I have a couple of hats with strings similar to the seen in this listing. I have always worn a hat with such a string with the string under my neck. That way, if a gust of wind comes along, or I bump into something, it doesn’t come off.
However, I see a lot of people wearing *this kind of hat with the string behind their head, where it functionally does nothing.
So. . . am I committing a fashion faux pas? I’m the first to admit that much of the concept of “fashion” is alien to me, and that my wardrobe is more geared to pragmatism.
*That is, hats with strings, not necessarily strictly the one in the ad.
might there be offered a link at that asterisk? Showing a hat like this?
Actually, if you cinch the strap/string at the right place at the nape of your neck/back of your head, it does secure a hat in all but the stongest wind. I learned this from a park ranger.
“Dork” is the default answer. 
Were these other people actively involved in doing things that might cause their hats to fly off? That would be the only time I would wear the strap in front. Otherwise it gets in the way. Also, as noted above, a properly worn strap in the back is fairly secure from all but a rising headwind.
I’ve got a hat with an adjustable string; needed it for a hiking trip. When the wind was strong, I’d put the string under my chin. Otherwise, it was just more comfortable to put the string behind my head.
My guess would be to help hold the hat in place if you have to bend over forward to pick something up, tie your shoes, etc.
Because it’s really dorky to have the string under your chin. And I say this as a person who is not fashion-conscious much, and as long as my clothes match close enough, that’s good enough. But I won’t tie the string under my chin. 
I have a Tilley hat and it has a two-part “wind cord”: part goes behind your head, part goes under your chin. It’s extremely secure this way.
Owner’s Manual
I love my Tilley! What model do you own? Mine is a LTM8 in khaki.
Under chin: Looks like when I was 3 years old and wearing my little cowboy hat
Behind neck: Looks cool
But yeah, I put it under the chin when a wind kicks up or I’m riding in a boat.
In our summers, ya gotta wear a hat or fry your brain. And it is often both windy and hot, so hats usually have a chin strap. The strap gets in the way if not pulled tight under the chin (like every time you tilt your head forward), so it goes behind the head if the wind isn’t too strong.
