With regards to Bitcoin: The value in a distributed block chain is to ensure participants don't double-spend their coins. An attacker in a Sybil attack would spend their coins, broadcast the transaction and (after the recipient believes he's received the transfer) use fake identities to "vote against" including said transaction in the public ledger. That way, he could then go on to spend the coins again. To prevent this, Bitcoin uses a proof of work function: each participant in the network gets a share of the voting power corresponding to the effort he or she spends on calculating sha256 hashes, not to the number of identities one represents.