I’m a sucker for simple handwaving arguments, since those are the only ones I can remember in full detail.  Please forgive my self-indulgence below, and don’t misinterpret my oversimplification as an underestimation of your intelligence!

IMNERHO, any discussion of relative hazards should begin with “normalization“:  the probability of a given person’s dying is (so far) exactly 1.0; put differently, the probability that all of us will still be alive 200 years from now is (so far) exactly 0.0 — barring exponential growth of life expectancy and/or “uploading” into hardware, we are all doomed.  The only things we have any realistic hope of influencing are (1) how soon, and (2) of what we will die.  Plus, of course, (3) what we will do in the time we have left.

That being established, we can look to epidemiology for the current status of (2): according to the Canadian Cancer Society, cancer will kill 26% of men and 22% of women in Canada; your mileage may vary.  Since cancer is what we worry about most from radiation exposure, I will neglect other modes of expiration.

Are all those cancer deaths due to radiation?  Since we cannot escape environmental radiation such as cosmic rays, that argument could be made.  How would we test that hypothesis?  Obviously, by comparing the incidence of cancer in populations with increased or decreased radiation exposure.  But this requires an additional hypothesis about how said incidence depends on exposure.  How do we choose that hypothesis?  We must let the data guide us.  We have such data, ranging from the exposed survivors of Hiroshima and Nagasaki to the denizens of Ramsar to patients receiving medical irradiation to airline pilots and so on.  This data suggests that there is in fact a threshold dose (let’s restrict it to whole-body all-at-once exposures, for convenience) below which there is no statistically significant increase in cancer.  There might even be a decrease, but let’s leave that for later.

To proceed further we need a much deeper understanding of mitosis, apoptosis and healing of DNA double-strand breaks.  Much of this is well understood (I gather) by various medical researchers, but is well beyond my feeble grasp.  So far no one has (to my knowledge) translated those understandings into what we need to make quantitative comparisons, namely a differential equation describing the time evolution of the probability of cancer developing under various radiation exposure schedules.  We therefore argue about various empirical toy models based on bulk statistics — an unsatisfactory situation, to be sure!

But there are still meaningful quantitative questions we can ask!  For instance, what if a radiation release from some reactor accident raises the probability of dying of cancer from 0.260 to 0.261 for a million men?  How many “extra” deaths does that mean?  Zero!  Every one of those men was already doomed to die!  “Oh come on, you know what I mean: how many extra premature deaths?”  [My reaction to that word is recorded at https://jick.ca/?p=383 ] — but most people would answer, “1000 men!”  That’s a lot!  Wait… when would they die?  If the answer is 10-30 years later on average, perhaps the meaningful calculation would be of how many years of life would be lost.  This obviously gets complicated, but note how our qualitative response depends on quantitative numbers!

A completely different question one could ask about the same scenario is, “Should any of those men be alarmed at the increase of their probability of dying of cancer from 0.260 to 0.261?”  Duh.  No!  And yet they all would be alarmed.  Because that’s how stupid human beings are.  And this is why the same person in Canada who enjoys skydiving as a hobby is terrified of tritiated water from Fukushima.