Some people are (unfortunately) desperate enough for work that they won't refuse a job despite the lack of a dosimeter. Which is why you should legislate that power plants must give dosimeters to their employees -- to ensure that those who cannot refuse cannot be placed in that position in the first place.

And this is entirely common-sense -- if a company doesn't provide protections for its workers, "just don't work there" won't solve the problem of the company not protecting the workers it does have. The workers who can refuse to work will (probably) do so, the company will then hire more desperate people, and the steady-state of this system is that such companies will be full of people who were unable to refuse -- thus the company can just continue not protecting its employees. This is basically the fundamental argument behind all employment protections -- substitute "dosimeters" for "lunch breaks", "minimum wage", "paid leave", or "overtime pay" and the same argument applies.

But what is the equivalent of a dosimeter for this job?