Minority shareholders are minority in effect, you don't get to decide if you're to sell.

By means of Voluntary Delisting or Buyouts, shareholders planning to take the company private will first have to obtain enough votes or voting rights to make the decision to go private.

That usually happens by announcing to acquire a certain fixed percentage of shares at or above market rates, and only that fixed percentage will be bought at that rate.

After obtaining enough voting rights, the major shareholder then could announce privatisation by shares buy-back at specific rates usually far below the previous buy-out rate.

So most shareholders being afraid to loss values to their shares would sell it out at the first proposal, by then privatisation is almost a done deal already.

Of course in actual world, there would be much more complications, shareholders bounded by terms, percentage of acquisition, forced acquisition, but the basic flow are somewhat similar.