Look at how bisq does it. Trustless, private transactions of relatively large sums, with escrow and arbiter resolved disputes. Bisq is the best crypto-fiat exchange system if it's ok for the transaction to take a couple of days.

For large transactions you have to put a lot of faith into the arbiter. What if they're not being impartial? What if they're corrupted? Eventually you want an arbiter that's "big enough" not to have an incentive to cheat you for any mundane transaction, like a bank or a huge company like Amazon. They're always available, mostly consistent with their rulings and can guarantee a huge amount of transactions at once without bottlenecks. I know that Amazon has no incentive to screw me over a $2000 purchase. Also since they generally have a history of transactions for both seller and buyer they can more easily identify fraud. The more information the arbiter has the more likely they are to rule correctly.

Suppose that a Canadian buys a DVD from a German, some Chinese guy is elected by the system as arbiter. The Canadian guy claims he hasn't received the DVD. What does the arbiter do? Book a ticket for Canada to check it out? Ask the German to send him the DVD first so that he can forward it? What if the chinese guy steals it and claims he's forwarded it then?

Here's how Bisq does it[1]:

>Arbitrator follows a protocol to request additional information from both parties and renders his decision based on acquired evidence.

Well that's very nice, how do you prove that you haven't received anything? What if you've received something but it's broken? Or not the thing you wanted? It seems so easy to game the system.

I have a hard time believing that distributed arbitration system like the one you're talking about could beat the speed, scale and efficiency of our current infrastructure. Maybe for certain niches it would could work though, for a cryptocurrency it might make sense to avoid centralization and a single point of failure.

[1] https://github.com/bisq-network/docs/blob/master/exchange/wh...

A bit of a late reply, but in case of bank transfers proof of transaction is actually an interesting topic. You use PageSigner[0] to make a cryptographically secure webpage screenshot of your bank statement. I'm still a bit confused about how TLSNotary (underlying technology) works, but apparently it does.

[0] https://tlsnotary.org/pagesigner.html