Is It Better to Be Vaguely Right or Precisely Wrong?

John Tukey is a famous statistician who said, “Far better an approximate answer to the right question, which is often vague, than the exact answer to the wrong question, which can always be made precise.”

This reminder is useful practically since people so often choose a wrong but easy to solve problem over a better problem that’s hard to solve.

However, the quote misses a key point I quickly discovered when I started trying to write provable / logical statements about problem solving.

Vague problems are not usually hard because you can’t get to an answer. They’re hard because there are many possible answers and it’s easy to be paralyzed by the options in front of you.

This might seem counterintuitive. Just look at the quote above! But I invite you to examine a vague question you faced recently and test my claim.

https://www.meta-problem.com/presentations/sharing-cookies-for-kids is a video I just posted aimed at elementary school kids on this very topic. I’ve now asked 4 classes full of kids how to share 6 cookies between 2 kids.

Only one of the groups had a student who realized there could be many possible options… if you don’t have to be fair.

When you are faced with a decision to make, or a question to answer, the unknown or unknowable are major drivers of indecision. It’s always worthwhile to invest more time and thought at the beginning of the process, clarifying what you really want to achieve and identifying the best set of problems to solve.

Tukey’s quote got something key right though: getting any sort of answer to that vague question is progress.

Let me know your thoughts in the comments!

Inspired by a recent xkcd comic https://xkcd.com/3104/ , and Tukey’s approximate 110^th birthday.