[teod]

For those out of the loop, miners work together in pools to combine their mining power. With more mining power, the more likely it is for them to mine a block (of the blockchain) and divide its payout among members of the pool. Pools cause centralization of mining power. You can see a list of pools and the percentage of their mining power at [https://blockchain.info/pools].

Looking at the chart, you can see that the top 5 mining pools can collude in being a single entity to "control" the blockchain (I believe this is called a Sybil attack [https://en.wikipedia.org/wiki/Sybil_attack]). Now keeping incentives in mind, the idea is that people using bitcoin have faith in the system. That gives bitcoins value. Miners get paid in bitcoin. If they were to manipulate the blockchain, that would most likely cause bitcoin's userbase to lose faith in the system and thus what the miners would be stealing would suddenly have little to no value.

I'm not positive, but I recall hearing that pools have been intentionally been made smaller to keep users' faith in the system. Perhaps the goal of these majority mining power is not to steal bitcoin but censor certain users? That may be a bit more complicated depending on the users' opinions on a case-by-case basis. Fun stuff :)

[wyldfire]

A Sybil attack is unrelated to consensus, but otherwise what you said is accurate.

A Sybil attack can occur when a system designer mistakes a system identity to be exclusive with other ones. e.g. you could create a website that used a phone number as a user identifier and give every new user a $5 signup bonus. But if someone found a way to create valid phone numbers for less than $5 each, they could exploit your new user bonus system.

If it's free/cheap/easy to create new identities, you must be careful how much weight to give those identities. e.g. reddit has some problems related to how easy it is to manipulate voting. They have probably made changes to their algorithm over the years to deweight new/unverified users and likely other clever things to detect voting rings.

[teod]

Ah ok, I think that a 51% attack is what I was describing. I would update my comment, but it appears that I can no longer edit it.