Suppose you discover that a medical procedure genuinely reduces your risk of dying this year.  When you look further, however, you learn that your risk of dying only falls from 10-in-1000 to 9-in-1000.  Here are three reactions in order of sophistication.

1. Sheer innumeracy.  Many non-economists will say, “Eh, that’s virtually the same.  Why bother?”

2. Elementary cost-benefit analysis.  Many economically literate people will rebuke to the innumerate with, “Dying is really bad.  Like, $10 million bad.  Multiply that $10M by 1-in-1000 – the change in the probability of dying – and you’ve got an expected benefit of $10,000.  As long as the treatment costs less than $10,000, do it!”

3. Sophisticated cost-benefit analysis.  Thoughtful analysts will realize this isn’t just about quantity of life versus dollar cost.  Quality of life is also key.  Most medical treatments are unpleasant; many are downright ghastly.  Obvious issues include: How much pain does the treatment impose?  How much time does it take?  Will it prevent me from doing my favorite activities?  Limit my diet?  Once you monetize quality of life effects, they can readily swamp modest quantity of life effects.  Example: What would someone have to pay you to endure one day of extreme pain?  $1000?  Then even with free medical care,  the preceding treatment is a bad deal if it imposes 11 days of extreme pain.  And if the side effect lasts for the rest of your life, even a modest daily cost justifies inaction.

Observation: In most medical debates, elementary cost-benefit analysis contends against innumeracy.  Innumeracy ends up looking very stupid.  But this doesn’t make the innumerate conclusion stupid.  Paying a large amount of money for a little extra quantity of life makes sense as long as quality of life stays the same.  Paying a large amount of money for a small increase in quantity of life paired with even a small decrease in quality of life is pretty foolish.  A little cost-benefit analysis is a dangerous thing.