I'm pretty knowledgeable about arbitration and mediation (collectively known as "alternative dispute resolution" or "ADR"). I'm not an arbiter, mediator, or attorney, but I am someone who uses contracts with arbitration clauses in them, has been advised about arbitration by attorneys, and has actually had a dispute resolved via arbitration. I became interested in this topic after overhearing someone talk about Bitcoin transactions being arbitrated or mediated. Here are my detailed thoughts:

The simple answer to whether transactions involving Bitcoins can go through ADR is YES. Bitcoin is simply a currency used in the transaction, and it's not at the heart of any potential dispute between the parties. The agreement between the parties is what's disputable and at the heart of the dispute. 

HOWEVER, let's dive A LOT deeper:

Why do parties seek ADR in the first place? The reasons can be many, but usually it's to keep the dispute out of the courts, keep costs down (maybe), and provide a more informal – though not that informal – process to resolve a dispute. Usually, arbitration clauses contain class action waivers and tend to favor one of the parties over the other in the agreement (usually the drafter of the agreement in a "take it or leave it" fashion). Decisions reached through arbitration are almost always final and unappealable. This differs from court rulings, which are appealable. This also differs from mediation decisions, which are not final and have no binding properties. Basically, mediation is an informal way to potentially resolve a dispute between parties by using someone who is neutral, but either party, at any time, can walk away and, if the agreement requires it, go through arbitration or the courts. Arbitration decisions are enforceable in court too. Arbitration agreements often have cost sharing provisions (I know mine does) to deter counter parties from bringing actions in the first place. This is great for the business, but not so much for the customer. Would a plaintiff sue you if they had to pay half of the court costs to find out if you owe them anything? Probably not, or at least they'd think twice! So, it's important to understand exactly what ADR is and why it's used in the first place. It's important to separate the agreement from the method of payment – they're not the same thing. If no ADR agreement exists between the parties (think buying a coke from a vending machine), there's no reason why the parties couldn't bring their dispute (lawsuit) to an actual court of law. So, please keep this in mind. 

Having said all of the foregoing, I do believe ADR would be particularly problematic in agreements involving Bitcoins for the following reasons: 

Firstly, the parties would have to sign an ADR agreement between them as apart of the transaction. In order to use ADR, the parties need to agree to it, which requires a written agreement. Remember, if there's a dispute, the parties are not going to be friendly towards one another. In fact, they'll be hostile towards one another. Hostile parties will dispute and disagree with what the other party says, and one party may even dispute that they agreed to ADR in the first place. So, an agreement proving the parties consented to ADR will be critical to using ADR. Again – Bitcoin is cash. You'd have to have a formal agreement between you and the other party, which agrees to ADR and lays out the details of the transaction/purchase. Not too many people whip out their arbitration agreements before conducting a cash transaction. This might be a little awkward, but if you're series about using ADR, you'll have to do it.

Secondly, arbitration derives its legal basis and power from the Federal Arbitration Act ("FAA"), a US law. This law may apply to parties within the US, but may not apply to parties outside of the US. If both parties are in the US and they can be identified, there will be legal recourse and, if agreed to, ADR recourse. If both parties are in different countries, you might as well forget about it! There's no hope of really enforcing an ADR agreement in that kinda situation. Maybe corporation to corporation (big boy to big boy), but even then it's uncertain. Maybe, maybe, maybe if it's a modern Western country or a country that has decent relations with the US, but even then it's still very dicey. There's no guarantee that a foreign government will even recognize the ADR agreement as legal, nor, and more importantly, is there a guarantee they'll enforce any foreign judgements/decisions you may have obtained against the other party within the US. Remember, enforcing anything and chasing down other parties costs money and is often very uncertain, even domestically. Chasing down assets and holding parties accountable overseas is very, very, very difficult AND costly.

This reason isn't really an ADR thing, but it's relevant nonetheless: A Bitcoin wallet is like the ultimate offshore bank. Yes, a court could order a defendant to hand over his or her Bitcoins to pay a judgement and potentially, in the right circumstances, hold him or her in contempt if they don't, but he or she still has the ultimate power to do so. And that's assuming the US (for example) can even reach him or her. Again – if they're offshore, forget about it and good luck! Maybe the Bitcoin wallet is controlled by a foreign trust and only the trustee has the ability to send the Bitcoins. In this situation, the defendant truly has AWESOME and STELLAR powers, and It'll be mission impossible to get the Bitcoins back. Even money in actual offshore bank in Hong Kong or Switzerland can't defend assets like a Bitcoin wallet can. Not that an offshore bank "defends" assets. An entity and/or a trust controlled by a trustee creates the separation between the defendant and his or her assets, but I'm sure you get what I mean. If a foreign defendant tells you to go "pound sand" in the face of a court judgement or ADR decision, you're pretty much screwed. 

Anyways…

One of the posters on this thread compared Bitcoin to sending cash in the mail. I think he or she is exactly correct! Sending cash in the mail is a total, 100% "on faith" transaction. You have no guarantees whatsoever that the other party will uphold their side of the bargain. At least with Bitcoin, one can be assured that the other party actually received the payment instead of the other party claiming they didn't receive it at all, but I wouldn't take comfort in this fact. Once the Bitcoins are sent, they're gone. Once the cash is mailed, it's gone. You're totally at the mercy of the other party to do the right thing. If they've lied about who they are, you're screwed. If you're going to pay in Bitcoins, do your homework on the seller. FInd out who they are and where they're located. Try to buy from registered businesses. Think of the payment as cash in the mail. Everyone knows the risks associated with that form of payment. Just use your head and be smart.