How do you call a system of government when power is literally forced on unwilling people ? (And who would decide which Cincinnatus to call for setting up this year's budget ?)

Even when people mention "randomly picking up people" ("stochiocracy") I assumed you could refuse :D

Jury duty is a bit of an example of that working in practice. Generally speaking (at least in my jurisdiction) in theory you can't refuse jury duty just because you don't want to do it. However, in practice the system does allow a large array of excuses (as concessions to practicality I suppose) that you may take, and generally the burden of proof for those excuses is pretty light.

For instance you could be excused based on your employer sending a letter that it would be inconvenient to their business if they lost you, etc.

So in practice, you can probably wiggle out of it if you simply don't want to do it, by finding a suitable excuse.

Another system where random service is still commonly used is military draft. That seems significantly more hardened against dodging (since the cost on the individual of going with it is drastically higher).

So generally, it seems that where current societies do use random sampling to select people for service, there is always an element of compulsion, but how "hard" it really is varies.

We have a system that does that. That’s how we do jury duty. We use sortition to decide important things every day

That's not how it was usually run, but say in Ancient Athen's the council that decided was whoever was at the council at that time.