There is no voting.
There is no 51%.
There is only mathematics and probability.
A person with 100% of the hashing power on the network has a 100% chance of solving the next block.
A person with 66% of the hashing power on the network has a 66% chance of solving the next block.
A person with 51% or the hashing power on the network has a 51% chance of solving the next block.
You're not understanding how proof-of-work works. In Bitcoin (or any Byzantine system), some nodes are good, and some nodes are bad (either malfunctioning or malicious), and you don't know which is which. Proof-of-work is one solution, in which it is assumed that the majority (51%) of computational power is held by good nodes, so in the event that two or more different nodes provide conflicting data, we go with whichever data set has the most work behind it.
The problem with requiring more than a majority is that it implies that the data set with the most work is not necessarily correct. It may be correct or it may not be, and there is not way to know. Say you have two conflicting blockchains, one with 50% more work than the other (and therefor represents 60% of the computational power of the network - more than 51%, but less than 66.67%). Is the chain with the most work the correct one and the other one a failed attack, or is the chain with the most work a failed 66.67% attack and the chain with the lesser work is correct? Which chain is correct? How do you know? This is the question you must answer in order to make your suggestion possible.
The problem with requiring more than a majority is that it implies that the data set with the most work is not necessarily correct. It may be correct or it may not be, and there is not way to know. Say you have two conflicting blockchains, one with 50% more work than the other (and therefor represents 60% of the computational power of the network - more than 51%, but less than 66.67%). Is the chain with the most work the correct one and the other one a failed attack, or is the chain with the most work a failed 66.67% attack and the chain with the lesser work is correct? Which chain is correct? How do you know? This is the question you must answer in order to make your suggestion possible.
These really helped too. Thanks a lot.
