for example, only let each miner perform one hash. whichever miner comes closest to the target is the winner. and they get to mine the block.
This idea you can implement it easily. Just ask everyone to calculate their A_hash:
hash = Hash(Block Head + sign(Block Head))And Everyone will broadcast its A_hash and everyone will know that this A_hash can be produced only by the miner itself and no one else.
Now the issue is how to find the consensus:
1- The closest to the target like in PoW.
2- The closest to the arithmetic average mod a Big N of all the A_hash of the network.
3- The closest to the geometric average mod a Big N of all the A_hash of the network.
4- Others
And the idea is how to make sure that everyone is OK on the outcome? Bitcoin PoW proposed the criteria of the fastest miner which push people to invest heavily in CPU.