Tuesday, March 1, 2011

Use Words To Convey Probabilities

William Strunk, author of what is surely the most highly cited text on writing, The Elements of Style, favors the use of words as vehicles for bold statements. From the foreword,
[H]is original Rule 11 was "Make definite assertions." That was Will all over. He scorned the vague, the tame, the colorless, the irresolute. He felt it was worse to be irresolute than to be wrong.
But what if you are not certain of a belief, something that should happen to reasonable people nearly all of the time? Apparently Strunk suggests you should hide this, as it makes you look "colorless" and low status. 

On the contrary, we should use employ the wide range of our language to calibrate our words to the probability that we assign to events. However, we want to use words that unambiguously assign probabilities. Ideally, we'd have a clear mapping between our words and the probabilities we assign to the events those words describe. There have been at least two attempts to do this, as described by wikipedia. Combining what I see as the benefits of both of these scales, going forward I'll try to use the following system:
  • "Surely" = > 99% probability
  • "Likely" = ~ 90 - 99%  probability
  • "Probable" = ~ 60 - 90% probability
  • "Chances about even" = ~ 40 - 60% probability
  • "Improbable" = ~ 10 - 40% probability
  • "Unlikely" = ~ 1 - 10% probability
  • "Surely not" = < 1% probability
One key arbitrary choice here is putting "likely" above "probable" in the hierarchy, which feels right but  doesn't have much precedence. Any suggestions?