The "judge shows" are usually based on the laws in the state where they are filmed/judge has practiced... In the case of Judge Judy that is (I believe) California.
And, in the states, we have "small claims" courts where the two parties come to court--without attorneys. Typically, the current limits for small claims court is around $5,000 (may be $10,000) in California. And in the typical small claims cases you can only sue and collect for actual damages--not pain and suffering or punitive damages.
You can read the Ebay support thread--but basically, the Judge Judy producers search for interesting court cases around the country. When they find one, they offer both sides plane fare, food, and possibly hotel rooms to come and present their cases. Both sides then file with the court to dismiss their cases and have them tried by mutually agreed arbitration (Judge Judy).
The producers also have a fund of, say $5,000 (don't know the exact amount--and it may change based on the cases) available. If the case is thrown out, the two parties probably split the $5,000. If one party wins the maximum judgment (and it does not involve the return of property), then one party will get the $5,000 and the other party nothing (but--in real life, they would have had to pay the $5,000 to the winner out of their own pocket).
I believe that Judge Judy, under arbitration, has the ability to order a sheriff to manage the transfer of property and such. And anyone can refer a case to Child Protective Services (or equivalent) or to the local prosecutor for further action.
And, by the way, even though the case was for ~$500, Judge Judy (I believe) ordered a $5,000 judgment to account for the actual damages caused by the fraudulent feedback on the two women's ebay account.
By the way, signing to arbitration is every bit as enforceable through the court system (property liens, till taps--cash register emptying by the police in a store, etc.) as with a "real" judge... And with arbitration--typically there is no right to appeal a judgment (out here, many health insurance plans--if not all--mandate that you only use arbitration and wave a trial by jury with limitations in liability even if the service provider is horribly at fault). In those cases, you first have to go to court to break the arbitration agreement (required to get insurance in the first place), before you can sue in a "real" court (i.e., trial by jury).
Does this help those outside of the US?
-Bill