Right. Obviously if they put the sign on nothing, no information would be communicated. And the same if they put it on "50% of things" (defined however you like

Right. Obviously if they put the sign on nothing, no information would be communicated. And the same if they put it on "50% of things" (defined however you like) because everyone knows the median thing isn't a real cancer risk. Maybe it could communicate the breaking of some threshold, but not a meaningful one. To be truly informative, binary cancer warnings should be rare -- they should appear near a threshold where reasonable people are likely to be swayed by them (but not certain to be swayed by them -- at that point we're probably labeling too few things.) But enough about binary labels, though. They should have to put figures on them: "Scientists believe that the cancer risk of this cup of coffee is statistically expected to decrease your lifespan by 5 minutes, plus or minus a day, with 95% confidence."