I just put my simple simulation results together at https://github.com/txngrid/posmodels/blob/master/POS_model.pdf.  Hope it helps understand the current PoS issues and why I am proposing this Pool of Stake solution.  It covers 2 models and here is the summary.

http://intocrypto.com/images/pos_100_90.png

1. A single miner is selected stochastically each time to create a block.  These are the issues with this model if too many miners are multiple voting

• It is difficult to tell which branch is the winner, even if a miner wants to be honest, because there is no clear winner in the short term (a few hundred blocks).
• Blockchain reorganization can happen frequently - each crossover in the above graph can be a reorganiztion.
• Forking happens naturally.

http://intocrypto.com/images/por_100_90.png

2. Multiple miners are selected to sign each and every block.  The issues above are greatly improved but the N@S attack is still an issue.  Still need a way to control double-voting.