good catch. Indeed - generating more blocks from the same stake will give you more bang for the buck, if you can claim a percentage of the destroyed coinage from the included transactions as a reward. Thus you have an incentive to have your stake existing as many small outputs. An indirect consequence of that is that you need to have more uptime for the stake - because smaller stakes have larger sampling requirements, i.e. need more online time.
That incentive may be so strong, that you may not have to modify the 1% per year reward at all to encourage POS miner to be online.
E.g take block 16924:
Coin-days Destroyed: 47119.621896
POS Generation: 0.43 Total (503.69*0.01*31/365)
Stake: 503.69
If you allow for 1%/365= transaction reward per block you have an additional reward of
47119.621896*0.000027=1.27
which is almost three times the actual POS reward. That means that a POS miner which is always online may easily effectively generate 3-4% on the used stake, which suddenly makes it much more attractive...
There is some incentive to include txns in PPCoin already. There is a fee that destroys currency. As a stake holder, the more currency destroyed the better off I am. It is a weak incentive, but it may be sufficient. You don't need to pay people to do something extremely easy. In fact, you certainly shouldn't pay them a lot. You would be wasting money.
That thread contains a good discussion. It points out some problems with txn fees in a PoS context. I go over some issues below.
Incentives in PPCoin are based on interest and not txn fees for good reason.
There is a fundamental problem with history revision in a PoS system. As a miner I have at least two choices:
1) Mine on the main chain using the official client
2) Mine on the main chain and older chains using a modified client. (naughty naughty)
The number of blocks I mine per unit time is random. If I do (2), I can explore alternate histories where I mine a larger share of blocks. If a large fraction f of users do (2), then there will be periodic reorganization events. If f=100%, then there will be perpetual reorganization and no "main chain."
In PPCoin, doing (2) is not rational. There is an infinitesimal personal benefit related to more frequent compounding of interest. There is also a cost because doing (2) undermines PPCoins market value. If you have a non-negligible stake, then you care about market valuation and it will never be rational to do (2). If you have a negligible stake, then what you do doesn't really matter anyway.
If we introduce piece rates for txns, the calculation changes. The benefits of more frequent mining become non-trivial. This encourages more people to do (2). I expect that for any txn fee, r, there will be a cut-off stake level, s*(r), where for s
What can be done about this?
a) Restrict yourself to weak incentives (e.g. interest perhaps with a time cap to weakly motivate more frequent mining) [This is what I am suggesting for PPCoin.]
b) Mitigate the theft risks of keeping coins online. This is probably a large reason why people would avoid mining. [Again I am suggesting this for PPCoin.]
c) Introduce a mechanism that makes it extremely unlikely that minority chains overtake the main chain. Essentially this means that (2) is irrelevant unless the fraction of people doing (2) approaches 100%. [I describe a mechanism like this here:
https://en.bitcoin.it/wiki/Proof_of_Stake. It is too big of a change to be a fork of PPC]
d) Find an incentive mechanism that detects and penalizes people who do (2) regardless of whether they succeed or fail. I think the solution here is to make mining "quasi- deterministic". Deterministic mining means there is only one true history. Quasi-deterministic mining means that there is a very limited set of alternative histories and you have to pay everyone coins to search through them. I'm working on a pure proof-of-stake system that does a combination of (c) and (d). The system would use txns to measure "time". I will post a brainstorming thread about it shortly. I would appreciate comments. [Much too big of a change to be a fork of PPC.]