The naive total-arbitrated-BTC solution wouldn't work, since someone can always arbitrate a bunch of 'transactions' between sockpuppet addresses they themselves control. But as long as there's some mechanism to pay arbitrators for their services, it seems reasonable to expect a small set of trusted arbitration services to spring up, analogous to CAs. Of course, once you're paying an arbitration fee on top of a bitcoin transaction fee, it's not clear that you're saving any money relative to a standard credit card transaction.