Variance Discount Flaw

Variance is the varying frequency of achieving a reward. Different hash power among miners implies rewards will be earned by some more frequently than others.

With 10% hash power one might expect to be rewarded 10 times more frequently than with 1%, though this multiple is greater due to the proximity premium. Furthermore, actual results are unpredictable and can vary significantly. But it is sufficient here in both cases to assume proportionality. In this example one miner receives a reward every 100 minutes and the other every 1000 minutes. Assuming identical rewards per block, the magnitude of the reward is also proportional to hash power.

Consider then that a tiny miner might have to wait years before any reward. Despite being rewarded proportionally a smaller miner is faced with a perceived deficiency in relation to the larger miner. It can improve cash flow to receive a fraction of the reward more frequently. There is also the possibility that a mine is misconfigured and can never succeed. For these reasons miners discount high variance. Smaller miners will convert their mines to grinds and pay an aggregating miner for reduced variance. This is the rationale behind P2Pool, but because distributed variance reduction is less efficient the pooling pressure remains.

The variance-based pooling pressure is a consequence of singular difficulty as required by consensus rules. Small miners must compete at high difficulty despite low hash power, which magnifies probabilistic variance. The proximity premium is another pooling pressure caused by consensus.

The defense that Bitcoin intends to raise is market defense against anti-market forces. To do this it must distribute hash power broadly among people so that it becomes difficult to co-opt. However pooling pressures inherent in the consensus work against this objective. This is why the characteristic is termed a flaw.