You know when put as clearly as Tim Harford does, the whole elk antler story just doesn’t stack up:
Consider the vast antlers of the north American bull elk: they’re the result of sexual selection balanced by other selective pressures. Elks with big antlers win fights with other elks, and mate with multiple females. However, they also get hunted down and killed by packs of wolves. Elks as a whole would be better off if they could all agree to shrink their antlers by a factor of four or five: the males with the biggest antlers would still get the girls, while only the wolves could object to faster, more agile bull elks. Sadly for the elks and happily for the wolves, that’s not how sexual selection works.
But it is the female elks doing the choosing. So they face the trade-off of choosing someone likely to generate big antlered male offspring whom other females will choose versus getting male offspring more likely to outrun wolves. So that is one equilibrium but is it the only one.
Suppose that females preferred ‘outrun wolve types’ rather than ‘beat up others’ types. Then if one deviated and choose a ‘beat up other’ type with bigger antlers, the chance of reproductive success will go down. So that wouldn’t be profitable and so there is another equilibrium.
So why do we see big antlers all over the place? The answer is likely that there is an actual benefit to offspring of having a big antlered dad. I suspect that it makes them more likely to die earlier and be a wolf target than their offspring; giving their offspring a better chance. Put simply, in mate selection you want mates that will leave the planet quickly.