- do you have another example for say a one week interval time frame calculation, or maybe a curve showing the relation between the interval and price stability?
- how will the peers decide on the market price of your hopdollars (when some of them are rogue or prefer say 2 USD/hopdollar)?
- where are they taking the hopbits? http://www.youtube.com/watch?v=z9Uz1icjwrM
Technical discussion:
It is really allowance for black swan outlier events that matters. This is the size of the state space. I cover a set of future backing realizations using a binomial tree issue. Moving from time t to time t+h there are 2^h possible voting patterns, each of which maps to an (approximately) unique change in backing ratio. That is a lot sure, however they have to span the entire state space of future backing realizations. It could be that 99% of the time, the t+h backing ratio is within 10% of the starting backing level at time t. Gamblers only need to worry about outcomes in that narrow interval of the state space. I also allow for exceptionally large outliers, covering changes of +-10^9%. This means that only a tiny fraction of the state space will lie in the interval of probable outcomes.
I guess the relevant question is what is the largest conceivable % change in price over h blocks. If you reduce this % then you can get faster convergence. Another alternative is giving miners more than 2 voting options. I feel that yes or no is the most idiot proof solution.
2) if more than 50% of PoS miners are honest than there is some interval h which is large enough to prevent gaming by the minority.
If you have say 66% honest miners and 33% who always lie, the interval is approx 3 times as large as if you have 100% honesty. Essentially you use up one honest vote to cancel out the dishonest vote. This leaves you with 1 influential honest vote for every 3 votes cast. So it takes 3 times as many voting periods to get things done. (Actually more because you need to cover a larger state space as you move forward in time, but I got that covered by being safe in (1)).