I recently underwent a minor bit of toe surgery and had to sign a scary-looking disclaimer form in which I acknowledged that there was a risk of infection, repeat surgery, chronic pain, amputation, spontaneous combustion, meteor strikes, and a plague of locusts o'er the land.

It was the most pointless damned form I've ever seen in a doctor's office. What are the statistical incidences of any of these risks? Should I be more or less worried about dying in a car crash on the way home? Taken literally, that kind of "information" is absolutely useless for making decisions. You can't translate something into an expected utility, even a qualitative and approximate one, if it doesn't come with a probability attached.

Taken literally, saying that there is a "possibility" of infection tells me nothing. The probability could be 1/1,000,000,000,000 and it would still be technically correct to describe the outcome as "possible". I'm not the litigious type, but I seriously wonder if it would be possible to sue based on the theory that "possibilities" with no probabilities attached to them are not useful information and therefore should not constitute a "disclaimer" under the law.

Staring at this pointless list of disasters, I also wondered why the form contained no useful information.

The thought that occurred to me was that, innumeracy being so widespread, no one would dare put numbers on that sheet of paper. If "amputation" is listed as a consequence with a probability of 0.0001%, patients will run screaming out of the office, crying, "Not my toe! I don't want to lose my toe!" No amount of patient explanation will suffice to convince them that they ought to diminish the emotional force of their fear by a factor of one million. Each extra zero after the decimal point would only be one more symbol for their eyes to glaze over; it would not diminish the emotional force of the anticipation by an additional factor of ten.

And so I don't get any useful statistical information! Hmph.

Clearly, innumeracy produces negative externalities and it ought to be regulated. In particular, we should impose a tax on people who can't properly diminish the emotional impact of their anticipations by tiny probability factors.

Two classic objections to regulation are that (a) it infringes on personal freedom and (b) the individual always knows more about their own situation than the regulator. However, my proposed policy addresses both of these issues: rather than administering a math test, we can ask each individual whether or not they're innumerate. If they do declare themselves to be innumerate, they can decide for themselves the amount of the tax to pay.

What do you think? Would this tax give people an incentive to become less innumerate, as standard economics would predict?