> With proof of stake, nothing is preventing you from 'mining' on multiple base blocks on the same time. Anytime you spend a coin and get the goods, you might as well try and see if you can 'mine' 2 new blocks to erase your transaction.
Ethereum's proof-of-stake approach appears to solve the "nothing-at-stake" issue, see the Mauve paper for more details: http://vitalik.ca/files/mauve_paper.html
TL;DR of their approach is that if you mine off-chain blocks they can get later-on included by other (PoS-)miners via the "dunkle" mechanism. If this happens there's a penalty for the original miner who mined a block that didn't make it into the current chain.
Seems like that site vitalik.ca is down. Do you have any other sources for that paper?
It's available in the Google cache: https://webcache.googleusercontent.com/search?q=cache:BPRBqz...
With proof of work, you can only mine on any one block. You make sure this is the last block in the chain because otherwise you'd need to mine 2 blocks in a row to convince everyone. This ensures it is really hard to rewrite history.
With proof of stake, nothing is preventing you from 'mining' on multiple base blocks on the same time. Anytime you spend a coin and get the goods, you might as well try and see if you can 'mine' 2 new blocks to erase your transaction.
I've seen proposed solutions that combine these 2. Basically, a block then requires both proof of work and proof of stake. This doesn't help (much?) with electricity costs, but helps somewhat with centralization of power.