Tried this approach today with a friend, and kinda worked, I think, so I'm sharing (also trying to figure out a way to convince non-tech, no-clue-about-market people).
This is taking place in a world where telepathy is a reality.
Your balance is stored in your brain, and can even be organized in there ("for the kids", "for my retirement", "for booze", etc.).
When you want to pay someone, you just think about her (or him), and send the amount you want from any sub-account you desire.
The recipient only knows he received a payment from your sub-account name ("for booze"), and won't be able to know who you are.
Cheating ? No way.Because whenever you issue a send order, it actually not goes directly from you to the recipient, but has to propagate through a few other people before it reaches her (or him).
Those "relay" people will propagate in turn, using telepathy, their knowledge of this transaction to their neighbour, who would do the same, etc. Soon, everyone knows the account "for booze" spent 3 coins in favor of "xhamster vip" account.
Since any payment you make hops through a few other people before reaching your recipient, they have full knowledge of all transactions that happened on the sub-account you're sending money from - thus knowing your balance. So if you're trying to cheat, they'll just block your payment and make sure it does not reach its recipient.
Of course, if you tried to create a "for booze" sub-account while I'm already using one with the same name, you wouldn't be allowed, because the name is already used. You'd have to go with a "for booze524".
If you never tell anyone you're the one holding "for booze" sub-account, people won't be able to figure out the account is actually yours.
"I can do the same with paypal!"
Yes. You can.
But then your payment, in the world described above, would ALWAYS pass through one single person, and ALWAYS the same one, before reaching the recipient.
When this person decides you can't pay... You can't pay anymore.
When this person decides they won't relay any transaction unless a fee of 50% is payed to him (or her)... You pay the fee or you sit on your money forever.
Using bitcoins, the knowledge is shared. It is collective memory.
You cannot cheat, because everyone's watching.
You cannot be harrassed or abused, because everyone's watching.
You cannot be stolen, because even the FBI cannot access your brain-wallet.Long post, but it takes less than 10 minutes to voice out...
Sorry about the dodgy english, I'm not a native speaker.