They dont control anything. If they left the network would readjust difficulty after 10 minutes and continue on the same way.

Seriously educate yourself. You're being the guy in the op comment.

It's not about them leaving the network, it's a matter of whether they could be coerced by an authoritarian government to alter transactions.

They cannot alter transactions, only deny/duplicate them. Their node would be blacklisted by those working around censorship.

Guys cmon its really childish the boring same issues thrown around when theyve been answered and addressed a million times.

For a forum of "hackers" most are just hacks.

I don’t think that answers the question. Denying transactions is certainly an issue. If it is true that the majority of mining power is in China, only a minority is outside of it. What mechanism does Bitcoin have for a minority of nodes to deny the transactions of a majority of nodes?

Majority of verification nodes are not in China.

No single jurisdiction approaches anywhere close to majority, with #1)USA@21% †

†: https://bitnodes.io/

The "verification" nodes don't do anything to prevent censorship by miners.

The threshold isn't quite 50%+. If one of the 49% nodes mines a block with a would-be censored transaction, the censoring notes have to make an economic decision to try to mine a replacement block and then a second block on top of that to rewrite the chain. At 100% this is easy, but at just 51% it's a costly gamble that will frequently fail at a huge dollar cost.

A block costs $200k at current prices. At just over 50% of the network, you are gambling at least two blocks to force a rewrite.

Finally a comment that is informed thank you

>The "verification" nodes don't do anything to prevent censorship by miners.

Absolutely agreed; however, eventually some non-hostile miner will randomly generate an acceptable `nonce` [entire point of hashing/energy-usage] which DOES include the censored-by-some transaction.

An additional function of the node-verification network (which uses essentially no energy, relative to mining) it to maintain the entirety of `mempool`, which is where unaccepted transaction-attempts live until mined into a block [which is then "accepted/denied" by same node-pool].

tl;dr: as far a probabilities go, unless you own exactly 100% of mining pool, it is impossible to censor a tx from the node's mempool; all you can do with <100% is DELAY transactions.

They can’t alter them? Can’t they do whatever they want if they collude to execute a 51% attack?

no, txns are cryptographically impossible to alter. The 51% problem is simply a double spend problem.

I am US-based and run one of ~8,000 global bitcoin verification nodes (i.e. not a miner). No majority of these nodes are based in any specific country †.

You should probably better educate on bitcoin protocols/mining before you go spouting off unfamiliar stats.

†: #1)USA #2)Germany #4)France #5)Netherlands #21)China (via bitnodes.io)