In various fairly common situations, demanding more can result in receiving less.
The kinds of situation I am talking about are ubiquitous, but we’ll start with employee hiring. Suppose you are running a job search, and are primarily interested in some desirable talent T. Perhaps T is years of experience using some application or programming language.
Now suppose that people come in two varieties, liars and truth tellers. Truth tellers will truthfully (or mostly truthfully) state their level of T. Liars will claim to have whatever level of T they think will make you most likely to hire them. Suppose further that every truth-teller who meets your expectations will apply, and every single liar, regardless of whether they meet your expectations, will apply. Assume the average T value is the same for liars and truth-tellers.
Let’s say the population=1100 and 100 of them are liars. Now suppose you set the required level of T at 2 standard deviations above the mean. Assuming a normal distribution, 25 truth tellers will apply, and 100 liars. If you have no way of telling liars apart from truth-tellers, you have an 80% chance of hiring a liar, if you pick from among the applicants who meet the threshold at random.
Meanwhile if you’d set the level of T you were demanding at 1 standard deviation above the mean, you’d have a less than 40% chance of hiring a liar assuming you pick from among the applicants who meet the threshold at random.
If, for example, the value of a candidate to you is equal to their T-value expressed in standard deviations from the mean (positive or negative) you will actually get a lower T score on average by setting the cutoff at T=2, than if you’d just set it at 1.
A lot of readers are probably thinking that our simplifying assumption that employers are no better than chance at spotting liars is too harsh. I have a few things to say to that, viz:
A) The processes most employers use to determine quality past the resume stage- referee checks and interviews- are in many ways easier to navigate if you’re a little bit loose with the truth. It would actually not surprise me if the real process filters out more truth-tellers than liars.
B) Available empirical evidence suggests that people are generally totally delusional about their ability to spot liars, and spotting liars is actually incredible difficult.
C) Even if employers have some skill in filtering liars, if that skill is less than complete, it remains true that, past a certain point, increasing your expectations simply makes it more likely you will get a liar.
One interesting sub-case here is where you are interested in multiple traits, some of which you can check in applicants more easily than others. In these circumstances it may pay to set relatively modest minimum thresholds for the traits you cannot easily check, but adopt a policy of “more=better” for traits that you can accurately check.
Perhaps the most extreme, and comical, variant of this phenomena companies that demand candidates who have more years of experience in programming languages than those languages existed. I don’t know if this has ever actually happened, or if it is just a persistent urban legend, but any company that tries this is guaranteed to receive liars.
Although job searches are among the most obvious areas in which this paradox arise, it comes up in other areas. For example, seeking quotes, choosing between products and any other domain where the phrase “too good to be true” comes to mind.
When we consider that a pattern of high demands might turn once truth-tellers into liars, something like this phenomena could explain the flourishing of hypocrisy in some morally rigorous communities. Past a certain point, lying becomes a more workable strategy than actually trying to better yourself.
Demand the very best and you might get much, much less.
One reader suggests that reasoning similar to this is why you should find scientific papers just short of significance considerably more trustworthy.
Another commentor on Reddit suggests that we leave out one very important specification- a third type of person he calls an exaggerator. An exaggerator does not lie to an indefinite degree, but instead exaggerates their qualifications by a fixed amount. If such people are common, it may be prudent to demand a T value of 2, if your real minimum is 1.
This is a really great point, and I guess the overall picture here is that it’s difficult to know in the abstract what kinds of demands and criteria are the most likely to work. We’ve certainly demonstrated that under some conditions, demanding more will lead to less in expectation. In other conditions though this doubtless isn’t true. If there is an overall takeaway here, it is that the matter is very complex and unintended consequences abound. I don’t really have any algorithmic advice, but it is probably worth thinking through a variety of possibilities and balancing different concerns against each other.