Quote from: iamnotback on February 19, 2017, 10:27:35 PM

Your assumptions about any second token not becoming centralized are incorrect.

Can you please be a bit more specific on that?

Interests are paid on account balance every time a block is built (by anyone), so in that regard it doesn't matter how many accounts you own.

As for the issue of buying & holding accounts in order to generate and sell child accounts later on, let me make the following gedankenexperiment.

Consider a situation where the market capitalization of the currency remains stable all the time. As money supply constantly increases by the interests, the exchange rate of the currency unit must inevitably decline. So, free accounts will make a loss, while the stake of minting accounts will be more worth over time. In other words, there will be a constant value transfer towards the minters.

Now, what will be the effect on the market price of the minting accounts? Well, still assuming a stable market capitalization of the currency (as the first token), the demand for new minter accounts cannot increase in the long run because the pool of total minters is growing as per protocol (note that existing accounts cannot be sold). An increasing demand for minter accounts would amount to a higher influx of new capital into the currency and thus increase its capitalization which is excluded in our gedankenexperiment. Therefore, if market capitalization must remain the same, it can only mean that the demand for new minter accounts will decrease or at most stay the same in the long run. As a result, the price of such accounts will either decrease or stay as the supply of new accounts is fixed by the protocol.

With that said, would it be rational for a new investor to buy minting accounts with the (sole) aim of selling their child accounts for profit? I doubt it. Depending on the age of the blockchain, an investor will have to wait years to sell its (first) child account and the price he gets will probably be lower than his purchase price. Of course, he could sell more than one child account over time, but for each additional child account he will need to wait even longer as the pool of minters gets bigger and bigger. Futhermore, the account generation intervals will also increase in absolute terms, since the average time needed to build the first block (and sell your first child account) mainly depends on the current age of the blockchain. The later you come, the longer you have to wait for your success.

In the long run, the discounted cash flow that can be generated by selling child accounts will tend to 0. And that is even true for scenarios of an increasing market capitalization since the latter cannot grow forever! On the other hand, by investing the purchase price into the currency itself instead of buying minting accounts, you will not only own a cash equivalent that can be sold anytime, but also receive interests on your stake. For this reason, buying multiple accounts will probably result in an economic loss, which should enforce decentralization of the second token (one man, one account, one vote) under the assumption that people are behaving rationally.

Of course, this assumption doesn't necessarily hold for irrational users who accumulate accounts for other reasons (e.g. to attack the blockchain). In that case, attackers with a lot of financial resources have an obvious advantage. However, their time will be limited just like the time of everybody else (as neither natural nor legal people are immortal), which lowers the risk of such attacks over time.

So, your statement that any resource will become power-law or exponentially distribute is not exact but too broad since time (in its absolute sense) is a good example for a resource that isn't power-law or exponentially distributed among people. Your statement only holds for resources that are negotiable. Time isn't.