However, if the customer can broadcast the double-spend transaction privately to a miner that controls, say, 10% of global hash power, over a non-public back channel, and if the miner agrees to replace the original transaction (the payment to the merchant in our example) with this new transaction, then the double spend will be successful 10% of the time.
If a miner offers this service for profit and if customers use it to deceive merchants, would you consider the miner to be complicit in fraud?
(This is not a discussion about enforcement, just whether or not this qualifies as fraud in your opinion)
Whoever would scam like this would be the dumbest criminal of all time. The double-spending miner would need 3 petahashes to have 10% of the network. That's at least $6-7,000,000 in asics to achieve that. But they would constantly need to add as the difficulty continues to rise. All this so that 10% of the time you are successful at a small purchase scam?
If you had that much hashing power wouldn't you just use it to mine bitcoins honestly, raking in around 900 a day?