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92.2% or so of men are taller than their heterosexual partners. This is usually attributed to women's preferences, although I'm sure there are some men who insist on their SOs being shorter than them. Avoiding people who think height is an extremely important factor may not be possible.

Source: https://fivethirtyeight.com/features/how-common-is-it-for-a-...

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Oh wow. I didn’t know it was that uncommon. I’m fairly short, so every gf I’ve had was taller. But it’s terribly clear women have filtered me out often because of my height. It’s depressing.

What would the percentage be, if it were random?

The source posted answers that too. In one of the studies contained in the 538 article, the probability of a woman being taller than a men if both are selected randomly was .102. Compare this to the observed probability of woman in a couple being taller than her male partner being .075.

How big is this difference? Well if 25 percent of women only dated taller men, and the other 75 percent of women were totally indifferent, we would see this. So not quite as extreme as one might guess from a statistic like "92.5 percent of men are taller than their partners".

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