But the network is only incentivized to be exactly secure enough from Sybil attacks that nobody bothers to try one. There’s no added value in being more secure to Sybil attacks beyond that. Just like there’s no added value in hiring extra fire-fighers once every fire gets an instant + effective response.

—————

The problem with Proof-of-Work systems that prevents this logic from actually translating to a sigmoid curve in number-of-miners, though, is that any left-over electricity that isn’t going into “good” mining, could instead be going into Sybil attacks. It’s as if every potential fire-fighter who isn’t hired as a fire-fighter, instead has a chance of being recruited by “Big Fire” to one day work together to all set fires at once.

If-and-when governments actually establish their own cryptocurrencies, massive distributed purchases of electrical capacity for the sake of mounting a Sybil attack are exactly the sort of thing that state intelligence agencies will try to track and prevent ahead-of-time, such that nobody will ever be able to gain that capacity in the first place. Just like right now nobody can really build a stockpile of plutonium.

But as long as governments don’t care, and attackers are free to be economic actors buying up electrical capacity, then there is a specific effect we see today: rather than the network’s electricity consumption just growing to a certain absolute amount, the set of all Proof-of-Work networks are incentivized together to consume a certain percentile amount of global excess electricity consumption — 51% of it, specifically. Such that, at any point, there’s not enough electricity left over to even theoretically mount a Sybil attack against the largest network. (The smaller PoW networks? Basically screwed.)

Sure but there’s also the benefit of mining coins right? So depending on the cost of Bitcoin it may be worth Alice spending an extra £100 on mining power to beat Bob, if the payoff is great enough.

Saying this I do agree with you about proof-of-work, I work on a proof-of-stake chain myself.

Yeah, that property is what would create the sigmoid curve in the ideal case: PoW chains aren’t inflationary (rather the opposite) so competition reduces mining margins to effectively zero, which translates to fewer and fewer people bothering to grab at surplus profit as the number of miners grows and that surplus profit goes to zero.

It’s why you see consolidation into mining consortiums. An inflationary PoW chain wouldn’t have that — everyone would be incentivized to mine for themselves (like a gold rush.)

Probably a dumb question, but would that also theoretically increase the likelihood of someone to doing a 51% attack as there would be fewer unique users mining as electricity becomes more cost prohibitive?

There are some economic and game theoretic elements in play here. Say you wanted to reverse a trade and could afford a 51% attack, the cost of the chain would drop massively so you’d not benefit by having a load of Bitcoin. The whole community could just fork from that point and pretend it never happened. And people with skin in the game would fund mining to keep the security up to avoid this happening.

Overall though the number of miners will reduce to a small group because the cost is prohibitive, however it should still be secure.

Could this be addressed more cheaply by moving from proof of work to proof of stake?

Yes, although I believe technically proof of stake isn't as secure as proof of work (although it's secure enough) because you're essentially picking randomly from a weighted sample based on how much the sample owe of the underlying token.