I often say to my kids that almost everything in life is some sort of scam or fallacy. OK, it's an exaggeration, but not that much of one.
Here's something you probably would never have thought of as a major fallacy, but it is. How many headlines have you seen about increasing risks of cancer, with the general implication being that more cancers must be caused by a deteriorating environment? Or is it just a fallacy?
An excellent blog called Numberwatch, by British mathematician John Brignell, has a short write-up in November 2012 on the "independence fallacy." This fallacy is particularly relevant when discussing the causes of death:
[T]he probabilities of cause of death are not independent. Because we all die of something, they are constrained to add up to 100%.
In other words, our very success in curing other causes of death leads of necessity to our living longer and eventually ending up with cancer.
This is not a trivial point. Much of the bureaucratic interference in our lives has been justified by the putative increase in cancer rates. The main reason that they are increasing is that we are not dying of the other diseases that have inflicted man throughout his existence.
Keep this in mind next time you see some study using an increase in cancer rates as the justification for increasing government involvement in some aspect of your life.