Please try to wrap up this discussion between you and I (which I'm feel was worthwhile for me). Because I don't have free time to expend on this.
But you aren't addressing the reason I mentioned that. Refer back to the prior discussion.
I don't expect everybody to become an investor and take part in mining. The majority of users will probably only use free accounts. But given the fact that the number of accounts will correspond to the number of blocks, there will be a considerable supply of new accounts at all times. (I'm not sure if I got your point though.)
The point remains that accounts will become power-law or exponentially distributed (if not relative to themselves then at least relative to free accounts) and thus be much fewer to attack to steal private keys than the number of freemium users.
Whereas, in my design, you also need plenty of time (years, even decades) or the necessary power/creditibility to control 50% of the active miners without buying accounts.
Now you are telling me new accounts can be sold? So why do you think these won't be power-law distributed? They always are.
New accounts can be sold on the market just like the currency itself. They won't get centralized because it simply doesn't make sense for an investor to have more than one account since he gets the same interests on his stake, while the profits from selling child accounts will get neglibile over time.
Ultimately, the attacker would have to keep paying the market price for at least 50% of the ongoing production of blocks/accounts as long as he wants to maintain his attack.
If mining is profitable why wouldn't the "attacker" (or natural power-law effect) do this? If mining is not profitable, why would anyone buy new accounts?
Investors will buy the accounts because they get regular interests on their stake
with every block attached to the blockchain, even if they never mine a single block.
However, everybody who owns an account has an incentive to mine since mining is profitable and the costs are very low without PoW.
The profitability of mining will decrease over time due to the growing competition. If you buy your first account 10 years after the genesis block, you will have to wait another 10 years on average to get your first child account (provided that every investor is actually mining). Now, you can decide if you want to sell your child account or keep it and retain your relative mining power. If you opt for the latter, you will have to you wait another 10 years to get your first grand child account. If you sell it, you can cash out with the current account price and will only have half the minting power as of now, which means that you would have to wait 20 more years for your first grand child account.
Accounts that haven't been sold at their birth, will be practically unsalable for the future due to the buyer's risk I already mentioned. That's a fundamendal difference to traditional PoS where you can grow your stake just by keeping it mining
and sell it any time you want. In my design, the price you pay for an account will be sunk costs. So, it's only profitable to mine once you own an account (which you have bought
in order to get interest on your coins). Whenever you get the chance to build a block, it will be more profitable to sell the child account and invest the price back into the underlying currency, rather than keeping the account in the hope of selling grand-child accounts later on.
You've clarified a key detail just now highlighted in bold above. So you are saying that users need one mining account to enable earning interest on their non-mining tokens (your prior descriptions led me to assume interest was per mining account and had nothing to do with tokens owned)? So you are saying that there is no reason to own more than one mining account, because mining does not return enough to recoup the cost of buying an account. So you are implying mining is not profitable in the sense of total ROI, but it does produce profitable operating income. You did not make that distinction clear in your description and terminology before.
That was not at all clear to me from your original summary of your system. I suggest you improve your abstract.
So you are claiming that as long as the starting distribution of mining accounts is nearly uniformly distributed (i.e. one person, one account), then it would be too costly to buy new accounts to maintain a 50% control on total supply of mining accounts, because the cost of buying them can never be recouped from mining alone (only from interests on tokens).
So now that I properly understand your design, I can more easily identify the flaws.
The flaw should be obvious to you! If the supply of new mining accounts is insufficient to match the number of new users who are buying tokens (which you state decline exponentially in order to make the mining account a sunk cost relative to mining profits), then it means competition in pricing for mining accounts means that only some tokens owners earn interest. So in order to earn interest, there will be competition to consolidate token ownership ever and ever more concentrated. So that the price of new accounts keep rising until the supply of tokens is owned by a very individuals. This will also drive the price of the token down and down, because eventually only a very few large token holders can justify buying new accounts. Even they can justify buying more than one new account, because their interest earned per mining account purchased is higher than their competition.
So you can see mining becomes centralized.
Really there is no way to stop nature from routing around your Coasian barrier applied to a fungible resource. Your attempt to make it not fungible plays right into why the concentration still wins the economy-of-scale as I explained.
I had stated before that if mining income is very small relative to interests earned, then no one will bother to do it. Thus that is another reason the mining will become centralized.
I am intuitively confident we will discover numerous ways this fails. But I don't have time to think about this too much.