Another important observation is that there are at least two very different ways of dressing "badly." One is dressing in a tacky and sloppy way with complete disregard for aesthetics, and the other involves breaking the conventions of formal wear but still dressing neatly and stylishly. The latter, I think, can be a useful signaling device in some situations where adherence to formal wear may lower your status by making you look like you're trying hard to please others.
The prime example would be situations like job interviews (especially in technical fields), where you're expected to dress up, but those you have do deal with are not, because they enjoy a position of superiority. When you show up for those wearing something obviously more formal than what you wear on a daily basis, you signal that you're trying hard to please the people you have to deal with. A much better signal can be achieved by dressing in a stylish but less formal way that signals all the right things in terms of social aptitude etc., but makes you look less like a supplicant, especially if it looks plausible that this is how you actually dress on a daily basis.
Of course, this can backfire if you exaggerate with informality, or if you use a wrong sort of casual style.
Yesterday I attended a meetup where the discussion turned to fashion for a time (because apparently the mini-camp participants were given some instructions on fashion as a useful part of instrumental rationality). (Unfortunately none of us knew much about the topic so the discussion turned into "how can we find an expert to advise us for minimal cost?") It was mentioned that dressing "badly" can be a useful signalling device, and some examples were given. Here's an attempt at a more complete list of possible signals one might be sending by dressing "badly".
The idea here is, if you do decide to start dressing "well", know what you're giving up first. (Of course you're also giving up possibly implying that nobody taught you how to dress and you're not sufficiently strategic to have thought of learning it yourself. Or implying that you don't have the mental, financial, and/or social resources to keep up with fashion. A lot of signaling depends on what your audience already knows about you, or can infer from your other signals.) See also Yvain's related post, Why Real Men Wear Pink and comments there.