I know that in the state that I live in (Minnesota) when you go to appeal a traffic violation you go talk to a DA representative before you go before the judge. If you can come to an agreement with the lawyer, you don't even go before the judge. And there's no cost to you (the defendant) for appealing. A lot of times if you don't have any violations on your record they'll waive the fine and give you a "Continuance for Dismissal" (CFD). With a CFD, you get the fine waived and then you can't have any violations for the next 12 months. If you do have a violation during the twelve months that the CFD is in affect, you have to pay the fine for the new violation, plus the one that was waived previously and both go on your record. If the DA representative is feeling particularly generous the day you talk to them, I've heard they may even just waive the violation altogether (with no CFD).

I don't understand why it works this way but it does. In my opinion, if you break the law and are fined for it, you should then be obligated to pay the fine. It's funny because whenever someone (especially a cyclist for some reason) gets cited for a violation; the fines suddenly become "unfair" or in the words of the OP "ridiculous". As though people should just be able to violate traffic ordinances without ever being fined. What's ridiculous to me is the fact that the outcome of an appeal has more to do with the mood of the lawyer (or judge) that makes the decision than it does the defendant's guilt.

Edit: I come from a family of police officers (although I'm not a cop myself). And in contradiction to what another response said; police (at least here in Minnesota) most certainly do get paid for their court appearances. If they're on-duty, it's just considered part of their regular "clocked-in" shift. But if they have to appear when they're off-duty, they "clock-in" for their appearance and they get paid. They even get overtime for it if they go over their regular hours. They're not expected to just show-up out of a "sense of duty" because Joe Schmo is challanging his speeding ticket.