One article I am reading said that proof of work system is used in Bitcoin to prevent double spending. More particularly:
Imagine we are protecting against double spending in following way. When Bob receives transaction from Alice saying that "Alice transfers some 1234 BTC to Bob", bob would broadcast this to entire network to ask them to verify whether this is a legitimate transaction. In the mean time say if Alice had sent also same message to Charlie (saying that she is transfering same 1234 BTC to Charlie), Charlie would have also broadcast this message and other nodes on the network would spot that Alice is trying to spend same 1234 BTC with two persons, and they would let Bob (or Charlie) know that this is invalid transaction. Or if all is ok Bob or Charlie would wait till some nodes send acknowledgment that this is valid transaction.
SOCK PUPPET ATTACK: Above scheme would work but Alice could cheat in the following way. She could create say one million fake identities on network, and they would lie to Bob and Charlie that the transactions was valid- making them accept payment.
Now comes my question. It seems proof of work was introduced in Bitcoin to prevent exactly the above kind of sock poppet attack. But I fail to see how proof of work helps protect against above sock puppet attack. Why would Alice not be able to introduce those fake 100000 identities on the network anymore?
Can someone ealaborate and explain?
ps. I know what proof of work is, this question is more related how and why it prevents above mentioned sock puppet attack.