This is a nice way of putting it.
My preferred 'most secure' system is different from the above: (requires X, but X is augmented by Y):
votes = (1+coins)^p*(hashes)^(1-p) where 0 < p < 1 [I would suggest p = 0.8 as a good value]
You don't need coins to vote in this system. Coins just give your votes more weight. By contrast, you do need hashes to vote.
My preferred 'most secure' system is different from the above: (requires X, but X is augmented by Y):
votes = (1+coins)^p*(hashes)^(1-p) where 0 < p < 1 [I would suggest p = 0.8 as a good value]
You don't need coins to vote in this system. Coins just give your votes more weight. By contrast, you do need hashes to vote.
The major issue I see with such a system is that it makes mining pools even more important. Also larger pools (or at least pools holding more coins in their reward address) are actually MORE efficient. We already see a massive migration to the largest pools (bigger get bigger) and the only advantage they have is lower variance. If Deepbit for example actually could generate more revenue per share than smaller pools in pretty short time we would have 1 pool.
I'll look at the rest of the response later, but I want to respond to this statement first. This is a misunderstanding due to me being sloppy and omitting details. Proof-of-stake or a mixed system can be arranged without creating increasing returns-to-scale in mining. Appropriate rule choices would allow for competitive small-scale mining operations. In fact, appropriate rules make independent, small-scale mining more viable than it currently is. I think a hybrid system would lead to a larger number of small pools and independent miners.
Here is my suggested rule choice which protects small-scale miners:
I would define coin votes in terms of 'coin-confirmations' rather than 'coins'. I define "coin-confirmations" as [coins associated with private key * confirmations associated with private key]. In words, coin-confirmations are the product of the number of coins in an account and the number of blocks found since these coins in this account were last sent (i.e. this is the number of confirmations on the coins). I would require coins to be sent every time they are used to mine a block, thus resetting the number of confirmations on the coins. These sends offer proof that the miner has access to the coins' private key. In this system, an account containing 1000 coins with 1 confirmation is equivalent in voting power to an account containing 1 coin with 1000 confirmations.
It should be clear that coin-based voting under this arrangement has constant returns to scale. Aside from reduced variance of payouts, there is no advantage associated with membership in a large pool. Moreover, payout variance is decreased across the board because random hashing outcomes determine only 20% of voting power. The across-the-board reduction in payout variance makes large pools less attractive. One would expect smaller-scale operations to emerge under these rules.