Imagine there are two countries, Eastland and Westland. Eastland has a much larger population than Westland. They are separate countries but with a common cultural heritage, common language, mostly common history, and so on. They are ethnically identical. They have otherwise identical government bodies, including otherwise identical bureaucracies and criminal justice systems. Imagine there is plenty of trade and cultural exchange between them. A foreigner from outside the two countries would be hard-pressed to know which one she was in, because they are so similar.
Now, everyone in Eastland prefers policy P, while everyone in Westland prefers not-P. Further, Eastland does not simply prefer P for themselves; they want Westland to adopt P as well.
Imagine Eastland decides to impose P upon Westland, after a unanimous referendum in Eastland. Every eligible citizen of Eastland votes, and they each vote that both Eastland and Westland should be bound by P. They recognize that had the Westlanders gotten a chance to vote, they would have unanimously voted no, but the Eastlanders don't care. They just want P for everyone.
So, Eastland declares P is now the law of both Eastland and Westland. Rather than invade Westland to impose its will, it imply places in special police officers or whatnot, who enforce P in Westland exactly the same as they enforce P in Eastland, and, indeed, exactly as Westland's own government would have enforced P had Westland issued P as law.
Here, most people think what Eastland has done is unjust. It wrongs the people of Westland by imposing P upon them and by enforcing it against their will.
Now, suppose instead, in an alternate world, that Eastland and Westland were suddenly joined into one giant country, Middleland. Suppose that right after they join, there is a referendum on P. Suppose all the people from the former Eastland vote in favor of P, while now all the people of the former Westland vote against P. So P passes and is imposed on everyone.
Hayek wonders (in a less formalized version of this thought experiment), why this would make any difference. If it's not okay for the Es to impose P on the Ws when they live in separate countries, why is it okay if they live in one country? What difference does that really make? In the thought experiment here, as I've laid it out, it's not clear why stipulating that they've joined into one country changes matters.
If we stipulated that the Es and Ws have moved around a lot, so that they are now spread out all over Middleland (rather than segregated by the former boundaries of their country), does that matter? Doesn't seem to.
Is the difference that in Middleland, the Westlanders could potentially overturn P in the next election by convincing enough Es to change their mind? That doesn't seem to do the trick either. After all, we can imagine that in the original case, when Eastland imposed its will on politically separate Westland, that Eastland also decided that in four years, they would have another referendum to consider overturning P. We can imagine that Eastlanders decide that they will consider Westlander's complaints and are open to changing their minds. But that doesn't seem to change the story.
Is it merely because Eastland didn't allow the Westlanders to vote in the original decision, in the version where they are separate countries? That doesn't seem to make a difference either. For one, everyone knows ahead of time that the Eastlanders would outweigh the Westland vote. There are far more Eastlanders than Westlanders. If you want, imagine that in the original version, when the countries are separate, that when Eastland announces the referendum on P, that it will allow all the foreign Westlanders to vote. As expected, the Eastlanders unanimously favor P and so the referendum passes over the unanimous disapproval of all Westlanders. Isn't this still just Eastland imposes P unjustly on the Westland people?
If you want, imagine the when Eastland and Westland are separate, that they are so mutually independent in terms of cooperation and their economy that if one were to collapse, the other would. (This will stave off arguments that what makes the difference is interdependence.)
So, why does being part of the same country make it okay for the majority to impose their will on the minority? (Note that I haven't said anything at all about what the content of P is.)