increased numbers. Yet, we may be inclined to argue that if the proportion of geniuses were to increase to 90% of the total population, our economy would suffer, if they psychologically could not accept the routine jobs that have to be done.
The Error of Linking Utility and Probability
However, it seems that psychologically, for many, if not most people, value and probability are not independent, e.g., the fabled case of “sour grapes”, when the low probability of successfully reaching the grapes out of reach not only kills interest in trying, but also in those grapes, period, as a palatable rationalization for not bothering to try.
Likewise, when things or people seem “too easy”, interest in them—and their value or utility—often decreases, when, mathematically speaking, in terms of expected gain rational-decision theory, it should not.
The implication for recruiting is that, in defiance of the mathematical axioms, some recruiters may be inclined to devalue a credential that seems plentiful and easily secured (with lower utility because of higher probability, like a woman of “easy virtue”), while especially over-valuing those that seem scarce, merely because of their small numbers and/or proportions (higher utility because of lower probability). This “logic” also partly accounts for our frequent and puzzling over-fascination with some gems largely because they are scarce.
This suggests that, among those recruiters unimpressed by the theoretical predictions for expected gain, the “wow!” factor is likely to be a psychological function of the “score”, the exposure to the credential—including that created by market demand, the number of candidates with a given rank and the proportion of the population attaining that score or credential, i.e., is a function of “intrinsic” and “market” value and of perceived “scarcity value”, or of a variable that is a function of a mix of these.
This, in turn, suggests a 4-variable model that determines the expected gain, the probability and utility and psychological impact of a candidate’s credential: total number, proportion, demand and exposure—with fine-tuning in terms of direction and speed of demand change, client or market demand-induced trivialization through repetitive exposure and even recruiter fatigue (“fed-upness”) and boredom with it all.
To reiterate, what makes all of this important is that the bottom-line impact of diminished/increased, over/under-rated, and an objectively unwarranted wow!-factor can be considerable, e.g., when a recruiter submits an overly tepid or effusive recommendation of a candidate based on it.
Applying the model, there are predictions that it suggests, illustrated here by just three out of dozens possible . A plus sign (+) means an increase; a minus (-) means decrease and a zero (0) means no change.:
1. numbers (+)/proportions (+)/exposure (+)/demand(moderate and stable): If, contrary to expected gain theory, the probabilities and utilities psychologically interact as interdependent variables, they may cause you to devalue the credential, because of diminishing scarcity—i.e., increasing triviality, unless a positive “critical mass”, strong demand and/or synergy effects (e.g., of successfully building a team of 10s) kick in big time. At the same time, you may unwisely cut back on your efforts to find clients or applicants looking for or offering that credential.
This scenario presents a risk of under-rating the candidate or the market because of the blasé-blahs.
2. numbers (+)/proportions (0)/exposure (0)/demand (moderate and stable): You probably will not revise your “utility of utility” estimates, i.e., the credential “score” will have the same “wow!”-impact, despite its becoming more commonplace in terms of numbers only.This is a harmless scenaro, impacting neither your efforts nor the outcomes.
3. numbers (+)/proportions (+)/exposure (-)/demand (0): High risk of over-rating the credential because of “scarcity illusion”, a.k.a., underestimation of the probability of encountering the credential.In applying the model, a sharp distinction must be made between “client demand” and “market demand”, since they may different from each other in terms of strength of demand.
One of the most common manifestations of the confusion of numbers and proportions or of utilities and probabilities is the tendency to paradoxically feel, as recruiter or as candidate, that as the intensity of competition for job opportunities increases, that competition becomes more trivial (in terms of value or “specialness” as well as in terms of probability or commonplaceness).
To grasp this scenario, just imagine you walk into a reception area and see 30 well-credentialed and spiffy clones patiently perched on the edge of their seats, waiting their turn to be interviewed.
An intense scene…
… yet somehow trivial.