Policemen and security guards wear hats with a peak that...

Policemen and security guards wear hats with a peak that comes down low over their eyes. Apparently this is for psychological reasons. Eyebrows are very expressive and you appear a lot more authoritative if you keep them covered up. The advantage of this is that it makes a lot harder for cops to see anything more than six foot off the ground. Which is why painting rooftops and bridges is so easy.