The blogpost does explain this if you bother to read it.
>And how do you determine how many meatspace people are voting for something? This problem was confronted by Satoshi and his answer was proof of work.
This is quite simple, people can agree on a representative in a democracy, hence it must be possible people will be able to agree on a blockchain to use.
As state previously in the thread, long range forks are not a concern as any state S with atleast N ancestor states will not allow any state S' to become valid if it is not a descendant of S. Therefore it can be concluded that after N blocks, a fork becomes impossible.
The remaining problem is therefore short-range forks caused by someone burning a lot of stake. Forking will inherently burn all your stake in the other chain while you burn everyone elses stake in yours. Any such fork attack then must last for more than N blocks to become permanent.
The blogpost dives a bit deeper into the fork prevention mechanisms but the TL;DR is that nodes will prefer keeping a chain over switching to a new chain significantly, going up exponentially as the new fork becomes older. In essence, a fork must take over the network almost immediately or the new fork will wither and eventually die out in favor of the original chain. (The speed of a fork is roughly a function of the time delay between the first and last node receiving a block in percent with respect to X, the amount of permanent control an attacker has)
The later part of the blogpost also explains that the weak subjectivity only poses a problem for nodes that have been offline for more than N blocks and in case an attacker can control large portions of the network for extend amount of time. It does not matter if a node sees 100000 other nodes with another chain until N blocks have passed or in the other prevention mechanism, the gravity of the new chain becomes greater than that of the current chain, which can take a while.
As suggested in the end of the blogpost, if a node stays offline for extended amounts of time, there is no safe way of knowing the state of the network, thusly the best option is to obtain a recent blockhash from a friend, a block explorer or their software provider. Human social interactions would be the prefered option, the trust on the network being in the right stake would thusly be equivalent to the trust you place in said friend. Or your software provider or blockchain explorer.
It can be argued that any entity which is sufficiently powerful to cause disruption over the chain consensus for longer than a year (the proposed value of N) then they will also be able to overpower any other proof of work algorithm or pursue alternative methods to disrupt the network.