The Mathematics of Equality

I sometimes wonder if so many folks don’t understand what equality is because they do not understand mathematics (perhaps among other things).  As I’ve mentioned before, equality is a statement about the value of things, specifically that those things have the same value.

This is often confused with identity, which is not identical with equality in either mathematics or logic, and certainly does not seem to be so in reality either.  This erroneous understanding of equality as identity is something that occurs across the political spectrum.  In the case of reactionaries or conservatives, they sometimes accuse those who are in favor of radical egalitarian policies of attempting to change the culture in such a way as to make men and women identical, and they point out (correctly) that men and women are not in fact identical, concluding that our social structures should reflect reality and make it clear that men and women are not identical.

This is generally not the case.  While it is true that liberals and progressives tend to want to break down social structures that have traditionally made clear that men and women are not identical, most of them will acknowledge (even the ones who favor regarding men who self-identify as women in our society as being women) that men and women are not identical.  If they did believe that men and women were identical or indistinguishable, then it would make no sense for them to advocate for accepting that self-identification with a sex other than the one assigned at birth as a meaningful category distinct from the other sex.

On the other hand, progressives and liberals can often fall into the mistake of at least implicitly regarding men and women as identical.  They are more prone to viewing men and women as interchangeable, at least in the sense that we can stick a men or a woman in the same job and have the result be the same, assuming that all skills and talents are equal and that the only difference is their sex.  This sounds an awful lot like identity in a mathematical sense of two functions which are defined in different ways, but always produce the same result because they are functionally the same.

We all know, of course, that men and women are not actually interchangeable on average.  Setting aside jobs that most men can do more quickly because of their larger upper body musculature on average, even in office jobs men and women are not interchangeable on average.  Progressives and liberals will often explain those differences (whether in conflict resolution, workplace relationships, or leadership styles) by attributing them all to differing social expectations rather than to something innate to their sex.  Reactionaries and conservatives are much more likely to attribute those differences to something innate to the sexes.

In my view, they are both correct in some areas and incorrect in others, but that’s an issue for another day.  Another issue for today is the matter of proportionality, which is yet another concept which is often confused with equality.  For example, a professor proposed a fairly common idea that the ratio of men and women in Congress should be proportional to the ratio of men and women in the general population.  I would agree, though I would point out that this is not a matter of equality in the sense of men and women being of the same value.

Let’s imagine for a moment a table with oranges, the total number of which is 10.  Out of the 10 oranges, 5 are mandarin oranges and 5 are navel oranges.  All of these oranges cost the same amount, which is to say that they are equal in value.  Let’s imagine that we want to give some of the oranges to a neighbor in need, and so we take 4 of the ten oranges out of the ten.  Whether we take 4 mandarin oranges or only 1 mandarin orange and 3 navel oranges, the oranges are all still equal.  Taking out 2 mandarin oranges and 2 navel oranges just means that they are proportional to the larger set of oranges.

It might be fairly said that this is a poor comparison to Congressional demographics, given that Representatives and Senators can do more to write, propose, and vote for legislation that benefits their sex.  I’m just not sure that it’s all that relevant a difference.  Most civil rights legislation recognizing for women the same civil rights which men have enjoyed for a long time was proposed and voted for by men.   Those pieces of legislation didn’t come about because there were more women in Congress.

Even in cases of political leadership, merely having lots of folks of one sex doesn’t guarantee good treatment for one’s sex, or even better treatment.  Just ask the men who get sent off for war after war by their fellow men, or the men who were killed at much higher rates by other men who were acting as slaveholders and police officers, or the men who were put out of work because of the poor decisions of other men, or the men who have to pay alimony for children who aren’t theirs.  It turns out that while human beings tend to favor people who share their characteristics, simply giving people power doesn’t mean better conditions for those who share certain of their characteristics.

This is not to say that proportional representation in Congress isn’t a worthwhile goal (I happen to think it is), but it is to say that proportionality will not cause equality, nor is it identical with equality.  And it is to point out that proportionality is not necessary or even useful in all areas of life.  What would be gained by having an equal number of male and female midwives?  What would be gained by having 50% of a men’s support group be women?  Equality and proportionality are not directly proportional, as reality shows us.

There is no need to insist that there be just as many men as women who have priestly roles in the Church of Satan or the Church of England, because the proportionality is no guarantee of equality and is not itself equality.  If women want to create a women-only business or an organization that is lead only by women, then I am fully supportive of that.  And the same goes for men who create a men-only business or an organization that is lead only by men.

If someone wanted to make a civil right or certain political positions available to one sex only, then we should rightly demand a high level of scrutiny on such a proposal to enact a disproportionate application of the law because such restrictions are rarely benign.  On the other hand, the level of scrutiny required for allowing disproportionate representation in private groups is not as high as the standard of evidence for equal rights under the law because private groups intended to support one sex or provide a safe space for that sex are much more likely to be benign.

All of this is to say that those of us who seek equality should do so in a meaningful way, not accepting shallow substitutes like proportionality or interchangeability in lieu of genuine equality.  To value equality is to value people equally highly despite their differences; equality is not created by making social groups more proportional or downplaying their differences.

If we want to have equality, then it would be helpful to examine the mathematics of equality so that we can define the problem in precise terms, because problems are generally much easier to solve once we understand them clearly.

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