user120461: Google says

As of now, there are roughly 12,130 public nodes running on the Bitcoin network.

So in a nearby small city, there are 70,000 people. If 1 household is assumed to have 3 people on average, there are 23,333 households.
Does that mean if each household runs a Bitcoin node using a US$5000 PC and provides some "fake data", now these 23,333 nodes become the majority and can alter the Bitcoin blockchain any way it wants to?
P.S. Maybe "fake data" is too vague.  How about: it is not all fake data, but just 1 fake entry that says, "transfer 10 BTC from address 1 to address 2?"

user48884: The blockchain is not determined by a majority vote and does not necessarily change if a significant portion of nodes claim an alternative chain is the main chain. Rather the main chain is determined by each node independently, and all nodes arrive at the same conclusion independently because they all are following the same set of rules.
So even if an attacker were able to have more nodes than honest nodes, and those nodes were broadcasting an alternate chain, all of the blocks in that chain would still have to pass validation by the honest nodes before those honest nodes will accept those blocks. This means that all transactions must be valid, the proof of work for every block must be valid, etc. That alternative chain must be valid for it to be accepted by other nodes, regardless of how many malicious nodes claim that it is the main chain.
If the alternative chain contained "fake data" that is invalid, then the entire chain would be rejected as invalid and no honest node would accept it. If the alternative chain is fully valid, and if it has more cumulative work than what honest nodes currently consider to be the main chain, then the honest nodes would switch to that alternative chain.

120461: <p>Google says</p>
<blockquote>
<p>As of now, there are roughly 12,130 public nodes running on the Bitcoin network.</p>
</blockquote>
<p>So in a nearby small city, there are 70,000 people. If 1 household is assumed to have 3 people on average, there are 23,333 households.</p>
<p>Does that mean if each household runs a Bitcoin node using a US$5000 PC and provides some &quot;fake data&quot;, now these 23,333 nodes become the majority and can alter the Bitcoin blockchain any way it wants to?</p>
<p>P.S. Maybe &quot;fake data&quot; is too vague.  How about: it is not all fake data, but just 1 fake entry that says, &quot;transfer 10 BTC from address 1 to address 2?&quot;</p>
 48884: <p>The blockchain is not determined by a majority vote and does not necessarily change if a significant portion of nodes claim an alternative chain is the main chain. Rather the main chain is determined by each node independently, and all nodes arrive at the same conclusion independently because they all are following the same set of rules.</p>
<p>So even if an attacker were able to have more nodes than honest nodes, and those nodes were broadcasting an alternate chain, all of the blocks in that chain would still have to pass validation by the honest nodes before those honest nodes will accept those blocks. This means that all transactions must be valid, the proof of work for every block must be valid, etc. That alternative chain must be valid for it to be accepted by other nodes, regardless of how many malicious nodes claim that it is the main chain.</p>
<p>If the alternative chain contained &quot;fake data&quot; that is invalid, then the entire chain would be rejected as invalid and no honest node would accept it. If the alternative chain is fully valid, and if it has more cumulative work than what honest nodes currently consider to be the main chain, then the honest nodes would switch to that alternative chain.</p>
