I see what you mean about how proof-of-work can be monopolistic as well, but I guess there are at least some extra steps involved. You need to take your earned

I see what you mean about how proof-of-work can be monopolistic as well, but I guess there are at least some extra steps involved. You need to take your earned coins, sell them for computers, and then turn those computers toward mining (as opposed to any other productive use). In proof-of-stake, simply by virtue of holding coins you obtain more coins. This also comes with an opportunity cost, of course, but not to the same extent I think. To respond to (1) I think I don't understand the mechanism of proof-of-stake well enough. I think (correct me if I'm wrong) that the reason pooling is incentivized in proof-of-work is because having more mining power doesn't give you more coins as much as it increases the likelihood of you receiving a coin. In other words, it's the statistical nature of proof-of-work that makes pooling necessary. For proof-of-stake to not incentivize pooling I think it would need to not distribute coins statistically, but more like how stock dividends are issued today. That being said I'm still not sure that the incentive for miners to pool is the same as a pressure on the network to consolidate holdings. I'll need to reflect on that. Regarding (2) I'm not sure I understand why or how you would punish participants. ie. how would the network differentiate a 51% attack from a "legitimate" use of 51% to steer the network, and what could it do as a result?