As a simplistic idea imagine that a block reward only occurs every X blocks but is more likely to favour the minter that has produced as many of those X blocks as possible (and also imagine that rules prevent them from being able to produce all of the blocks).
Some observations and questions:
1. You need some way to enforce the rule which prevents minters from minting every block. In PoW/PoS this would be:
probability of mint = hashing power(stake) / total hashing power(total stake)
2. What benefit is there to only rewarding every X blocks, instead of rewarding
reward/X every block?