To my knowledge, Bitcoin doesn't have this--you just mine a block and send it out to the network. They don't require anyone to approve the block before-hand because creating an invalid block is mathematically impossible. You must base it on a previous block, and you are incapable of including invalid transactions (such as spending more than you have). Such blocks are rejected by the network by default. Is that not also the case with Ethereum?

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Ethereum proof-of-work works as you desecribed.

Ethereum proof-of-work will be switched to proof-of-stake this September.

You can read more about how proof-of-stake works and why it works like it does in Ethereum documentation.

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