Account A makes his account special.
He now has 10 NXT in instant balance.
What's stopping him from sending 10 NXT to both peer B and C as payment if they are not connected? I mean sure, it could be prevented at the next block, but that isn't instant.
B and C would both send the goods to account A instantly and then get screwed 1 minute later when they find out it was a doublespend.
If he sends 10 NXT then he has 100 NXT on the balance and 20 NXT will be charged.
Taking this to the logical extreme, what if he sends it to 11 merchants, and gets 110 NXT worth of product instantly? This approach is good but not airtight.
Ok, check this solution out.
Account A wishes to make his account instant.
On the next block Account A requests 10 checkpoints (peers) from the forging account,
The forging account will send 10 peers to Account A and send one signed message to each peer telling them that they are a checkpoint for Account A.
Account A sends one declaration of checkpoint acceptance to each checkpoint in the form of a signed message.
These checkpoints save that message for one hour and generate a list of pending transactions for that account (At this time 0). All active checkpoints for account A communicate with each other as soon as account A's balance is updated.
Account A saves this list of peers and the account that generated them as a file.
When account A wishes to make an instant transaction he will include this file with the signed transaction information.
Account A will send this file to a receiving account.
The receiving account will check the timestamp on message (valid for one hour), check if the account that determined the checkpoints forged the block, and send the signed transaction information to each peer.
Each peer will confirm the new account balance.
They will generate a response telling the recipient if his account balance is large enough to complete the transaction.
If everything checks out this will approve the transaction.
The beauty here is that X number of peers are chosen at random by a deterministically chosen forging account. This prevents account A from having their own set of fake peers to validate fraudulent transactions. These few peers hold a temporary ledger of where account A's money is, it doesn't have to be mass distributed across the network. It is impossible to double spend with this system, and account A's full balance could be used for instant transactions.