Thanx for your interestign reply.
You seem to think that if ...
No. I do not think that.
these are independent Poisson processes (tied only via occasional difficulty adjustments) with different rates, meaning that you will simply find 100 times the blocks I will. So over a period where 1010 blocks were found between us, about 1000 will be yours and 10 will be mine.
I completely agree.
Now suppose it is you and me and some 40 other guys with the same hash performance as you have in your example. Suppose I want to claim 100 BTC bounty for every block instead of the standard 50 BTC. Chances are next to 100% that I will manage. Since, on the avaerage, I am faster than you (and all the other guys combined), I will dominate the longest chain in the long run.
If that's all you're after, mission is already accomplished.
No. It is not my mission.
let's say that in this system a person with a computer finds one block per month. Then four people with a computer each should find a total of 4 blocks per month, right?.
Why?
The perspective I am looking at is not the single block but the development of the block chain.
As soon as one of the four people found a block, this person broadcasts this block and the puzzles the other three had been working on becomes obsolete (at least that's my understanding on what the reference implementation does). Only a cheater would be interested in continuing to work on "his" version of the block; however, having lost the block in question, chances are getting higher that he will not manage to push "his" version of the next block.
Four people with a computer would rather find a total of 4 blocks in FOUR months - and these blocks would be the four blocks chained next to each other, ie a block chain of length 4.
And, once more - pools are not a security threat ...
How do you prevent a pool from pooling more than 50% of the hashability and then imposing its own understanding of Bitcoin upon the remaining nodes?
Edit: Parallelism means that an at-home miner can plug in his computer and contribute to security/receive rewards exactly in proportion to what he put in. Non-parallelism means his effect will depend in complicated ways on what others are doing and usually leave the poor person at a significant disadvantage (since others are using faster computers), which is the opposite of what you want.
I agree to the interpretation of the parallel PoW situation. I disagree with the interpretation of the non-parallelism situation - there is not yet a final proposal for a non-parallelizable PoW, so we do not know yet if this is a necessary consequence. However, I am grateful that you are pointing out this argument, since it is a possible problem. I will take this in consideration in my future work on this - it is a helpful objection.
Block finding follows a Poisson process, which means that the time to find a block follows the exponential distribution (where the variance is the square of the mean). The variance is high, but that's an inevitable consequence of the fair linearly scaling process.
Again you are raising an important aspect. The task thus is to see that two goals can be balanced: Linear scaling and small variance.
I agree that the Poisson process is a very natural solution here and prominently unique due to a number of it's characteristic features, such as independence, being memory and state less etc. A non-parallelizable PoW will certainly lose the state-less property. If we drop this part, how will the linear scaling (effort to expected gain) and the variance change? We will not have all properties of Poisson, but we might keep most of the others. The question sounds quite interesting to me.