Suppose we are not interested in “the best” or the “is qualified” premises and merely seek to stock our organization such that diversity of physical characteristic is maximized. That is, we forgo requiring ability or even minimal competence. Is diversity then possible?
First let’s ask what is on the list of measurable human characteristics. Chiefly sex and race–which some of those who seek diversity are at pains to say does not exist, yet it is the trait they most assiduously track (even “gender” is said to be fluid). Secondary measures are birthtime, birthplace, location, height, weight, age. Tertiary objects: hair quantity and color, blood type, fingernail length, wart quantity, freckles, exact genetic structure, and on and on. The number of measurable characteristics is thus very large; not infinite, but it may as well be.
Within a limited scope—the professoriate within Behemoth University, say—to maximize diversity of characteristic is thus impossible since you can only hire a finite number of people, yet we must track a (practically) infinite number of diversifiable characteristics. So no matter how the professoriate is stocked, some traits will not be represented. This horrible injustice will give cause for complaint to those possessing the excluded characteristics—if the hiring process is announced and known to be based on maximizing diversity.
Other traits will exist in multiple copies: for example, those with a complete set of limbs. Should these fully formed folks be balanced with those who are forced to make the sound of one hand clapping in the exact proportion in which they are found in the population? The whole population as it exists now? Or the past, too? In just a limited geographic area? Or the Earth as a whole? How shall we count? But suppose we sort all that out. We then face the problem that once we balance the limbed with the not-so-limbed, we have to turn to the other repeated characteristics (hairy versus bald, those over 5′ 10″ versus those not, etc., etc.) and try to balance them proportionally, too. This is impossible. Not just unlikely: impossible. Thus, even without “the best” or the “is qualified” premises, maximal diversity of physical characteristic is impossible.
Modified definitions of diversity are theoretically possible. If we say diversity (within a limited scope, like our university) means choosing members randomly from all humans without regard to any characteristic except life, then diversity is possible. I know of no individual who has ever claimed this is what they meant by “diversity”; and of course it is a definition that could only be cherished by anarchists. This definition can be saved by joining it with “the best” or the “is qualified” premises. Meaning that, for the task or scope at hand we pick randomly from the pool of people who are minimally qualified (each scope would have its own qualifications). “Picking randomly” has to be explicated: one method is first come, first serve (of the able). This sensible definition of diversity—random hiring of the competent—is evidently not what is meant by “diversity” as used by the sincere, however.
Another way to make maximal “diversity” possible, and the method loosely chosen by the sincere, is preferentially picking a limited number of characteristics to track, eschewing all others. I say “loosely” because scope drift often appears: just when you think you have nailed down a list of preferred traits, the sincere spring a new one on you. Once more, get them to agree in advance in writing of what they consider a worthy physical trait.
Like most do, pick at least race. Now, either race exists or it doesn’t (a tautology; further, I make no claim either way). If it does exist, it must be measurable: the sincere give many indications that it can be measured. Application forms for nearly every place of employment contain check boxes to indicate race. As far as I know, the information offered in these check boxes is not quantitatively verified. Therefore, given the preferential treatment accorded some races, it’s a wonder that more people haven’t hit upon the idea of checking the boxes of the race offered the most awards and advantages. If the sincere wish to deny a claim, they must then reveal whatever apparatus they have that they claim quantitatively, and without error, defines race. If this ever happens, it will be fascinating spectacle to behold. Just imagine a prominent member of the sincere claiming such eugenical prowess!
But this is carrying us too far afield. Suppose that, despite the check boxes etc., race does not exist. Skin color and the like surely does, though, and it is these traits that can be offered as proxies to something like race. Unfortunately, we run into the same problem as above. Skin color alone has nearly infinite gradations, thus true diversity of skin color is impossible. In any hiring scheme, some tones will be left out. And then we have to marry the secondary “racial” characteristics with skin color. The number of dimensions increases rapidly, and all hope of maximal diversity is lost.