Several people have inquired as to my opinion on the OKCupid post The Mathematics Of Beauty. I’ve blogged data from this dating website in the past, in particular, the differential race consciousness of women vs. men. But that material is a different class than the current post. As I have noted before, there is a robust result in the social science research over the past decade which suggests that women express & reveal more race consciousness than men when it comes dating & mating. The previous OKCupid analysis wasn’t ground-breaking, it simply added some wrinkles into a series of patterns which were replicated in the literature. The current results are different insofar as I haven’t followed the academic literature which relates to this in detail. This matters because unlike most of my peers I’ve done very little online dating (basically 2 weeks in the summer of 2002), and so can’t bring a personal familiarity with the topic to the discussion. To be sure, plenty of my friends have discussed their issues with online dating with me, so I’m not ignorant of the phenomenon. My male friends routinely complain how difficult it is to get the attention of women who are bombarded by messages from all directions. A female friend who is in her mid-30s chronologically, but physically resembles a women in her 20s, has complained how men clearly have automatic age filters set for searches which are working against her.
Let’s start at the beginning. To the left you see a scatter plot of # of messages received by women per month as a function of their rated attractiveness. They controlled for background variables (e.g., race). On the one hand, the results aren’t surprising. You see that more attractive women receive more messages. But on the other hand, the residual (noise) around the trend line is enormous, especially in the top half the distribution. I am personally rather surprised at the enormous variance of message # at the higher ratings. But here’s an important point: this is the mean rating of attractiveness. It turns out there’s a substantial variance around the means of attractiveness for any given mean value. There are two ways to look at this. It seems there is a general consensus about a mean of a distribution as to someone’s attractiveness level. In other words, you don’t have a preponderance of uniform distributions, suggesting that attractiveness is extremely plastic. This is in line with what evolutionary psychologists have found: people from “small scale” societies can ascertain who is, or isn’t, attractive in a set of photos of Europeans. But there’s another part of the story: differences in opinions about physical attractiveness of the same person from the vantage point of outsiders.
To the right you have the top line results. The plot shows the response # as a function of variance of assessments for women at the 80th percentile of attractiveness. As you can see it looks like the number of messages starts to rise as a linear function above the center of the variance range. Below the curve you see an equation which predicts the number of messages as a function of the shape of the distribution. Apparently OKCupid attractiveness measures range from 1 to 5, and the coefficients in front of the values indicate the effect upon the final number of messages. So, if all the men rated a woman a 5, then you’d expect an increase of messages above expectation. The weird thing from the equation is this: according to the model it is better to have everyone evaluate you a 1 than everyone evaluate you a 4. Look at the signs of the coefficient. I don’t personally believe this outcome is valid. In fact, I assume that there’s no one in their data who was rated a 1 by everyone, or, a 4 by everyone. These sorts of models are giving us precise inferences, but the models themselves are only rough correspondences to broader underlying dynamics (which is why people argue over which model better “fits” data and such). Pushing a model to ludicrous extremes doesn’t necessarily give us insight. Rather, it suggests that we should be careful about confusing the model for reality (just as we should be careful about confusing a mean for the totality of the shape of the distribution). I suspect the equation would be different if one constrained the range of attractivenes (e.g., 50th to 100th percentile vs. 25th to 75th percentile), but the qualitative result would hold. The model may be precise, but the inferences we make should be a little less precise.
The authors of the OKCupid post implicitly give a nod to this, illustrating the peculiar pattern of variation in message responses. Their data set indicates that a woman who received more extreme reactions would receive more messages than a woman who received more uniform reactions, even if the latter had a higher average rating than the former. This is certainly counterintuitive. What’s going on here?First, let’s present the OKCupid explanation:
Suppose you’re a man who’s really into someone. If you suspect other men are uninterested, it means less competition. You therefore have an added incentive to send a message. You might start thinking: maybe she’s lonely. . . maybe she’s just waiting to find a guy who appreciates her. . . at least I won’t get lost in the crowd. . . maybe these small thoughts, plus the fact that you really think she’s hot, prod you to action. You send her the perfectly crafted opening message.
“sup”
On the other hand, a woman with a preponderance of ’4′ votes, someone conventionally cute, but not totally hot, might appear to be more in-demand than she actually is. To the typical man considering her, she’s obviously attractive enough to create the impression that other guys are into her, too. But maybe she’s hot enough for him to throw caution (and grammar) to the wind and send her a message. It’s the curse of being cute.
In some ways this was the model that my college roommate was espousing. His argument was that the key was to find a woman who you found more attractive than the average bear. That way, you were in a better bargaining position to select good mates from this pool of women, who don’t necessarily know their own leverage over you, because they have to assume that you’re the typical male. The “win-win” scenario is where two people perceive each other to be better “catches” than the general population when it comes to looks. There are a lot of such cases presumably because of the residual you see above, but there are plenty of other factors in mates where one can be choosy. By maximizing the disjunction between between population-wide assessment of attractiveness and your own perception of a woman’s attractiveness you can “negotiate” for someone “better” on the other characteristics you value than you otherwise might be able to. If you want to be happy the key isn’t to find a woman you find ugly, it is to find a woman who you value more than the going “market” rate.
Alex Tabarrok has another plausible explanation:
….Rather I think there are certain types of beauty that greatly attract some men but repel others. Analagously, some people will pay hundreds of dollars for an ounce of caviar that other people won’t eat for free. The reason some people love caviar, however, is not that other people dislike it. Instead, it just so happens, that the thing that some people love is the very thing that repels others. We see the same phenomena in art, some people love John Cage, other people would rather listen to nothing at all….
Alex’s model is not totally exclusive of the one OKCupid was espousing. Both of them clearly suggest that distinctiveness matters. Individuals have their own “brands,” and accentuating brands can allow for your “market segment” to target you. Back during my 2 weeks of internet dating I put “atheist” under religion, and indicated that I did not want inquiries from someone who was religious. I was well aware that this was putting me into a “sausage surplus” market, as there seems to be a preponderance of males among those who espouse such frank irreligiosity. But I recall hoping that my honesty about this would at least attract the attention of women who shared a similar disinclination toward religion (this turned out be a good move, a woman who was raised Jehovah’s Witness but had left religion contacted me). That being said, I did have my limits. I did not play up the fact that I was a Republican, as I judged that the pool of atheist Republican women in Portland, Oregon (where I lived at the time), was very small. It must also be admitted that my personal experience is that similar politics is less important in the success of a relationship than a common “metaphysic.” In my case this is partly probably a function of a general weak passion for politics at this stage of my life. But even when I was a very strident libertarian politics was never a litmus test for relationships and friendships.
At this point I’d like to introduce a stylized model. In Survival of the Prettiest Nancy Etcoff introduced me to two different types of beauty. The first you should be well aware of: more symmetry means that you are more attractive. Composites of a range of individuals are almost always more attractive than the individuals themselves. This is attributed to the asymmetry which is introduced in development due stochastic, environmental, and genetic factors. Being lopsided is not a good sign of health, whether the cause is endogenous or exogenous. But there is another sort of beauty: that focused on secondary sexual characteristics, which are sex specific. Symmetrical beauty is applicable in the same manner to both sexes. This secondary sexual characteristic component is not. A powerful robust chin which may indicate rugged good looks in a man does not do so on a woman. Large eyes, a small nose, and a pert mouth, may be attractive on a woman, but they may seem ludicrous on a man (unless you’re Speed Racer). In the case of symmetry being at the mean is the best. But in the case of secondary sexual characteristics exhibiting some deviation from the mean of your sex in one particular direction is probably ideal. Let’s call this “good” deviation.
Finally, there’s a third component. To some extent this is like “non-shared environment” in many behavior genetic models. It’s a whole host of factors thrown together to explain the residual which can not be accounted for by the two other variables. So that’s why I labelled it “X” factor. Probably the easiest sub-component to pick out here are cultural influences as a function of space and time. To the right you see two photos. One is of the Bollywood actress Karisma Kapoor, while the other is of the Indian actress Freida Pinto. To be honest the photo of Ms. Kapoor is probably more flattering when it comes to the range of her photos than that of Ms. Pinto. A large fraction of the reason that Ms. Kapoor is a Bollywood star is contingent. She’s from a showbiz family, and nepotism seems to count for a lot in the film entertainment industry in India and the USA. But another factor is that Ms. Kapoor is extremely “fair” by Indian standards. In contrast, Ms. Pinto is more conventionally Indian looking. My personal experience is that Westerners, and brown folk raised in the West, have a hard time understanding how someone who is as “conventional” looking as Ms. Kapoor could be a leading lady. But she is very unconventional in complexion in South Asia, and in a good way. In contrast, Ms. Pinto is more conventionally good looking. She is of normal coloring for a South Asian. I am willing to bet that most Westerners would judge Ms. Pinto more attractive than Ms. Kapoor without makeup. Anyone who has encountered 19th century Chinese foot binding literary porn will be rather aware of how cultural expectations and norms can reshape and distort beauty standards. In a Western context the shift toward slimness away from a more ample form is often used to illustrate the principle of variance of tastes and standards over time. But these realities should not allow us to forget that common factors do tend to remain invariant. It is famously observed that though the size of the ideal woman in the West has shifted a great deal, the ideal ratio of proportions have moved far less.But there may be genuine differences which are not so temporally or cultural sensitive. Another component of the third dimension of assessment of attractiveness is probably just individual differences. The domain of behavior genetics, as opposed to evolutionary psychology. There are after all “legs” and “breasts” and “butt” men. Granted, the proportions vary across cultures, but there nevertheless remains a mix in most cultures of preferences. I believe this aspect is the one that may explain much of the pattern in the OKCupid results. There are men who prefer very small breasts, men who prefer corpulent women, and so forth. Whatever the origin of these preferences, even assuming relative cultural invariance in the sample population (I believe this is so for the middle to upper middle class Western target audience of OKCupid) there will remain individual differences of taste and preference, as noted by Alex Tabarrok. Women sharply deviated from the population norm on many traits may produce an average decline in aggregate attractiveness rating, but still may command a premium among the target audience of men who prefer the deviated traits (e.g., attractiveness drops as the number and extremity of piercings increases for the general population, but increases for a minority who find that attractive). Quite often it is preferable to be a second choice, but in this case women who are blandly “cute” may suffer because of the way in which men allocate their time and energy. Dating sites such as OKCupid have many more potential target matches than not, so why not focus on those individuals with whom one is the best match with, instead of the second best? In this way OKCupid is perhaps very different from the small villages or tribes of yore; you have thousands of “first matches.”
Finally, I want to observe something about the images on the OKCupid post. Quite often it seemed that the women who had higher variance ratings used more salient photos, with harsher or higher key lighting. A woman who uses a classic “MySpace angle” photo that’s a touch on the blurry side may get higher ratings than a woman who uses a more crisp image without makeup, but I suspect that many men would prefer the latter to the former. One can’t rate someone lower just for being clever with lighting and selection biasing, but, one may change one’s behavior explicitly and implicitly taking that into account.
In any case, I’ve gone on long enough. I was asked my opinion, and I gave it. What’s your take? (this is not a call for retarded comments by the way. You know who you are)
Image credit: Xavier449, Bollywood Hungama, Lili Ferraz.
"Wat betreft de voorlaatste alinea over de fotokwaliteit, ook dat is geanalyseerd, zie alhier bij OKCupid, en voor de ¨non-shared environment¨ kan men ook op OKCupid terecht.
Het gaat er volgens mij om dat de aantal ontvangen berichten toeneemt als er een groter meningsverschil over de attractiviteit van de persoon in kwestie bestaat zoals OKCupid beweert en wat betreft de deviatiegraad en de variantiefunctie van OKCupid indien ze wel geldig is: mannen houden niet van ondernemende vrouwen maar wel van impulsieve chicks, weet je dan het resultaat? Dat mannen er ook niet van houden dat ze in een ander cafe zit dan in die ene waar hijzelf zit.
En .4*5 - .5*4 - .1*9 + .9*1 + k= nul berichten maar ook 19 kiezers waarvan 9 haar ondergemiddeld waarderen en 10 haar bovengemiddeld waarderen. En waarom stuurt ook die ene die haar perfect vindt geen bericht? Omdat die 9 die haar met een 4 waarderen ook niks doen, dat is niet counterintuitief, maar normaal als ze aan iedere vinger 10 man heeft waarbij die 9 afwachten wat die ene doet. En bij een ondergemiddelde waardering lijken de kiezers elkaar meer te steunen. Maw. in deze variantie of stemgedrag ontvangt men dus geen berichten.
Er zijn echter 49 manieren waarop 60 kiezers die eenmaal verplicht stemmen en toch nul berichten zullen versturen. Er zijn zelfs 1032 manieren om nul berichten te versturen als niet alle 60 kiezers hun stemmen verdelen en sommige zich dus van stemming onthielden, waardoor het gemiddelde dan zweeft bij 74,52% kiezers die dan wel eenmaal gestemd hebben.
En bij 5 verstuurde berichten ligt bij vrijwillige deelname aan stemming bij 60 kiezers het aantal manieren van waardering op 1418 en zweeft het gemiddeld aantal kiezers op 73,44%
Voor verschillende populatie grootte kan men de volgende grafiek beschouwen (en k van de formule buiten beschouwing is gelaten) waarbij op de x-as het aantal msgs en op de y-as het aantal varianties in de manier waarop men gewaardeerd kan worden bij dat specifiek aantal msgs (afb1a):
 | |
| afb 1a |
Het zig-zag patroon in de grafiek (afb 1a en 1b) waarbij dus 1 msgs meer word verstuurd bij een langzame vermindering of sprongsgewijze vermeerdering van manieren van waardering kan komen doordat men niet de kans wil laten ontglippen? Dan lijkt het erop dat 4 pogingen ongeveer de maximale moeite zijn, alhoewel het ook afhankelijk van de grootte van de populatie lijkt. (afb 1b)
 | |
| afb 1b |
 |
| afb 2 |
Voor iedere populatie geldt dat de deelname aan stemming steeds begint onder de 75% (afb 2 en 3) en als 100% van de populatie wordt bereikt (afb 3) dan zijn er ook maximaal nog slechts 4 varianties van waardering. In het begin wil de lijn nog krullen (afb 2) en loopt deelname zelfs nog terug bij de eerste 10 berichten. Maar waarom het aantal varianties soms spronggewijs toeneemt bij een toenemende participatie of betrokkenheid is me niet duidelijk, kritische massa misschien?.
 |
| afb 3 |
Het verschil tussen de verstuurde berichten bij het bereiken van 100% deelname van de verschillende populaties (afb 3) is steeds 13 of 14 msgs. maw. bij 15 mensen meer kan men ongeveer 13 msgs meer verwachten bij 100% deelname.
Om 125 msgs te ontvangen moet dus extrapolerend de populatiegrootte minimaal ongeveer 150 mensen zijn.
 |
| afb 4 |
Op de lijn (afb 4) staan de populatiegroottes waarbij het aantal msgs (x-as) bij het maximale aan varianties (y-as) steeds verdubbelde.
Hoe groter de populatie hoe groter de kans op meer msgs. (afb 5)
 | |
| afb 5 |
