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Jiang Zuouer of BTC.top posted a rather… interesting analysis of their plan to fund BCH development with 12.5% of the BCH coinbase award for 6 months starting in May. If you haven’t seen the proposal, the idea is for the miners to form a cartel where they will orphan any blocks that don’t give the developer subsidy, meaning they have some assurance that they have at least 51% (more likely in the 70% range) to make good on this threat. The game theory on that is interesting, as BCH has a 10 block rule that will make any orphaning with less than 60% of the total BCH hash power pretty risky, but that’s a post for another time.

What I want to focus on in this article is Jiang Zhuoer’s claim that BTC miners are actually partially paying for this plan.

The Claim

Let’s break down the claim step-by-step.

Because of the hash ratio between BTC and BCH, and the difficulty adjustments that maintain an equilibrium, it is the entire set of SHA-256 mining (including BTC mining) that bears the cost under this plan.

The hash ratio between BTC and BCH has a theoretical equilibrium point based on price. We’ll use round numbers here for the sake of simplicity. If BTC is worth $9000 and BCH $1000, given the same block reward, 90% of all available SHA256 hash rate goes toward BTC and 10% to BCH as that’s the game-theoretical optimum. If miners move from BCH to BTC, they lose money in opportunity cost, same for the reverse, provided the price stays the same. Whenever price changes, (say BTC is worth $9400 and BCH $600), BCH miners are making less money and BTC miners are making more, causing BCH miners to move from BCH to BTC. The hash rate ratios quickly go to 94% for BTC and 6% for BCH as about 4% of all miners are incentivized to move to BTC.

The 12.5% tax is similar to a price change. A miner that was making $1000/day on BCH now starts making $875/day on BCH because of the dev tax. This means that the hashing power of BCH will lessen by 12.5% given that everything else stays the same.

Thus far, we have no reason to believe that BCH won’t be paying the cost of the 12.5% tax. In fact, BTC will get more hashing power and a more secure network at the cost of BCH hashing power and less security on their network!

Assuming a Static Global Hash Rate

This is counterintuitive: With 12.5% of the coinbase being donated, then on first glance, it would appear that BCH miners simply give up 12.5% of their rewards and would then lose 12.5% of their hash as well.However, after difficulty adjusts on BTC, it is a different story.

The difficulty adjustment does put some difficulty into the calculation. BCH’s difficulty adjustment algorithm adjusts pretty quickly to keep the blocks at 10 minutes. This was done because they experienced a much lower percentage of the total hash rate and there were many 12-hour periods during their first difficulty adjustment algorithm era where they found few, if any, blocks.

What the difficulty adjustment algorithm does is make each block easier to find so that the blocks continue being produced at 10 minute intervals, regardless of hash rate. The algorithm has some serious security vulnerabilities, but that’s a post for another day.

Assume round numbers for illustration: BTC is 97% hash and BCH 3%.If BCH gives up 12.5% of its reward, that 3% goes to about 2.6%, and BTC would go to 97.4%.
0.375% of the total SHA-256 rewards are being pulled out of the entire system, but this cost will be split between BTC and BCH in the same ratio as the hash (97:3).The BCH hashrate will be diminished by 12.5%, but BTC mining will bear 97% of the cost of the diminished profitability, because there will be more hash competing for the same BTC rewards.

So here’s the meat of the argument. Essentially, Jiang is arguing here that BTC miners are actually bearing the brunt of the cost because more hashing power is needed per block after BTC’s difficulty adjusts to reflect the new miners coming in from BCH.

First Order Effects

To illustrate the deceitfulness of this argument, let us use an extreme example. Say 90% of the reward is going to the BCH developers. If BTC/BCH hashing power is split 97%/3% before the reward goes into play, 90% of the miners on BCH immediately leave after the reward goes into play. The hashing power split becomes 99.7%/0.3%. The difficulty on BCH quickly adjusts to allow 0.3% of all SHA256 hashing power to mine a block in 10 minutes. The hashing power on BTC eventually adjusts to allow 99.7% of the total SHA256 hashing power to mine a block in 10 minutes.

So what’s changed here? 99.7% of mining has to compete for the same rewards as 97% from before, so there’s roughly 3% less reward on a per-hash basis. Same for the 0.3% in BCH, as Jiang has pointed out. As far as the reward analysis goes, this is true. Seems like a free lunch paid for by BTC, as Jiang is asserting.

Second and Third-order Effects

But there are further, second-order effects here. 3% more miners on the BTC network mean that the profitability has changed and the miners at the margin will now no longer make profit. If all costs and prices stay the same, the miners whose profit margin is less than 3% of the reward will simply stop running their miners. In other words, supply of hashing power will react to the reduced demand.

Depending on how many miners are operating at the margins, the amount of hashing power dropping out may be more than 3% or less than 3%. If it’s more than 3%, the difficulty will adjust again and equalize at a level that’s actually more profitable than before the whole dev tax began to the miners on BTC. If it’s less than 3%, the difficulty will adjust and equalize at a level that’s less profitable than before the whole dev tax began to the miners on BTC, but more profitable than the simplistic situation Jiang outlined. Of course, making it 3% easier will bring back those marginal miners as a third-order effect, but this is why claims like this are ridiculous. You can’t examine just the first order effects and claim the cost is being paid only by those.

First-order Security Costs

Furthermore, BCH is paying out the same 6.25 BTC per block for 87.5% of the security as before the dev tax! The BCH network is essentially paying their miners the same amount for less work so they can pay their developers. And who pays for the BCH network? Well, it’s really the holders of BCH. They are the ones whose percentage of BCH is being reduced by the inflation. In a proof-of-work system, the inflation and fees pay for security. And since the fees on BCH are negligible, the cost of the security goes up proportionate to the amount of the tax. The holders of BCH are getting less security for the same dilution.

Consequently, exchanges and merchants will need to increase the number of confirmations needed by 14% (1/0.875) to get the same level of security against double-spending attacks, slowing everything down.

In a coin supposedly focused on transacting frequently, this is a strange trade-off to be making.

Conclusion

The cost to BCH is not just “BTC is going to pay for 97% of it”. As I’ve shown there’s a significant amount of costs in security and second order effects. Jiang’s argument is the equivalent of saying if Canada raises taxes, it’s actually the US that pays for most of it. With the logic being that anyone who leaves Canada will go to the US and cause more competition in the US labor markets and that will allow Canadians staying to make that money back. This is theoretically true if examining cherry-picked first-order effects, but those effects are only a small part of all the consequences.

What BCH is doing is removing a part of the market for SHA256 hash power, which is, of course their prerogative to do. Essentially, they are lowering the demand for all SHA256 power with the dev tax. By this cherry-picked logic, changing the proof-of-work algorithm or killing proof-of-work altogether would be even better since then SHA256 power has to all go to other places, making BTC mining less profitable at least on a cherry-picked, first-order basis.

The shortsightedness of this policy is truly something to behold. What are they going to do after 6 months if this tax policy is successful? Continue it? What happens after the next halving if the price hasn’t changed? How about the halving after that and the halving after that? Long term, the block reward becomes less than the dev subsidy meaning something will have to give. The BCH developers are obviously going to want to continue the subsidy. Do the miners screw over the developers by ending the subsidy? Or is BCH just going to change their inflation schedule to fund both the miners and developers?

This policy has the potential for a whole lot of drama and I, for one, will be getting some popcorn.

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