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Right... so then the question is "will the MYBITCOIN-like intermediary be able to verify transactions quickly without opening themselves up to systematic fraud."
Without requiring users to pre-deposit funds with them, because users ain't gonna do that.
Here's another possible simple rule for miners that might work (but, as Hal said, requires Deep Thought):
"When I see a new block with transactions that I didn't see broadcast previously, mark those transactions as suspicious. If I see double-spends of those transactions, stop building on that block-- assume it is cheating. Switch to the previous block (or alternate block if there's a block race going on)."
Miners won't try to rip off a grocery store for $50 worth of groceries if doing so makes their $50+ bitcoin reward for finding a block disappear.
This rule would also give miners a strong incentive to detect and refuse to include EITHER side of a double-spend in their blocks (if they get both spends while they're working on the block).