centralized cryptocurrency

[zack]

One computer is the leader. It creates all the blocks.
If each user's software is written to ignore invalid blocks, then the leader will be unable to influence the network with invalid blocks. If he creates 2 blocks at the same height, then the blockchain freezes.
The worst he could do is censor transactions, which would reduce his own income.

If the leader is hidden in a gossip network, it can be very hard to find him among all his users.

If the leader disappears, it should be easy for others to fork a moment in history, and launch a cryptocurrency with the same distribution. Forking a cryptocurrency like this should be expensive in either POW or in burn, otherwise there will be too many forks to deal with.

Advantages:
*no complex consensus algorithms like POW or POS
*Minimize redundancy

When the leader dies and 100+ alternatives show up to replace him, it can be difficult for the network to decide which blockchain to use. It is possible that people will split onto different blockchains. The same transactions will be spendable across all those competing chains, so they will all have nearly identical state. One way competing chains differ is in the order of the transactions, which changes user's balances slightly.

Another way they can be different is by who is collecting the transaction fees. If a block leader tries to spend the tx fees he gathered, it only works on his own chain.  The transaction-fee money will be traded at a much lower value than regular money, until there is consensus on which chain to use. At least one of the potential leaders will be an altruist, and will delete all his transaction fees. The community will prefer his blockchain.

So transaction fees only get spent if there is a very small number of people interested in being leader. Even without transaction fees, the leader has some advantages. He looks at every block first.

It is possible for the leader to censor, but if everyone is pseudo-anonymous, it isn't much of a problem.