Monday, November 04, 2013

AUCs: They Don’t Mean What You Think

The androsphere (see here and here) is taking issue with a comment, originally appearing on Dalrock’s blog and echoed by Susan Walsh, by “Kelly the PhD Statistician” on the difference between men and women with respect to their changing sexual market values over their lifetimes:

SMV

Dr. Kelly opines:

Those graphs are wrong because, with a fixed number of people in the world, equal between the sexes, you have to scale the curves so that the area under each one is the same.

I wouldn’t make a firm assertion either way as to whether the area under the two Excel graphs above are equal or not – appearances can be deceptive – but I do want to offer qualified support to my fellow PhD’s contention that the areas under the SMV curves of men and women are equal – or if you prefer, that the useful comparison is between normalized curves – provided we stipulate the curves are derived from weighted averages.

That the curves are averages of their respective sexes is beyond dispute:  nobody is likely to pretend that individuals’ curves don’t differ substantially in both their AUC and their shape over time.  But the weighting of individuals’ curves is likely to escape many readers’ consideration.

I would argue that the curves should be weighted by not less than two factors:

  1. The relative attraction that each has for members of the opposite sex.

    All parties to this discussion recognize that, considered collectively, both men’s and women’s “buying power” is in inverse proportion to their attraction.   (Attraction here should be understood as “demand for” in general, not just sexual attraction.)  I stress that this only applies collectively; no single market player magically increases his individual buying power by being disinterested, not if there are lots of other buyers and sellers.  But if the downward-sloping demand curve moves left, the price increases.  Again, I will not make a dogmatic assertion that the attraction men and women have for each other are equal on lifetime averages, but I will say that there is plenty of circumstantial evidence that the relative demand has changed over time, and that such changes have in the last few hundred years raised the relative attractiveness of women.

    Consider, for instance, the discarded custom of dowry.  The cultural assumption of yore was apparently that the only way to persuade a young man to take a woman off her parents’ hands was to pay him some amount of money or other goods.  In contrast, while no money changes hands today, it is a commonly accepted generality that a man must earn more than any prospective mate, at least as far as marriage is concerned.

    Consider also that philosophers, from (for instance) Francis Bacon in the 17th century to Nietzsche in the 19th, could be taken seriously when they wrote that women in their sexual capacity were mostly nuisances not worth the bother.  (My apologies to those philosophical historians who can better characterize the nuances of their thoughts on this subject.)  To the extent their opinions were representative of the men of their station, such views required women to bring more to any effort at attracting them.  But I doubt such opinions would gain mainstream attention today – yes, because of feminist sensibility, but also because, lower-order physical needs having been broadly met, sexual gratification remains in relatively high demand as an important element of both physical pleasure and self-actualization.

    Meanwhile, on the distaff side of the supply-demand curve, the need of an individual woman to obtain the assistance of an individual man in her own material provision has, in the modern economy, mostly dissipated.  That’s not to say that women don’t desire men for their own sexual gratification, but this leads us to the second weighting of the SMV curves:

  2. The extent to which polygamy is tolerated.

       Specifically, any given man’s SMV should be weighted by his relative ability, desire, and permission to monopolize the attention of multiple women.  In a society in which monogamy is the legal and social norm, then each man’s SMV curve carries equal weight in the averaging.  But if a man’ s attractiveness is such that he can command the affections of, say, three women, either serially or simultaneously, then his effective contribution to the SMV average for the duration of this arrangement is thereby tripled.  Likewise, the (mathematically necessary) two uncompetitive men have their SMVs, whatever they might be, multiplied by zero for the averaging purposes, since they are not market players.  Of course, in the by-and-by, if either the well-endowed man or his women tire of the polygamous arrangement, there may be an opportunity for the two remaining men to get back in the game, and the SMV averages must be adjusted accordingly.

    It is a well-established critique of contemporary social arrangements that many women today embrace, if not formal polygamy, then at least a willingness to rotate in and out of the sexual orbits of sufficiently attractive men.  For their part, men may have always been willing to enjoy the affection of multiple women, to the extent they could afford them, although this demand was latent under the pressure of socially-enforced monogamy.  That pressure, while still present when children are at issue, is otherwise quite diminished, and the standard of “affordability” in the monetary sense has been obviated by female economic emancipation.  Notice that, in contrast to the first weighting, this would predict the increase in the area under the male SMV curve rather than a decrease.

With these caveats in mind, then, I would concur with Dr. Kelly’s judgment that the AUCs of the male and female SMV curves are identical.

But I find it somewhat ironic that, confronted with SMV curves that imply (maybe) that men have higher lifetime average attractiveness than do women, feminists* turn to arguing in favor of SMV equality as a first-order principle.  I could point to numerous comment threads here and elsewhere in which they see no problem pairing average men with far-left-tail war-pigs on the grounds that, “Hey, that’s who’ll have you!” ignoring the extent to which, say, de-facto polygamy makes that possible.

UPDATE:  Here is my own Excel graph of the Rayleigh distribution with modal SMVs at 25 and 35 years old for women and men respectively and subtracting the years prior to the onset of puberty (ages 10 and 11 according to Wikipedia).  I hasten to say that there is no theoretical reason why the Rayleigh distribution would apply here except that it seems to be shaped right and has the advantage that the AUCs are mathematically identical.

image

It occurs to me that one of the implications of these graphs is that the average female at her peak attractiveness has no equal among the average men at any age.  In practice, I would argue that the male SMV variance at any age is higher, so women will have equals among men.  But there are necessarily fewer such men, which is why the competition for them among hypergamously inclined women appears so fierce.  And the rest?

They settle.  Women at their peak attractiveness who accept an average man are betting that 10 – 15 years on, the man is still around.  That strategy is not without risk, but the divorce statistics imply that men tend to be pretty loyal to the women they fall in love with at their peak beauty.

Of course, many women do not settle.  They keep “chasing the alphas” until their own SMV has fallen below the male average.  This strategy is also not without risk:  many men are out of the game at this point, and the average male SMV of those that remain is (in general) much lower given their higher variance.  But I will leave women themselves to testify to the extent this strategy secures their happiness.

* Used here as a pejorative meaning “women I disagree with”.  I have no idea whether, say, Susan Walsh qualifies as a feminist in the philosophical sense.

1 comment:

vultureofcritique said...

Thank you very much for injecting some scholarship into the maelstrom.

I am sadly untutored in Rayleigh distributions, but I hope to improve myself, little by little, if I can make the time to give this kind of issue serious, focused attention.

I am leery of making curves of "market value." Such abstractions are beyond my limited grasp of business mathematics. I feel more comfortable with the data reported from Indiana University and discussed at:
http://iconicmen.wordpress.com/2013/10/24/smv-is-it-real/