The dropdown of a select is part of what's called the ShadowDOM. In the current CSS specs, level 3, there's no way to target most ShadowDOM elements. You can read the specs on the ShadowDOM here, though there's not much in there regarding what you want.
Chrome has a few proprietary selectors to change some shadowDOM elements, but not all. Firefox has even fewer (as far as I know), and Opera has none. IE is probably just as bad or worse.
Your best bet with compatibility in mind is to use a Jquery plugin to mimic the select using other HTML elements if you really want to style it. Here's a neat one.
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