I have been thinking about another possible solution, that might improve the POS security, similarly to constant per-block reward. Let us consider it, if only for the sake of discussion. I suspect that it is probably doing the same thing as the constant per-block reward, and is slightly more complicated, but it could also have interesting advantages. Please, let me know what you think about it.
As I was showing, the situation optimal for security at current money supply would be if all blocks had reward 4 PPC, but median block reward is ~0.3-0.4 PPC and the network effectively feels (through POS difficulty) reward ~0.2 PPC. It is caused by fact, that 60% of block rewards is concentrated in fewer than 5% of blocks based on very big stakes. This undermines the security to some extent (although not very seriously for now). One solution to this problem is the constant per-block reward calculated in such way, that Peercoin keeps it 1% inflation. Alternative solution is this: Let us cap the maximum stake that can be consumed in single block. The cap should be, for example:
Maximum stake coinage = 2 * money supply / 144 coin-days,
which currently leads to reward 8.07 PPC. This is double of the would-be constant per-block reward (4.03 PPC). If the stake has bigger coin-age, the special mint transaction will work so that only the maximum stake coinage is consumed. The stake in question starts with non-zero coinage after the mint so that the stake owner does not lose more coinage he was rewarded for. 30 days of zero probability of finding block and linear approach to the final value between day 30 and day 90 are kept in place.
Note that the new coinage of the stake is not written to the blockchain, only the way how the coinage is calculated is changed to take into account this different minting.
Imagine stake of 10,000 PPC that was kept in cold-locked wallet for 3 years. Today, the reward would be 300 PPC. In the proposed system, reward would be 8.07 PPC, and after the mint, the stake would start with coinage 2.92 coin-years. For 30 days, it would have zero probability of finding new block and between day 30 and day 90, the probability would linearly approach the value corresponding to 2.92 coin-years. With such coinage, the stake would probably quite soon find another block and collect the reward 8.07 PPC, until all its coinage would be consumed eventually.
[ul][li]Big stake-holders must mint often if they want to get their 1% reward. This is the same as in constant per-block reward system.[/li]
[li]For small stake-holders, things are not so wildly random. While in constant per-block reward, you either gain much more than your stake, or you wait without success for quite a long time. In this system, the small stake-holder, if he is lucky to solve a block, will get his fair reward.[/li]
[li]Small stakeholders have no incentive to mint on all alternative blockchains (forks).[/li][/ul]
[ul][li]It is more complicated to explain than the constant per-block system.[/li]
[li]Might lead to hoarding of small stakes with long age (to claim the reward).[/li][/ul]
Here I post an analysis of what would capping of the max coinage consumed per block do with existing block rewards in the blockchain. The capped distributions were created so that the stakes above the threshold were replaced by block with the cap size in such amount the total number of coins was conserved. So there is more blocks than in the red (real) distribution. I rescaled them so that the X-axis ends at the same point. The scaling factor is the increase in difficulty.