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Instead of POS (see my previous post), it would make much more sense to adapt the Nimble Wimble approach of making it so that validation is P2P whenever both parties are online. If I buy from you and you agree, then the purchase should been validated with 2 confirmations. Since we both agree that the transaction is made, it's no-one else's business if the transaction is valid. This would be much less resource intensive than even POS and be faster. If only one party is online at a time, it should be possible to have 1 confirmation and the other confirmation can be delegated to a miner. If neither are online at the time, then the usual POW takes place. Of course, that would mean that all wallets would have to be validators, but since you're only validating your own transactions, it should be light weight.
While I agree that a transaction is mostly the business involving the two parties transacting, they still need to adhere to the network rules. And that's were the miners step in. They don't care which two persons are transactig as long as they pay for it and it's in general a valid transaction (according to the network rules).
I agree with this idea