This equation is inherently misleading.

There are at least three ways to talk about scaling Bitcoin: scaling the number of nodes, scaling the number of transactions, scaling the number of users. Each one needs to be considered separately, or at least independently acknowledged.

That equation deals with the number of nodes and the number of transactions.

"Decentralization" isn't a well-defined term, but here it's something proportional to the number of nodes.

That sounds scary, but it really isn't because no single entity is responsible for paying the entire network's cost by themselves.

What happens to that equation when you consider the per-node network cost?


Data size is proportional to the transaction rate, therefore the cost of operating the node is proportional to the transaction rate. According to gmaxwell, the quadratic component to scaling the number of nodes can be made small enough to ignore with good network design, so I'll take him at his word.

Clearly the only threat to decentralization is the lack of price discovery for transaction relaying. If users paid for this service, then nodes would have revenue proportional to the transaction rate, therefore their revenue would increase at the same rate as their costs. Problem solved.

Fix the lack of price discovery in the P2P network, and the network will do an embarrassingly good job of solving its own scaling problems without tending toward centralization.

As hinted above, that assumption has been incorrect the entire time. I'll prove that more thoroughly shortly.