Ayyyy I'm Collin Cusce from the dev team on AVA. Feel free to ask me whatever you'd like about AVA or the Avalanche protocol. I'll try to answer the best I can :-)
You need to control 2/3rds of the stake and be able to coordinate decisions with each staking node before the block time is over to fuck up the network. Considering that PoS can enable more tunable block times as validators no longer will churn out random numbers on GPUs/ASICs to mine a new block, I think this will be a non-issue.
There's a lot of misinformation regarding PoS. Vlad Zamfir has spoken a lot on cartel attacks and how they're mitigated, but the biggest, and I mean bigger than biggest, argument against all of these attacks is that it's always detectable by honest nodes shy of 2/3rds attack and it defaces the value of the coin itself to attack at that volume.