Suppose that in community Libertopia, in response to customer preferences, all of the better restaurants ban smoking. In nearby community Paternafascista, there is a law that bans smoking in restaurants.
...In both Libertopia and Paterfascista, smokers are not able to smoke in the better restaurants. If someone insists on trying to smoke, he may end up forcibly removed by the police.
...Government policies take away more liberty than equivalent private policies. The reason is not that government policies are backed by physical force. The reason is that government has broader jurisdiction. With private policies, when I am adversely affected by a policy, I can choose an alternative service provider at relatively low cost. With government, because its jurisdiction is so extensive, the cost to me of escaping adverse policies is much higher. It is not the armed force that makes government feel more like tyranny. It is the absence of competition.