Why PPC and similar coins are less affected by the Nothing-at-Stake problem

The Nothing-at-stake problem is a well-known problem or weakness of Proof-of-Stake currencies.

The essence of it: Minters don't have to waste external resources to mint on several chains at once. So they can mint "costlessly" on several chains.

Now the question is: Why should they? What is the incentive?

Well, in currencies where you get a fixed block reward (e.g. 15 coins), the answer is that they have a higher expected reward. Every block they mint increases their income, and if they mint on a fork and the fork eventually becomes the longest* chain, then the block reward is theirs. So if they mint on all forks, they may get blocks more often, and may get more rewards.

The same thing happens with currencies where the main income for PoS minters are transaction fees (NXT, NEM, Waves ...), although to a a bit lesser extent, because transaction fees are typically smaller than block rewards.

But there are currencies where there is no such incentive. In Peercoin (PPC) and similar coins, there is a low block reward that is only a percentage of the money you own (e.g. 1% of your stake per year). That seems to be not of relevance, but it has an important consequence: If you mine on all forks and thus get blocks more often, you won't get more rewards than if you minted only on the longest* chain.**

Let's have an example:
- A minting node must take the decision to follow one of two chain forks
- One of both is longer*, so it's the fork that probably will win.
- The probability that the longer chain wins is 80%.
- Now let's say that the minter, because of his stake amount, has a probability to get 1 of 10 blocks.
- Consequence: If he mints on both forks, he'll get ~1 block every 10 blocks. If he only mints on the longest* chain, then he'll get ~0.8 blocks, because there's a 20% probability that the fork wins.

Now the interesting part:
- If there is a fixed block reward of 10 coins each block, that means that he gets 2 coins more each 10 blocks than if he minted only on one chain.
- If the block reward is a percentage of his stake per year, then he'll get the same reward if he mints on both chains.

So there is normally no incentive for the PPC minter to mint on both chains - the main exception** is that he wanted to attack the system.

*In PoS coins, blocks get "rated" by a number that takes into account the "stake" wasted on them. This number, in Peercoin-based coins is called "chain trust". The fork that has more accumulated chain trust, becomes the "longest" chain.
** There is another exception: Small minters that most likely won't get 1 block per year could be incentived to mine on more than one fork. The same is true for coins with a high percentage reward like 10% per week (called often erroneously "PoS interest"), because in these coins the minters compete in a shorter timeframe. High-Interest staking coins are therefore more insecure.

PS: There are other N@S-related attacks that can be carried out also in Peercoin-style coins. But on all these attacks, multiple forks benefit the attacker.