Introduction

I have often encountered the idea, that mining decentralization would be improved by rotating proof-of-work hash functions. In addition, I have also encountered the idea as well, that improving mining efficiency would also improve mining decentralization.

Unfortunately, following economic logic carefully, we find that neither will help mining decentralization in the long run. Instead, it is something completely outside of software or hardware design of mining hardware that can assist mining decentralization in the long run.

Mining Centralization Pressures

Eric Voskuil notes two important centralization pressures: Proximity Premium and Variance Discount. One would note that neither rotating proof-of-work functions, nor increasing miner efficiency, affect either of these two centralization pressures.

Let us then suppose that the solutions do not, in fact, attempt to fix Proximity Premium or Variance Discount.

This leads us to ask the question: what are the other centralization pressures involved? Or equivalently: in a universe where neither Proximity Premium nor Variance Discount exists, would we still expect miner centralization, and why?

The Heavy Nature of Gravity

Suppowe I were to hand you two randomly-selected, extremely large, but equally-sized, cubic sections of the universe. These cubic sections are so large, that they would contain multiple galactic clusters. I then ask you to measure the density of these cubic sections, i.e. the mass divided by the volume, or equivalently, how much matter-energy is in the same cubic area.

My understanding of physics at the time of this writing is that sufficiently large cubic sections would have roughly the same density.

That is, we can say that from a sufficiently high-level view, the distribution of energy (matter) is roughly “flat” across the universe, or equivalently, that the distribution of energy is equal.

However, any Earthbound sentience can realize very readily that the distribution of energy across the universe is not, in fact, quite as flat once you zoom in. Assuming you the reader are also an Earthbound sentience, you can easily determine that you are within a gravity well caused by a mass of matter, called “Earth”, that is itself is a captive gravity well of an even larger gravity well, the “Sun”.

Thus, we can realize that at lower scales, energy distribution is relatively “lumpy”, i.e. there are concentrations of matter-energy.

Energy as Factor of Production

In Bitcoin mining, electricity is the form of energy that is utilized. In fact, all that is necessary is a good Internet connection, mining hardware, and electricity. Administration of the mine by a human is also necessary, but is fairly small.

This is in contrast with a good many products and services. Most products require raw materials in addition to energy in order to create. Most services require significant numbers of human beings to operate.

In Bitcoin mining it is almost entirely electricity which dominates the operating cost of the mine. Factors like hardware deprecation, ISP fees, and system administrator salaries are fairly small compared to the electrical price, and it is expected that mines will seek to expand their operations until the addition of another mining unit will earn about as much as it costs to operate it, i.e. MR = MC.

Now, the cost of electricity is basically the local price of electricity, and the price of anything is proportional to the demand and indirectly proportional to the supply. Thus, all other things equal, a source of electricity is a supply of electricity and being in the vicinity of such a source translates to reduced cost of electricity, which translates to increased earnings for mines.

We can thus conclude that, in the absence of Proximity Premium and Variance Discount, Bitcoin mines will naturally grow around electricity sources, or equivalently, they will centralize into areas where the local price of electricity is low.

Even in a world with the Proximity Premium and Variance Discount, it is expected that the first mines will arise in areas where the price of electricity is low, and Proximity Premium and Variance Discount will only exacerbate this initial centralization around electricity sources.

On Equality Of Effect

Increases in mining hardware efficiency, is often presented as improving decentralization, by the following simple mechanism: profitability is increased, thus locations which are currently infeasible for mining now become feasible.

Rotation of proof-of-work hashing function is also imagined to make CPUs profitable for mining, removing the supposed unfair advantage of ASICs. Thus, it is imagined that mining centralization is reversed.

The issue with these solutions, unfortunately, is this: locations with electricity oversupply (low electricity price) remain the best place to put your mines in, regardless of mining efficiency, or that mines are datacenters filled with CPUs rather than ASICs.

That is, all other things being equal, the effect of both solutions is also equal regardless of where you are. Unfortunately, other things are not equal: the distribution of electricity sources is known to be “lumpy”, which is the root cause of mining centralization. You cannot fix an incorrect equation by adding the same term to both sides of the equation: they would just cancel out.

The real fix has to cancel out the profitability of a location near an electricity supply, or equivalently, has to increase the profitability of a faraway location without also increasing the profitability of locations near to electricity sources.

Electricity Transport For The Win?

So far, the only solution I can think of to fix the underlying root problem — unequal access to cheap electricity — is improvements to electricity transport.

This is because, if eletricity transport technology improves, the benefit of this technology increases the further you are from an eletricity source.

If you are at an electricity source, then you have no increase in profitability from improving electricity transport technology. If you are instead very far from the nearest electricity source, then you gain a massive increase in mining profitability.

A lesser solution would be improving electricity production, but only to the extent that such electricity production can be deployed in more locations (i.e. resilience against various local conditions, not raw efficiency). Increasing the efficiency of electricity production has the same non-effect as the other proposed solutions: it also increases the productivity of miners already at electricity sources in tandem with the productivity of miners far from electricity sources, cancelling out and returning to the status quo. To reiterate, what is needed, is the resilience of new electricity production technologies to be deployed in many more places, not efficiency of electricity production.

Conclusion

The ultimate root cause of mining centralization, further exacerbated by Proximity Premium and Variance Discount, is that electricity sources are not perfectly evenly distributed. Improving electricity transport from sources to consumers will help fight this centralization pressure much more effectively than increases in mining efficiency or rotating of hash functions, because electricity transport specifically increases profitability of areas far from electricity sources without increasing profitability for areas already near electricity sources.