That's why, for example, the death penalty requires an extreme amount of due process. Your trial is lengthy and ideally involves a massive amount of proof before you're given a death sentence. It's also easy to appeal.
That's actually one of the legal arguments against the death penalty here: you can never be 100% certain someone committed a crime, so you should never give them the 100% punishment of death.
People who advocate for instant death penalty for heinous crimes, like murders or rapes, don't consider that. You can just never be sure that someone is guilty, even if they confess, and our legal system has decided to err on the side of allowing a guilty person to go free rather than punishing an innocent person. At least in theory.
For traffic fines, you get almost zero due process. Most of the time, you just plead guilty on the spot. A judge won't spend much time on your case, and you have to pay the court for using that time (often nearly as much as the fine itself).
So if someone making, say, $100,000 had to pay $1,000 for a speeding ticket, there'd be more due process required. It's not fair to basically assume someone is guilty (as we currently do with speeding tickets) when the fine is that high.
Even if we accommodated the due process required, it would add more load to an already way overburdened court system. It's just not possible.
There's also an argument to be made that $1,000 is a punishment that does not fit the crime of, say, driving 85 mph in a 70 mph zone without causing any harm or damage. Again, there's the concept of guilt, and whether the radar gun malfunctioned or the cop was being malicious or whatever.
It would probably discourage wealthy people to drive fast, but the price in trial/lawyers would probably be too high for the police department for it to be feasible (also, if the ticket lacks proofs, I assume the defendant could file a suit against the departement?).
There are some exceptions (court can decide that each side pays their own way, or decide the winner can only reclaim a reasonable amount considering the position of the loser) but the frivolous speeding ticket challenge would not be one of them.
Sentencing judges already have the opportunity to impose fines and consider the defendant's means when deciding the amount to be levied. I would personally say that "$1,000 is not a lot of money," and that if a $150 fine for 85mph (reckless here) is appropriate for a person earning $15000 p/a then that actually favors $1000 for a subject earning $100k in an ends of justice/deterrent argument. Maybe more than that because the $100k defendant will be paying from a discretionary budget, not the money for food/rent.
A 1,000$ fine for somebody with 20,000$ yearly income is a catastrophe. A 1,000$ fine for somebody with 1,000,000$ yearly income is at most a small annoyance.
Since the whole point of fines is (to a large extent) to act as a deterrent, you must take into account the fact that money has a decreasing marginal utility.
Your point about due process is interesting, but similarly needs to be scaled to the defendants wealth: Once you go down the road of talking about different amounts of due process required based on the potential effects of the punishments, it is clear that the amount of due process must be based not on the absolute value of the fine, but rather on the punishment's effect on the utility/well-being of the defendant.
http://tabloidwhore.blogspot.nl/2006/07/mel-gibson-calls-pol...
Once inside the car, a source directly connected with the case says Gibson began banging himself against the seat. The report says Gibson told the deputy, "You mother fucker. I'm going to fuck you." The report also says "Gibson almost continually [sic] threatened me saying he 'owns Malibu' and will spend all of his money to 'get even' with me."
The report says Gibson then launched into a barrage of anti-Semitic statements: "Fucking Jews... The Jews are responsible for all the wars in the world." Gibson then asked the deputy, "Are you a Jew?
The deputy became alarmed as Gibson's tirade escalated, and called ahead for a sergeant to meet them when they arrived at the station. When they arrived, a sergeant began videotaping Gibson, who noticed the camera and then said, "What the fuck do you think you're doing?" A law enforcement source says Gibson then noticed another female sergeant and yelled, "What do you think you're looking at, sugar tits?"
At least the way it works in Sweden, you're not fined a specific amount, you're fined X days wages. The judge handing out the fine neither knows nor cares what the fine works out to be in actual money. So from a judicial point of view the punishment is exactly the same for everybody.