Well, the linear assumption is only applied in the limit of low doses. The problem is that for many large-population radiation exposures, the total release is d

Well, the linear assumption is only applied in the limit of low doses. The problem is that for many large-population radiation exposures, the total release is dominated by very small dosages to very large numbers of people, and we're not able to extract the dosage-response curve from data for arbitrarily small dosages. (If I get one extra gamma ray, does my risk of cancer rise by 10^-10? Hard to check...) There are alternative theories that small amounts of radiation are neutral or even positive since they are within the natural radiation background and the body has various mutation repair machinery. https://en.wikipedia.org/wiki/Radiation_hormesis https://en.wikipedia.org/wiki/Radiation_hormesis However, these theories tend to be emphasized by nuclear-power proponents, and of course the data doesn't say. In any case, I believe the linear no-threshold model is consistent with the data and is generally considered conservative (i.e., an upper limit on the number of ill-effects).