Measures — quantities to which some arithmetic can be meaningfully applied — can be fitted to some human attributes, even if not to others. When attempting to compare some populations to others, an assumption is made that the properties of the individuals within these populations are subject to quantification of some sort, and that the quantities are commensurable across populations. But usually these assumptions are implicit and unrecognized, and even those who have some awareness that they are dealing with quantities very often don't have a proper grasp of elementary issues.

Very often, people try to understand distinct populations in terms of some notion of averages. If each and every member of every population were exactly average in every regard, then averages would be perfect measures of the populations as such. More generally, if for any two populations the share of that population deviating from average by some specific amount were the same, averages would be sufficient for any comparison of the attributes of populations, except for population sizes. But if the overall variance from average in one population is different from that in another, then thinking in terms of averages can go very, very wrong.

Here are hypothetic distributions for some attribute within two populations, each population having the same number of members:[1] For both Population A and Population B, the median[2] of the attribute is the same, but Population B has more variance from the arithmetic mean than does Population A. Even though each of these two populations have the same median, more members of the population of greater variance are below some some measure, and more members of that same population are above some measure. Population B₂ has the same variance as Population B, but the same arithmetic mean (rather than median) as Population A. Again, even though the center is, by some measure, the same for both populations, more members of the population of greater variance are below some some measure, and more members of that same population are above some measure.

Even if a population has a higher center than Population A, if it has a greater variance then it will dominate the lower range of measures below some measure. And even if a population has a lower center than Population A, if it has a greater variance then it will dominate the higher range of measures beyond some measure.

If a measurable attribute correlates positively with social success, then ceteris paribus, a population of higher variance is going to dominate both social winners beyond some level and social losers below some level. If a population generally has greater variance amongst its attributes, then — discarding the assumption of ceteris paribus — that population is going to dominate both social winners beyond some level and social losers below some level; even if it has the same median or same mean or even a lower center than another populations.

In fact, though I cannot readily graph the cases in which attributes are only partially ordered and not measurable, the reader should see that the underlying point does not depend upon the measurability of the attributes, but only upon one population having greater propensity for variance than another.

But

• If one is only looking at the losers and thoughtlessly assuming that their numbers are explained by averages, then one is going inappropriately to infer that the population is generically inferior.
• If one is only looking at the losers, while thoughtlessly assuming that the averages are the same and that nothing else about the population itself can explain the difference in outcomes, then one is going inappropriately to infer that the population are victims of systemic bias.
• If one is only looking at the winners and thoughtlessly assuming that their numbers are explained by averages, then one is going inappropriately to infer that the population is generically superior.
• If one is only looking at the winners, while thoughtlessly assuming that the averages are the same and that nothing else about the population itself can explain the difference in outcomes, then one is going inappropriately to infer that any rival population are victims of systemic bias.

In each case, if we look at the other end of the distribution, the thoughtless conclusion falls apart.

When the last of these errors is made, an attempt may be undertaken to offset illusory bias, by putting an institutional thumb on the scales to shift Population A generally forward, until the the number of social winners at every level is at least the same. But notice what is then really happening as the relative outcomes for most members of the population of greater variance fall increasingly below those of the population of less variance — at previously targetted levels the population of lower variance comes to enjoy greater social success than does the population of greater variance. And notice that the population of greater variance necessarily still dominates above some value, albeït that the value increases as the institutional thumb comes down ever harder in a misguided attempt to match the upper tails of the distribution.

Only actual systemic bias can bring the number of social winners across populations into equality above any given level of social success beyond the center; and, the larger the population, the greater the required bias for such an outcome, and the more that most of the population of greater variance are victimized.

If the two populations are not equal in size, then the foregoing analysis would simply need to entail talk of proportionality. But one might as well speak and write of two populations of the same size, because the real-world application involves two populations that are very close to the same size in most first-world nations. The greater variance of one of those two populations is a consequence of the greater chaos in the formation of one of that population's chromosomes and of a lack of redunancy for another.

Unfortunately, most of the attempts to analyze what has been happening has entailed ham-fisted theorizing about differing averages.

[1] A population with finite membership cannot perfectly conform to a continuous distribution function; but, the larger the population, the less the necessary non-conformance.

[2] The median for each population is the point such that as many members of the population are above it as are below it.

Often, when talking about the distribution of measurable human attributes, people refer to the bell curve, which is to say to a Gaussian distribution, more commonly known as a normal distribution.

One immediate difficulty is that the Gaussian distribution extends symmetrically without lower limit to measurements with positive probability, whereas the natural measures of most of the attributes that will interest us have lower limits of possibility (typically at or above zero). For example, no one has negative weight or negative height. Simply truncating the lower bound of a Gaussian distribution usually doesn't make a great deal of sense, because few people will even be near the lower bound, rather than a fair number at it or just barely above it.

Instead, the distribution will more typically look something like this:

Mind you that measures can always be transformed, and a measure that has a lower bound of b can be transformed into a measure without lower bound simply by the device of subtracting the bound and then taking a logarithm: measure₁(x) = log_e[measure₀(x) - b] Some set of transformations can surely be used to arrive at one with a distribution that is well approximated by a Gaussian distribution. But, for the most part, I'd rather use natural or familiar measures than manipulate the data to arrive at a Gaussian distribution, especially as one otherwise typically needs to invert the transformations at the end of the analysis, to make sense of things.

In the near future, I plan to post an entry about misreading the consequences of different variances in different human populations. What I have to say could all be expressed in terms of Gaussian distributions, but I don't want to do so, nor did I want that future entry to begin with a discussion such as that here.

Imagining all of a society's various generation and allocation of goods and services as if the creation and distribution of one big pie is very much analogous to imagining all of the sexual interactions of that society as one enormous orgy.

Shortly before mid-night on 21 February, I submitted a copy of my paper on Sraffa to yet another journal.

The submission software of the previous journal still lists my paper with a status of Submitted to Journal. Perhaps they don't have a mechanism in place for removing an entry when an author has responded to abuse by withdrawing work at that stage; perhaps someone is hoping to avoid the attention of a manager with greater authority. I've received no further communication from the publisher, nor any from the editor.

On 19 January, I received an expected desk-rejection of my paper on Sraffa from the journal to which I'd submitted it a day or two earlier. The editor wrote that he'd enjoyed looking at the paper but that it were not the style of work that the journal published. I don't feel slighted by the lack of an explanation, but I'm more unhappy with something that might be mistaken for an explanation that doesn't actually explain anything.

(My paper on indecision was more than once rejected without explanation for the rejection, but with meta-explanation that providing an explanation would delay my submitting to some other journal.)

Upon receiving the rejection, I looked for another journal. What otherwise might have seemed the best choice required a €100 submission fee, not refunded in the event of a desk-rejection. I instead chose a different journal, in part because it is headquartered in Italy, where I expect more attention is paid to Sraffa even by mainstream economists.

The submission process was stalled by a failure of the software used by the journal's publisher, and a weekend had to pass before that failure was corrected. In the early morning of 23 January, I completed the process. Since then, the reported status of the paper has stood at Submitted to Journal. That report is supposed to change when the paper is assigned to a specific editor.

Once more, a desk-rejection is highly likely. Most papers that are sent to reviewers are rejected by the reviewers. Most papers that are not rejected are returned to the authors for revision. Most papers returned for revision are accepted after revision, but not always.

I've submitted my paper on Sraffa to yet another journal. Fortunately, this latest journal wanted the initial submission to be in PDF, and wants accepted papers in LAΤΕΧ.

I expect a rejection from this journal, simply because they receive an enormous number of submissions, and will probably decide that their readers would rather not digest a thorough examination of a heterodox theory to which few of them ascribe any credibility, which examination reaches conclusions that, over all, will not surprise them. But I'll hope for an editor to think otherwise.

And, unshockingly, to-day my paper on Sraffa was rejected by the journal of history of economic thought to which I submitted the paper. In my previous entry, I wrote

A few problems threaten this submission. […] Third, historians might — rather reasonably — see the article as better placed in a journal of theory than of history; I do not, for example, much discuss the position of Sraffa's book in historic context.

Well, the editor didn't suggest submitting to a journal of theory, but did say that it didn't fit the mission of a journal of history of thought.

If I again submit to a journal of theory, then I'll make a note to its editor of the history of rejection. But I'd like to find a respected journal that publishes both articles on theory and articles on the history of economic thought, so that the editors won't pass the buck based upon such distinctions. I'd also very much prefer not to submit to any journal published by Springer, given the abuse to which they subjected me in the case of my paper on indecision.

As anticipated, my submission to a second journal of my paper on Sraffa received a desk-rejection, in the morning of 8 January. The editor at the second journal, like that at the first, suggested submitting to a journal on the history of economic thought.

I decided to go ahead to do just that, but found that my first choice amongst such journals both wanted the article to be submitted in the format of Microsoft Word, and was somewhat particular about the appearance of formulæ. I do not have any recent versions of MS Word running on any computer, and the computers on which I have old versions installed are old devices, tucked-away, and of course I wouldn't in any case want to reënter the whole article from the keyboard. So I wrestled with going from LAΤΕΧ (by way of LyX) to DOCX by various means, with the formulæ repeatedly trashed in the process. I stepped-away from the problem a few times, rather than become over-stressed.

Finally, early this morning, I had a version that I thought were good enough to submit. I stepped-away again until to-night, and then effected a submission.

A few problems threaten this submission. First, the journal normally wants articles of 11,000 words or fewer, whereäs this article is about 12,665. Second, as may be inferred from their insistence upon the format of Microsoft Word, this journal leans away from mathematic presentation. Third, historians might — rather reasonably — see the article as better placed in a journal of theory than of history; I do not, for example, much discuss the position of Sraffa's book in historic context.

If the paper is rejected in whole or in part on that last basis, then of course I will make a note of such objection in any subsequent submission to a journal of economic theory.

As to how I effected the conversion, I used LyX to export a file in ODT format, then used LibreOffice Writer to do extensive clean-up and export to DOCX, then reïmported the DOCX file into LibreOffice Writer, and effected a second extensive clean-up, the results of which I later submitted.

In keeping with my expectations, albeït not with my hopes, during this morning I received a desk-rejection from the first journal to which I submitted my paper on Sraffa. The editor wrote

I read your paper with interest. I appreciate the ambition and breadth of the work as well as the care you put in writing the paper in an accessible and engaging way. However, the contribution is more appropriate for a journal that specializes in the history of economic thought, rather than for a journal that focuses on modern contributions to economic theory.

Two conceptions of modernity seem to be confused here. If the editor were to say that Sraffa's work were not at or near the cutting edge, then I would completely agree with the editor. On the other hand, only if the applicability of that work were without living controversy would discussion properly be restricted to history-of-thought, yet Sraffa's work is at-or-near the center of thought for academically active schools.

Mind you that something could reasonably be treated as within the scope of history-of-thought without being restricted to that scope, so I may indeed submit the paper to a journal on the history of economic thought. But, before taking that route, this evening I submitted the paper to a different journal of economic theory. Yes, I do expect another rejection, and probably another desk-rejection. Still, I gambled on a hope of acceptance.

If-and-when I submit to a journal of history of economic thought, I face some threat of my paper being rejected as too mathematic for the readership. (One reason that I have not submitted the paper to The Cambridge Journal of Economics is that their guidelines for authors suggest that they would reject the paper with the excuse that the exposition relies too heavily upon mathematics.)

Before receiving the rejection, I had effected some minor revisions to the paper. I corrected a typographic error, replaced adjectival -ical with -ic wherever the latter would do, and removed most of my expletive uses of it and of there.

Although expletive uses are grammatic and I've not seen them condemned in any book of style, after I first completed a draft of that paper I became uncomfortable with those uses. That discomfort is part of a prior trend of my becoming uncomfortable with expressions that facilitate conceptual illusions. Saying or writing it is X suggests that something is X; sometimes something is X, as when we say it is sad that you couldn't come, in which case the something is that you couldn't come. Even then, it is a forward reference, and forward references are generally very bad things. But sometimes the it is just a way of satisfying the grammatic need for a subject, as in it's raining. Saying or writing there is X or there are X suggests that X is-or-are at a specific location, but likewise is often just a way of satisfying the grammatic need for a subject.

Usually, one can easily do without these expletive uses, but I acknowledge that sometimes they actually produce more easily understood sentences. Indeed, I left two such uses in the paper because no alternative occurred to me that did not create ambiguity.

[Up-Date (2024:01/07):Alas, I have found more expletive uses in my paper. My search string was naïve, and missed cases with modal auxiliaries. I don't know when or even if I will eliminate those further cases.]

Late last night, I finally got around to submitting to a journal a draft of my paper on Sraffa's Production of Commodities by Means of Commodities; Prelude to a Critique of Economic Theory [1960].

My attention was first directed to Production of Commodities in the mid-'80s. I did no more than to skim the work at the time, but I planned someday to critique it carefully, and developed an expectation that I would write my critique for academic publication. In the spring or summer of 2015, I finally took-up that task. I completed a working draft by 18 May 2016, then entitled The Begged Questions and Confusions in Mr. Sraffa's Theory of Price, and began providing copies to other economists.

I've made no profound changes to the paper in the time since, but I'd hoped to complete and have published my generalization of decision theory before publishing this paper on PoCbMoC. And editors and reviewers seem likely to treat my paper either as uninteresting or as anathematic; I've been unsure about to which journals I should submit it. But some dreadful lines of thought have been resurgent, and I have grown concerned that Sraffan thought — which epitomizes much left-wing thought about economics — may soon have accelerating popularity. So I've decided to seek now a respectable journal to publish my paper, with the title Mr. Sraffa's Theory of Price; A Thorough and Critical Examination.

I can expect that the article will be rejected by several journals before it finds acceptance. Editors who reject the article without sending it to peer-review may take a few weeks. Peer-review in each case is likely to take four or more months. So perhaps a couple of years will pass before the article is accepted, and then perhaps the better part of a year will follow before it is published.