> Proof of work is the leader election phase of consensus.

This is a common misconception stemming from looking at PoW through the Paxos/RAFT prism. In Paxos a leader is elected, then the leader decides the order of events. But that's not a valid comparison, because in PoW the supposed "leader" does not get to decide anything at all - the block has to be put together prior to "winning the election" (because the block is the input to the SHA).

PoW is a radically different approach - there is no leader, but there exist indisputable points in "blockchain time", and the order of blocks is determined by the longest chain, which is essentially a matter of chance.

Another related misconception is that PoW is good, but proof-of-stake is better. In fact, PoW is the evolution of PoS, not the other way around. A PoS based digital money was described 1998 by Wei Dai [1], but that approach had flaws that would only be overcome by a system described Nakomoto's Bitcoin paper.

1. http://www.weidai.com/bmoney.txt (B-Money, Wei Dai, 1998)

  "Each server is required to deposit a certain amount of
   money in a special account to be used as potential fines
   or rewards for proof of misconduct."

Leaders don't decide. They propose values (such as a block of transactions). There may be multiple leaders with different proposals and participants get to a consensus about which proposal gets accepted for a given slot.

You speak authoritatively, saying "this is a common misconception", but blockchain is a distributed consensus protocol and I don't think you are familiar with multileader and leaderless flavors of distributed consensus.

> In Paxos a leader is elected, then the leader decides the order of events. But that's not a valid comparison, because in PoW the supposed "leader" does not get to decide anything at all - the block has to be put together prior to "winning the election" (because the block is the input to the SHA).

Who picks the transactions from the mempool that will be serialized into history?