Or you can just buy / steal the private keys to coins that have already been spent, and then simulate alternate histories.
The trouble with these schemes is that it is quite easy to make them more difficult to review, without actually adding any security. In both cases I saw earlly versions that were criticized for being entirely insecure, then there were some iterations that added no security, until it got complex and the people involved learned to not provide free consulting, which I won't do here either: the objections to proof of stake schemes are general. It can be shown that any proof of stake scheme must be broken by simulation. It's just a matter of showing what the necessary procedure is for a given scheme, which can be made arbitrary difficult to review. One of the guys I work with quiped that this "cryptographic security against review." That shouldn't be mistake for actual security.
There are general results showing that the security being advertised is not possible, the perpetual motion sense. It's a waste of time for credible people to spend their time disproving perpetual motions machines, particularly when their proponents can make them arbitrarily difficult to review. Do not mistake a lack of review for an indication of security.
Vitalik says cryptocurrency developers should "reach out to LessWrong more", in order to not be ignorant of advanced computer science and game theory topics.
https://blog.ethereum.org/2014/12/31/silos/
I think Vitalik raises several major important points, namely:
* Bitcoin's $600 million wasted on electricity yearly in order to secure the network is a huge problem. Various Proof of Stake algorithms are attempting to improve upon this. The ideal solution would be one which combines the low cost of the Proof of Stake algorithm, with the high security or Proof of Work. I not enough of an expert to be able to say which solution is best, but both the Ripple consensus algorithm and the Bitshares Delegated Proof of State algorithm look promising. I am interested to see what algorithm Vitalik will choose for Ethereum.
* ASIC miners are a problem due to the resulting centralization. They have also lead to increased centralization in Bitcoin, as the network is now increasingly controlled by a few large mining pools.
* Blockchain technologies have a great potential to change the world, and solve governmental and organizational problems that society is facing. Beyond simply revolutionizing money, blockchain technologies could also be used in the future to support prediction markets, voting/consensus building, exchanges, etc.