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Statistical controversy over “trophy wives”

Aaron Gullickson writes:

I thought you might be interested in this comment (of which I am the author) and response (by Elizabeth McClintock) that just came out in ASR. The subject is about whether beauty and status (e.g. education, income) are exchanged on the marriage market. The reason I thought you might be interested is because of my second critique starting in the “Log-Linear Model Interpretation” section where the error is basically a variation on your article about whether differences between stat sig and not stat sig are themselves stat sig. Basically, the original author used interaction coding to look directly at the effect of men’s beauty and the difference in the effect between men and women and concluded that nothing was statistically significant. However, if you reverse the reference category or use two separate main effects rather than an interaction term, you get a strong effect of beauty for women, which I tend of think is what most people’s priors would be. Figure 1 in the article summarizes all of this. Its surprising to me how hard it has been to explain this simple concept to some of my colleagues. The author seems similarly confused in the response and believes that I have (incorrectly) estimated a different model rather than re-coded the 1’s and 0’s in the same model.

Gullickson provides further details here. [link updated]

The articles in question are called, “Comments on Conceptualizing and Measuring the Exchange of Beauty and Status” and “Support for Beauty-Status Exchange Remains Illusory,” and the article that started it all is “Beauty and Status: The Illusion of Exchange in Partner Selection?” by Elizabeth McClintock.

Back when I was a student at MIT, there was this expression:

Brains * Beauty = Constant.

This formula ostensibly applied to girls, but in retrospect I think we were talking about ourselves without realizing it.

Anyway, to get back to the above discussion, I’m not really happy with how Gullickson or McClintock are looking at the data.

I have a few problems with what they’re doing. First, it seems pretty clear, from various stories we hear about in the news, that trophy wives do exist. Gullickson writes, “The subject is about whether beauty and status (e.g. education, income) are exchanged on the marriage market.” I can see how people can “exchange” beauty in the sense that if you marry someone beautiful you then get the consumption value of basking in their beauty, and of course you can exchange income. But I don’t quite get how you can exchange education.

But let’s set aside the terminology, and just accept that, by “exchange,” McClintock and Gullickson are just talking about marriages where one partner has more beauty and the other has more income and social status. Fine. But then how can it be a question of “whether” beauty and status are exchanged? Of course they are exchanged, in some numbers. The question is how much. I prefer McClintock’s formulation in terms of “the prevalence of beauty-status exchange.”

But I’m still hung up on the definitions. What is the definition of “beauty-status exchange” being used by these scholars? They disagree on their conclusions but I still can’t figure out what exactly they’re talking about.

McClintock refers to “the claim that individuals (generally women) of relatively high physical attractiveness barter their beauty to attract a partner of higher socioeconomic status,” and that seems pretty clear. But, again, I don’t see how they’re getting to this from their data.

The statistical debate has to do with coefficients being compared in different regression models, and Gullickson has a good point that the apparent interpretation of a coefficient can change, and easily be misunderstood, when flipping variables around going from one model to another. This statistical issue does seem relevant to the substantive questions being asked, but I still feel that a couple of steps needed to be added before I can understand this debate.

P.S. Alessio D’Aquino sent along the above image of two creatures who fit together very well.


  1. Dale Lehman says:

    link to further details is broken

  2. J says:

    I have no dog in this fight, but this is the central issue from McClintock’s 2014 piece:

    “This article revisits the claim that individuals (generally women) of relatively high physical attractiveness barter their beauty to attract a partner of higher socioeconomic status.”

    And socioeconomic status is defined here:

    “Socioeconomic status is an abstract concept, but it is often approximated by education, income, or occupation-tangible and quantifiable characteristics.”

    (from here:

    The key here is that education, occupation, and income are markers of social class, and so you can “marry up” by snagging a partner with higher levels of these things.

  3. dlr says:


    Brains * Beauty = Constant

    is demonstrably untrue. Some people, indeed many people are both smarter AND prettier. But, a related, and important concept is true:

    (Brains * Beauty) IN PEOPLE WHO WILL DATE YOU is a constant.

    Or rather (Brains * Beauty * Agreeableness * Income * 10 other things) IN PEOPLE WHO WILL DATE YOU is a constant.

    Among the people who will date you, you will have to trade off Brains vs Beauty vs. Agreeableness vs Income vs 10 other things, because if the combined score of their desirable traits is noticeably greater than the combined score of your desirable traits then they are going to level up and date someone who’s combined score is great than yours.

    There are a pool of people who will date you. In that pool of people some are prettier, and some are smarter and some are nicer and some are richer. You have to trade off. But if your combined point score for beauty/wealth/brains/agreeableness was noticeably higher than it is, then a whole different pool of people would be willing to date you. And their combined score of beauty/wealth/brains/agreeableness would be higher too.

    That’s not fair! But it is Just. :-)

    • Andrew says:


      I’ll accept your argument as long as you add an error term! There are tradeoffs but there’s also a lot of variation in who considers you attractive and appealing. There may well be an “efficient frontier” among the set of people who will date you, but that frontier is pretty noisy.

      Or, to put it another way, not everyone when dating is seeking to maximize a “combined score.” There are things like compatibility which are properties of the dyad and not of the individuals.

      • I get the impression that men prefer higher status women even if they are not as attractive as they would like. So if they come across ‘brains and beauty’ they behave awkwardly, unless they think they are as intellectually capable as their ‘brains/beauty endowed interests are. Of course I get my opinions from males themselves. So not simply my own observation. I can usually tell who is close to my own intellectual stamina. Not always sure whether I am a good judge of compatibility. However I know who has good intent toward me. I on the other hand haven’t been attracted to rich men b/c I worked in a hotel and saw what went on.

        • Kyle C says:

          This whole area is hopelessly confounded (IMO) by an issue that is obliquely identified in the Gullickson comment: female beauty is for practical purposes a “constant” (a beautiful woman is generally beautiful to heterosexual men), but male beauty is manipulable over time if a man makes a woman feel good (thus, a funny or otherwise skilled man “grows on” and becomes beautiful to a woman he interacts with). The beautiful woman who marries a troll usually doesn’t see him that way anymore.

          • Nadia Hassan says:

            Female beauty isn’t necessarily a constant. A lot of people describe what Kyle says, that men just respond to the physical characteristics and think of a woman as beautiful or not, and women change their views based on how a guy makes them feel.
            But, this article found that consensus decreased among men and women. For consensus to decrease, people’s views have to change.
            Eastwick, P. W. & Hunt, L. L. (2014). Relational mate value: Consensus and uniqueness in romantic evaluations. Journal of Personality and Social Psychology, 106, 728-751.

      • I would list my criteria here. But It will just make you laugh

    • Carlos Ungil says:

      Your preferences for partners might be described by iso-utility surfaces in the 14-dimensional (Brains * Beauty * Agreeableness * Income * 10 other things) space, but people who will date you will be scattered on that space depending on other factors: the utility functions for those people, the full distribution of utility functions for every match in the population, the strategy used by each participant to determine who they will date based on partial information…

      For a discussion of the two-sided optimal stopping problem see for example

    • Brad Stiritz says:

      The Onion nailed this topic, years ago: “Rich man, beautiful wife somehow make their marriage work” ;)

      I’ve long wondered, what type of distribution captures the way people talk about ratings of physical beauty? Here are some ideas —

      I couldn’t find free access to McClintock’s paper. Does she clarify some presumed distribution?

      dlr>(Brains * Beauty * Agreeableness * Income * 10 other things) IN PEOPLE WHO WILL DATE YOU is a constant

      OK, so “brains” (i.e. IQ) distributes normally.
      Is Agreeableness probably normal?
      Income is known to be lognormal.
      Beauty ratings : possibly a simple log-scale, in both directions away from “5”? IOW, for every (1) “10”, there are (10) “9”s, etc

      But how does the dynamic nature of dating and dateability factor in here? dlr, what is happening in your equation, when men and women game the system? E.g., from the man’s side —

      Andrew, is this what you meant when you pointed out the missing error term? So would we say, that true PUAs are able to exploit inherent measurement error in female perceptions of male attractiveness?

      • Andrew says:


        It’s been said that one advantage of being a quirky person is that if someone wants to be with you, they’ll have a good reason for it. If you have good pick-up skills then all sorts of people might want to be with you, even if they’re not so compatible with you. Compatibility is important!

        I say all this based on personal impressions. Speaking as a statistician, I’m not sure how one would best measure all this. I guess I could take a look at the research in this area.

        • I have never come across a quirky person with good pick up skills. I find the pick up skills of some men comical.

        • Brad Stiritz says:

          Andrew, regarding your stress on a shared sense of compatibility, isn’t it still true that love is blind? We can hope that our partner shares our love for him/her.. but after all, maybe we’re just being gamed? So is your dyad proposal possibly a best-case scenario? I’m sorry to have to be so cynical here!

          Also, just to clarify, please : dlr’s suggested “formula” can be thought of / recast as a Generalized Linear Model, right?

      • Roger Bohn says:

        Multiplying 14 variables together?? I always thought that beyond 3 or 4 variables, multiplicative scoring results were likely to be unstable and therefore unreliable. And that therefore when there are lots of variables, an additive model is the best we can do.

        Scaling also matters. I presume that Beauty is measured on a 0 to 1 scale, and brains probably the same. But wealth, as we learned in 2009, can go from a big negative number to a big positive number, or rather the other way around. This throws off any multiplicative model. (I believe Dr. Stiritz was confusing pdfs of populations, with construction of scales for subjective judgments. Mr. LIkert believed that all scores must be integers between 1 and 5, except if the questionnaire was written on weekends it could go between 1 and 7. In either case, a linear transform to [0,1] seems like a reasonable simplification.)

        We also need a system that gives cardinal values, so that divorces are possible. For example, my wife chose to marry me (my composite score at the time was about 3.7, according to the Visicalc spreadsheet I created in an effort to woo her), and we remain married after several decades. But if we believe economists’ additive utility theories, she would have been better off to marry a 2.5 man, divorce him after a few years, and then marry anyone better than about 1.5. (We can estimate that the pain of divorce is equivalent to about -.1 * number of children). This corresponds to maximizing lifetime happiness.

  4. Marcus says:

    Looks like there are some confusing typos in the Gullickson paper. For example, on page 1095 in the parentheses highlighting the constraints it should probably be “b1= -b2” and not “b1= -g1”. On page 1096 Gullickson writes “…highly educated men have fewer opportunities to marry women less educated than themselves” but I assume he meant “…highly educated men have fewer opportunities to marry women more educated than themselves”.
    Much of the material on difference score interpretation was covered by Jeff Edwards back in 1993-1994 (and probably by others before him) but it is always nice to get reminded of these issues.

  5. Andrew should get into matchmaking research business. I wonder if he is trying to match up some unidentified individuals. lol

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