Yeah difficulty doesn't work that way. It is hard to understand what you are trying to accomplish but when you just start making up new meanings for words like "difficulty" it is hard to take is seriously.
If difficulty is cut in half without an equal reduction in hashpower, it will be twice as easy to find a block and thus in the long run blocks will be found twice as fast. If in any interval twice as many blocks are found then the average time between blocks has to be reduced in half.
Definition of difficulty: the threshold below which you must find a hash. The lower the hash, the lower the chances of finding it, the longer (on average) it takes to find it.
The problem here is that there are THREE variables changing at the same time and you are having a hard time thinking about how all 3 interact. I can assure you I know how difficulty works and am not an idiot, so stop trying to take the short cut and assume I am nuts and start thinking through how these THREE variables interact. The variables are: 1. reference difficulty 2. reward 3. hashes/sec.
1) If mining difficulty were cut in half and hash-power stayed the same, blocks would be found twice as fast. The network would notice this and double the difficulty such that 50% of the hashing power equals 100% of todays hashing power and thus maintain the 6 blocks an hour invariant. No matter what the network can adjust
reference difficulty to maintain an average block rate of 6 / hr.
2) Given the reference difficulty, miners have two choices: mine at the reference difficulty and receive 100% of the reward or mine at half the reference difficulty and receive 50% of the reward. Either way, the network is paying the same BTC/hash for hashing power.
The result is that the more people that choose to mine at 50% reward the higher the reference difficulty would get. Like I posted earlier, if 50% of the miners adopted the 50% fee for 50% difficulty then you would see the reference difficulty go up by 33%.
Bytemaster, I sense your frustration - I
think i get it (although quite possibly, i don't).
I think you are suggesting simultaneously offering two difficulty thresholds at the same time, high and low.
High = 25 BTC reward per block.
Low = 12.5 BTC reward per block.
The network adjusts the difficulty of each threshold to reflect the proportion of hashpower mining at each threshold, such that the COMBINED block find rate remains at 1 per 10 mins.
In this scenario I suspect most people would ignore the inflation incentive you refer to and simply mine whichever difficulty is most profitable at any given point in time, because any disproportionate difference between difficulty thresholds would produce a greater profit incentive to switch difficulty than any long term benefit of lower/higher inflation.
I also suspect that in reality most miners would simply mine at both levels simultaneously, submitting any valid blocks on discovery, regardless of whether they meet the high or low threshold, because at the point of having found a block which meets the low difficulty threshold, the chances of making money are greater if it is submitted than if it is thrown away in the hunt for a more valuable block. This means all network hashpower is always dedicated to both levels (rather than a 50% low, 50% high model).
All this would eventually lead to a necessary stabilisation point at which low difficulty blocks can be found on average say 15 mins apart, and high difficulty blocks at 30 mins apart, in which case the end result of 30 mins mining would remain at 3 blocks (one every 10 mins on avg), and the net coin inflation would be 50 as opposed to the current 75.
It's an interesting idea, and the effect on inflation would be real, however I don't think the reality would deliver the split mining model you propose, instead the mad scramble for MORE bitcoin would simply continue with people going all out to get whatever they can, and probably grumbling about the lower overall ROI along the way.
