From the whitepaper:
The block chain with highest total consumed coin age is chosen as main chain.
I'd have to think about it a lot harder than I'm willing to right now to be absolutely sure, but that seems like a mistake to me.
If peers have to fetch inputs and compute coin age to determine whether or not a chain is longest then it seems like that could be leveraged into a denial-of-service attack. Because an attacker could do minimal proof-of-work (or proof-of-stake) but then broadcast a chain with
JUST a little-less consumed coin age than the current best chain.
Their chain will be rejected, but their peers will waste time figuring out that it should be rejected.
DoS attacks is only a secondary problem with this proof-of-stake proposal, the main problem is that this protocol is unsound because it's susceptible to easy double-spending attacks by stakeholders, simply by releasing a forked branch with higher total consumed coin age.