Wheel turning king runs the country without stick or sword, what does it mean? In Nikaya, it is said that wheel turning king runs the country without using stick or sword, since that term is quite abstract, what does it mean?

Some of my interpretations:

1/ Without waging war, since stick and sword are the symbol of weapon. But then what is the role of military, or how can he protect his people when needed?

2/ Runs the country without punishment. I don't see this as an realistic option, as even the sangha has offenses for monks, and managing the world without punishment is impossible.

3/ Without violent punishment. For example, jail is not violent but torture, beating or cutting hand of robber are violence. I see this as the most realistic interpretation, but I am not sure.

So what does it mean? Reference in Nikaya is appreciated.
I believe "wheel" refers to tradition (in the broadest sense) and "turning" refers to establishing and/or continuing the tradition.

The wheel turning king (or, in modern terms, leader) rules by setting up a way of doing things that (most of) people find compelling enough to follow, without being forced to -- this is what I feel is referred to as "without stick or sword".