I would propose the following to get a really fair coin distribution for a 100% PoS coin:
Add the bitcoinj library to the NEX code and let it run in SPV mode.
Every NEX node continuously scans the bitcoin blockchain for P2SH transactions that are going to a proof-of-burn address.
You define a sliding window (i.e. 100 bitcoin blocks) and distribute rewards proportional to all bitcoins that were sent to the burn address within the last 100 bitcoin blocks.
You can define a decreasing reward curve for the next 1-4 years, such that after this initial bootstrapping rewarding phase the bitcoinj library can be excluded from the source code.
I think this would be the most fair distribution model, because there is no initial IPO. The price of the new coin will be determined always by the free market: If there is a period where more people are willing to burn their bitcoins for NEX coins, then they each get less NEX coins for their bitcoins. On the other hand if there is a period were no one wants to burn their bitcoins to get NEX coins, then everybody could just jump in and burn just a few satoshi to get almost the full NEX block reward without much competition. So you see fair distribution by market value.
It would make sure that the new coin actually really starts at value zero and will gradually improve to gain value. Therefore from an economic standpoint this would be the same distribution model as with Bitcoin.
It will borrow the fair distribution model from Bitcoin and the nice proof-of-stake model from NXT.
Of course this distribution model also has a much lower barrier to entry for every current bitcoin owner, even if he decides only after half a year to exchange some bitcoins for NEX coins. He could just look if he gets a better price at some exchange or if he goes the way to directly convert by burning bitcoins. This is the same mechanisms as someone interested in bitcoin could decide to buy a mining rig or to directly buy bitcoins on an exchange.
So instead of an initial-public-offering the coin has a continous-public-offering with decreasing reward over the next few years. This makes sure that the coins will be distributed quite broadly to many people.
The problem with this is the value of bitcoin is not static, and so one day someone may get 10000 NEX for 1 BTC and the next 12000 NEX (or vice versa). In fact over the course of one year the price of bitcoin may triple, and so what? You are tying the price of NEX to the highly volatile and speculative BTC. This is not a good idea.
What if the price of BTC tanks over the course of one year? So at the beginning of the year you get 1000 NEX for 1 btc, but by the end of the year when you SHOULD be getting less NEX due to the tapering down of the burn reward system, they can buy 3x as many bitcoin for the same amount and so get 3x the NEX? So NEX has to decrease in value by 66.66% for no other reason than bitcoin took a dive.
Otherwise this idea is great.
edit: elaboration
I think you slightly misunderstood how it would work. The following is not true, because the reward is not coupled to a certain amount of BTC!
they can buy 3x as many bitcoin for the same amount and so get 3x the NEX?
No, they would get the same amount of NEX for their USD.
The reward is fixed to a certain time interval and NOT a fixed conversion rate to BTC!
Therefore the reward system is independent from the volatility or value of bitcoins.
Please let me elaborate using an example:
We could use a sliding window of one day (864 bitcoins blocks). The amount of distribution of NEX per day is fixed in the protocol and does not depend on the actual number of bitcoins destroyed:
1. Year: 1000 NEX per day
2. Year: 500 NEX per day
3. Year: 250 NEX per day
4. Year: 0 NEX per day
No matter how bitcoins volatility changes the total number of distributed NEX coins stays the same! These total rewards are distributed to all individuals who burned bitcoins proportional to the bitcoins that they destroyed during the last 864 blocks. If more people burn, their individual reward gets smaller. If less people burn, their individual reward increases. But the total amount of reward is fixed. Very similar to bitcoin mining power.
So now let's illustrate your example of a highly volatile bitcoin price using two scenarios:
Scenario A:
1 BTC = 1000 USD (very volatile)
1 NEX = 1 USD
1000 NEX are distributed per day
The free market will make sure that rewards are distributed worth of 1000 NEX per day. Therefore the market equilibrium fill be reached, when "miners" will burn 1 BTC per 24 hours, because 1000 NEX = 1000 USD = 1 BTC
Scenario B:
1 BTC = 100 USD (very volatile)
1 NEX = 1 USD
1000 NEX are distributed per day
The free market will make sure that rewards are distributed worth of 1000 NEX per day. Therefore the market equilibrium fill be reached, when "miners" will burn 0.1 BTC per 24 hours, because 1000 NEX per day = 1000 USD per day = 0.1 BTC per day
So you can easily see that the bitcoin volatility does not effect the reward distribution of NEX. If NEX has a stable USD value then the mining reward has also a stable value.
I can't entirely agree that this would be a fair system.
From a laymans points of view one day one group of 1000 people may burn 1 btc each and the next only day a group of 100. If 1000 NEX were released both days, one day they all get 1 NEX the next they get 10 NEX. This hardly seems fair to the first group to reward the second group 10x the amount based on random chance.
What would happen in this scenario is people would watch the burn address to know how much NEX they would get out on any given day. This might make it more profitable to just buy the NEX from someone else if the daily burn was oversaturated (that is, the amount of NEX you could receive from the burn would be less than taking that BTC and exchanging it for NEX directly).
In this case, the price of NEX would be tied to the amount of NEX you could get from the burn on any given day, or vice versa, the amount that people would/could burn would be directly tied to the price (would it be profitable to burn X amount of BTC if I'm going to receive Y NEX?)
It seems like instead of being used for people to adopt NEX, this burn/faucet would be monopolized by bots whose soul purpose was to eek out small profits whenever they could get more NEX by burning during a burn period than by buying on the exchanges.
In fact, no one would burn except within the last minutes/seconds of a burn period so as not to dilute the share of NEX dispensed (why burn when you don't know how many others are going to burn and at what amounts? It might be more profitable to buy off an exchange)
What am I arguing about? I don't know. But someone has to.
