It's not just because women are, on average, shorter than men.

Men are bigger and stronger than women. That generalization, although true, doesn't adequately describe how sex affects our modern lives. In the first place, men's and women's size and strength are distributions. Strong women are stronger than weak men, so sex doesn't tell you all you need to know. Otherwise, as retired colonel Martha McSally put it with regard to the ban on women in combat positions, "Pee Wee Herman is OK to be in combat but Serena and Venus Williams are not going to meet the standard."

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Second, how we handle that average difference is a matter of social construction: We can ignore it, minimize it, or exaggerate it. In the realm of love and marriage, we so far have chosen exaggeration.

Consider height. The height difference between men and women in the U.S. is about 6 inches on average. But Michael J. Fox, at five feet, five inches, is shorter than almost half of all U.S. women today. On the other hand, at five-foot-ten, Michelle Obama is taller than half of American men. So how do people match up romantically, and why does it matter?

Because everyone knows men are taller on average, straight couples in which the man is shorter raise a problem of gender performance. That is, the man might not be seen as a real man, the woman as a real woman, if they don't (together) display the normal pattern. To prevent this embarrassment, some couples in which the wife is taller might choose to be photographed with the man standing on a step behind the woman, or they might have their wedding celebrated with a commemorative stamp showing her practically on her knees—as the British royals did with Charles and Diana, who were both the same height: five foot ten.

But the safer bet is just to match up according to the height norm. A new study from Britain—which I learned of from the blogger Neuroskeptic—measured the height of the parents of about 19,000 babies born in 2000. They found that the woman was taller in 4.1 percent of cases. Then they compared the couples in the data to the pattern found if you scrambled up those same men and women and matched them together at random. In that random set, the woman was taller in 6.5 percent of cases. That means couples are more often man-taller, woman-shorter than would be expected by chance. Is that a big difference? I can explain.

For illustration, and to compare the pattern with the U.S., I downloaded the 2009 Panel Study of Income Dynamics, a U.S. survey that includes height reported for 4,600 married couples. These are the height distributions for those spouses, showing a median difference of 6 inches.

Clearly, if these people married (and didn't divorce) at random we would expect the husband to be taller most of the time. And that is what we find. Here is the distribution of height differences from those same couples:

The most common arrangement is the husband five to six inches taller, and a small minority of couples—3.8 percent—are on the left side of the red line, indicating a taller wife.

But does that mean people are seeking out taller-husband-shorter-wife pairings? To answer that, we compare the actual distribution with a randomized outcome. I made 10 copies of all the men and women in the data, scrambled them up, and paired them at random. This is the result:

Most couples are still husband taller, but now 7.8 percent have a taller wife—more than twice as many.

Here are the two distributions superimposed, which allows us to see which arrangements are more or less common in the actual pairings than we would expect by chance:

Now we can see that from same-height up to "man 7 to 8 inches taller", there are more couples than we would expect by chance. And below same-height—where the wife is taller—we see fewer in the population than we would expect by chance. (There also are relatively few couples at the man-much-taller end of the spectrum—at 9 inches or greater—where the difference apparently becomes awkward, a pattern also seen in the British study.)

Humans could couple up differently, if they wanted to. If it were desirable to have a taller-woman-shorter-man relationship, it could be much more common. In these data, we could find shorter husbands for 28 percent of the wives. Instead, people exaggerate the difference by seeking out taller-man-shorter-woman pairings for marriage (or maybe the odd taller-woman couples are more likely to divorce, which would produce the same result).

What difference does it make? When people—and here I'm thinking especially of children—see men and women together, they form impressions about their relative sizes and abilities. Because people's current matching process cuts in half the number of woman-taller pairings, our thinking is skewed that much more toward assuming men are bigger.