How? If you award a “lucky farmer” the whole fraction then you create an unbalanced gamable system but to remain fair then how can it be done? the system has 9/10ths of a coin’s worth (for instance) and the farmer needs to be paid 1/10000th of a coin? So how can it. That MD is stuck until someone’s share is reduced to zero.
Also for that coin any use of it has to use the full amount of the share since there can be no more division.
If a user has only that one share in their whole account then they cannot pay anyone unless that person also has a share in that coin.
To rule out the use of this as a suitable coin division mechanism I only have to identify one major issue, and this is more than a major issue, its a show stopper. Yes it might be worked around but any such work around that I can come up with has just as many problems elsewhere.
But I identified many issues.
Any modeling is preceded by a number of thought experiments in order to formulate the model. If the thought experiments show major failure before you even model then no use modeling.
The fact that coins can be stuck with the system owning a large portion that it cannot give out in rewards is one. Two is the situation where a person has only one share in a maxed out (division wise) coin they cannot pay/transfer an amount smaller than their share unless that person has also a share in that one coin is also a show stopper. Yes external exchanges may solve some of it, but introduces greater problems for the system, fees, complexity in core code, and so on because the system has to be able to “exchange” through the external exchange.
tl;dr
The thought experiment shows that it is unworkable because of the VERY limited divisibility. Even if you could increase that to very large amounts then you could, but in doing so there will be times when the system is doing many thousands of transactions just to transfer a few coins worth of divisions.
For modeling you have show that coins will not be filled up with divisions over the days/months/years of operation. Otherwise actual modeling past thought experiments will just get stuck on fully divided coins. Most likely around 256 to 1000 divisions.
####There are simpler and so much more efficient ways to divide than using a very limited method like this.
EDIT: I have not even talked about the recycling problem. A coin can only be recycled when all shares are removed and only the system has 100% share. Have a serious think about how many coins will be completely owned by the system when 4000 people have shares in the coin and are randomly trading in those coins. If and only if the majority >80% of the coin use is to pay for PUTs will you see a significant number of coins become completely owned by the system. BUT if as we hope the coin becomes a major unit of trade then paying for PUTs will not realistically reach that tipping point and there will always be an increasing number of coins being fully divided.