Whatever happened to that crisis where a single party got control of 51% of total network mining power giving them essentially 100% control over the blockchain? [1]
For an attack to be possible, the attacker needs to generate an alternate blockchain faster than the honest blockchain. This problem can be thought of as a binomial distribution where the "success" is the honest blockchain mining a block and extending its lead by a block and the "failure" is the attacking chain being extended by one, reducing the gap by 1 block.
p = probability of honest blockchain extension by 1 block q = 1 - p = probability the attacker extends by 1 block
If p <= q, the probability of the attacker catching up at some point in time is 1. This is what makes a 51% attack possible.
If p > q, the probability of the attacker catching up is (q/p)^z where z is the number of blocks behind at the beginning of the attack.
There is a reasonable possibility for small values of z (small number of blocks behind), that 40% control would allow for the creation of an alternate blockchain longer than the honest chain, but this is mitigated by the fact that transactions require confirmations, which extends the number of blocks and makes the likelihood of an attack very unlikely.
I don't agree with your conclusions though— at 40% a determined attacker reorgs 6 confirmations with a 50% success rate. Many users don't wait even six.
Consider, even with 20%— thats analogous to having five parties 'signing' blocks— a result which is less decentralized than a fair amount of traditional financial systems. (The comparison is better than it would be with other pools because ghash primarily physically controls their own infrastructure).
Even though this is all quite concerning, Bitcoin is very dynamic— the current state isn't something that will last, one way or another.
It's interesting to see that the market price is completely decoupled from such problems coming into public attention...
I'm holding on to my stash for now, but unless the network is hard-forked to solve this issue (and other major ones on the way), I don't see a real future for bitcoin anymore.
The price could still hit $20k, but the coin would be tightly controlled by then if mining remains centralized.
It's seems "decoupled" because investors know that there is a fairly high chance that the problems will be fixed when it becomes apparent that it's posing a serious threat. Ultimately what Bitcoin is is a social consensus, and that social consensus has rapidly changed before in the face of exploits and will probably do so again. Secondly, at a technical level solving the flawed incentives can be done in a backwards compatible soft-fork upgrade - a hard-fork where everyone upgrades at once is not required, which makes agreeing to and deploying such a change significantly easier.
Then how do you explain that apparent lack (or at least, very low rate) of such attacks? It seems to me that what we observe is evidence against your description of the incentives.
Imagine that 2 court orders (one to GHash, one to the next largest pool) are enough to reverse a transaction, or to "freeze funds" by not allowing TXs from a certain key.
If the incentive system encouraged independent mining, this would not be possible.
Yup. Hello, tragedy of the commons. Albeit in a slightly different form from normal.
[1] http://en.wikipedia.org/wiki/Bystander_effect [2] http://en.wikipedia.org/wiki/Diffusion_of_responsibility [3] http://en.wikipedia.org/wiki/Volunteer's_dilemma
It's the same reason why most bars don't take your drink order and money and then refuse to give you the drink. Obviously, in isolation it would be more profitable to take the money then refuse to give the drink. It's illegal, but you're unlikely to sue because of the cost of litigation. The reason the bar gives you the drink isn't that they want to sacrifice their profits just to make you happy, and it's not that they fear litigation. The reason is that it's more profitable in the big picture for them to give you the drink, because people don't tend to visit bars if they hear that the bartenders take money and don't give drinks in return.
The 51% attack problem is something that needs to be solved for bitcoin. But it isn't as bad as you think it is.
I used to think that someone who took over the network could spend my bitcoins even without my private keys. But that is not true. The actual attacks possible with 51% are significantly more minor than stealing bitcoins.
Thats pretty huge.