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Not one that you need to trust.

You need to trust either the buyer or the arbitrator actually. In this case some money might have been lost due to malicious buyers (and the absent arbitrator).

You have to trust the arbitrator to make fair decisions, but the arbitrator has no ability to steal the money.

The transaction simply moves funds between buyer and seller. If buyer and seller both sign the transaction, it completes without the arbitrator's involvement. If buyer and seller dispute, then the one who hopes to complete the transaction signs it and contacts the arbitrator, who will either sign, or not sign, but either way never gets possession of the funds.

If both the buyer and the arbitrator are anonymous, how do you know that they aren't the same person?

They're actually pseudonymous, so they can have reputations. If the other party insists on an arbitrator you've never heard of, you probably shouldn't agree to those terms.

The arbitrator will usually be known by reputation, i.e. always the same key id.

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