The stereotypical example of that is known in sociology as a “beauty-status exchange”—an attractive person marries a wealthy or otherwise powerful person, and both win. It’s the classic story of an elderly polymath-billionaire who has sustained damning burns to the face who marries a swimsuit model who can’t find Paris on a map but really wants to go there, because it’s romantic.

All you need is money or power, the notion goes, and beautiful lovers present themselves to you for the taking.

When Homer Simpson once came into a 500-pound surfeit of sugar, his id instinct was to turn it into fortune and sexual prosperity. “In America," he said, half dreaming after a night spent guarding the mound in his backyard, "first you get the sugar, then you get the power, then you get the women.” That’s an homage to Scarface (in the movie the quote was “money” instead of “sugar”), and it’s where both Simpson and Tony Montana went emphatically astray.

University of Notre Dame sociologist Elizabeth McClintock has done exhaustive research on the idea of people exchanging traits. Her work was published last month in American Sociological Review, looking at data from 1,507 couples in various stages of relationships, including dating, cohabiting, and married. “Beauty-status exchange accords with the popular conception of romantic partner selection as a competitive market process,” McClintock wrote, “a conception widely accepted in both popular culture and academia.” She referred specifically to the gendered version, “in which an economically successful man partners with a beautiful 'trophy wife,'" as commonplace.

But McClintock found that outside of ailing tycoons and Donald Trump, in the practical world it basically doesn’t exist. Where it does, it doesn’t last. The dominant force in mating is matching.

What appears to be an exchange of beauty for socioeconomic status is often actually not an exchange, McClintock wrote, but a series of matched virtues. Economically successful women partner with economically successful men, and physically attractive women partner with physically attractive men.

“Sometimes you hear that really nice guys get hot girls,” McClintock told me, “[but] I found that really nice guys get really nice girls. [Being nice] is not really buying you any currency in the attractiveness realm. If the guys are hot, too, then sure, they can get a hot girl.”

Because people of high socioeconomic status are, on average, rated as more physically attractive than people of lower status, many correlations between one partner's appearance and the other partner's status are spurious and misconstrued.

“Women spend a lot more time trying to look good than men do,” McClintock said. “That creates a lot of mess in this data. If you don’t take that into account then you actually see there’s a lot of these guys who are partnered with women who are better looking than them, which is just because, on average, women are better looking. Men are partnering 'up' in attractiveness. And men earn more than women—we’ve got that 70-percent wage gap—so women marry 'up' in income. You’ve got to take these things into account before concluding that women are trading beauty for money.”