Balance, coin age, incoming and outgoing transactions play a role in calculating the importance. Having the importance the rest is a deterministic random algorithm like nxt.
Litmus test: Does chance of generating a block depend on a snapshot of the system only? (Without taking into account state transitions like transactions.)
CFB I put some weight in your judgement. You very clearly understood nxt (you were the one who explained it to me) and you understood the reason behind all of its various mechanisms, the attack vectors that it faced, and how it cleverly dealt with them. I really very highly doubt that this "Balance, coin age, incoming and outgoing transactions play a role in calculating the importance." wont be able to be gamed. I'm already imagining the attack vectors in my head. Someone creating a ton of accounts and interacting with himself between his accounts inorder to make his activity appear valid in accordance with the demands of w/e schemes the dev comes up with. What do you think?
*edit* i need to point out that im not saying that the system wont be secure, the extent to which it is proof of stake may provide enough security, the real question is whether all these extra bells and whistles added to the consensus mechanism will actually decrease the security of the network.