Any judges or lawyers out there?

You are.

While arbitrators generally follow the jurisdiction's law, so that the arbitrator will build a reputation as being fair and logical, they are generally not required to follow it. In fact, it has even been held that where the arbitration agreement between the disputing parties specifically provides that a certain state's law must be followed, the arbitrator does not have to! (The arbitrator, not being a party to the arbitration agreement and not being a third party beneficiary of the contract, is not bound by it.)

The TV judges typically deal with cases that need only an application of the generally followed principles of our country's common law and they usually state these principles when issuing their decision. But they don't have to.

Court TV, as you noted, is a form of arbitration.

You'd pretty much have to look at the full agreement signed by the TV "litigants," but arbitration may normally not be appealed on the basis that the arbitrator did not follow the law.

If the parties could appeal on this basis, there would be no meaningful benefit to arbitration.

The nearly universal rule is that binding arbitration cannot be changed or set aside except in the case of fraud, clerical error or the like.

This makes you right and your friend is wrong.

Well, one of the rights given to a judge to hear the case is the discretion to determine the credibility of any witness. If the TV judge thinks the credibility of either Plaintiff or Defendant is no good, then the case will go to the party whose credibility survives--despite what the law may say.

However, most the these TV judges (if not all) were judges in real life, and, all things being equal (which they almost never are) would go with whatever state law dictates. Rarely would federal law be an issue in these cases, and local laws only to the extent that municipal regulations apply.

You are. Arbitration is, by definition, a private resolution of a dispute. You can set any rules you want. For example, the parties can agree that the one who can eat the most hot dogs in a minute wins. The rules and laws applicable in a traditional court simply do not apply, unless, of course, the parties agree that they will apply.

It depends. (If you were wondering whether I'm really a lawyer, now you know.)

An abritration can be governed by any law, if it says so in the contract. So the citations to authority may not be superfluous -- if the contract requires the "judge" to decide the case according to (for example) New York law, then s/he would probably want to cite to such law before rendering a judgment.

So your friend is right, presuming that the arbitration agreement states what law is "applicable." Btw, to be on the safe side, you can always assume that any proceeding is governed by "applicable" law -- the question in choice of law analysis is one level down, i.e., what law is "applicable."

have you tried reading the material on the web sites of the shows?

Money. I heard mentioned on one of the news shows that Judge Judy (herself) makes $1 million PER SHOW !