PoW distributes the leadership (block creation) via crypto puzzles. PoS tries to use economic incentives to make bad behavior more expensive than good.
There's work being done (which I personally believe is the right way to go) in using a leader election-based system that works like a lottery (Algorand[0] is an example). The basis of such a system is going to be the creation of non-biasable pseudo-random number generation.
Along these lines one of the more intriguing projects is called RandHound[1]. It's a way of creating distributed randomness (according to the paper's title). I think chains secured via lottery leader selection protocol has more promise than PoS.
Edit: for clarity
A lottery-based system works because the "winning numbers" (imagine a winner being a node whose public key when XOR'd with the winning number is below a certain value) are known to all (a protocol like randhound ensures that all nodes know the winning number). A winner's bundle of transactions are validated as his/her's by cryptograpic signature (which can be verified using the same public key that is used to confirm this person is truly a winner). Those are the broad strokes. Obviously there's a lot more to getting it to work. I've been working on it for months and still haven't gotten around to putting it down on paper.
Probably what you meant but I still wanted to mention it: Bitcoin (or most PoW schemes) work like a lottery. Think of each attempt at generating a nonce below the required difficulty as a lottery ticket. The more nonces you generate (the more hashes per second you compute) the higher your chance of winning. The system works because people who spent lots of money on lottery tickets in the past (and maybe won one or two times) are incentivized to keep the lottery running in an honest manner (so their prize keeps its value - if they haven't spent it).
> Along these lines one of the more intriguing projects is called RandHound[1]. It's a way of creating distributed randomness (according to the paper's title). I think chains secured via lottery leader selection protocol has more promise than PoS.
Another notable mention is dfinity (dfinity.org). They have a very interesting technology stack and I'm hoping for discussions about it in the future on HN.
One way to view how SCP avoids leader election is to consider that it is effectively emulating the leader. SCP has two phases, a nomination and a balloting phase. The nomination phase is effectively like one or more instances of an asynchronous broadcast protocol (which don't require a leader since multiple nodes can choose to broadcast). The balloting phase is like Paxos, except that the value to propose is embedded in the ballot number so nodes don't require a leader to tell them what is being proposed--they can each emulate the leader themselves.