Probability: “Common sense” vs. context-dependent views of “likely” and “not likely”

In an student’s write-up for a course in medical ethics I noticed the following interpretation of the word “not likely”

The provided cases stated that the

“neurologist believes that this patient has a good chance of recovery with little functional deficit; ….[she] might have right-sided paralysis but will likely regain cognitive function”.

A student’s summary noted:

“ she has a good prognosis but is not likely to regain function in her right side”.

Note the shift of probability assessment.    This kind of shift was quite common and, when made, always tend toward increased likelihood.  Thus I never saw a student suggest that “it is unlikely that she will have right-sided paralysis”.

Comment: Probability in decision making is complicated, and few Americans are educated to appreciate the complexities of probability statements or the nuances of rhetoric dealing with probabilities.  Such modifiers as “can”, “may”, and “might” are often used indiscriminately.  The public is notorious for handling proportions poorly, and common usage in law plays off the enormous ambiguity of probability statements.

For example, according to the  Texas Civil Commitment-Outpatient Sexually Violent Predator Treatment Program (OSVPTP) Health & Safety Code, Chapter 841, civil commitment requires a jury answer this question in the affirmative:

“Does the person suffer from a behavioral abnormality that makes him/her likely to engage in a predatory act of sexual violence?”

Now the typical citizen (based on a unscientific sampling) would answer that the word “likely” as in the phrase “it is likely to rain” or “I am likely to get hit by a car crossing that road” means, roughly, “more likely than not” or, in mathematical terms, “occurrence is expected in more than 50% of the opportunities.”   In this view,  affirmation of predator status might mean “Of one hundred convicts for which we find in the affirmative, we expect at least 51 to engage in a predatory at of sexual violence”.

In contrast, the common usage meaning of the term “not likely” seems to be NOT  “less than likely” but “rare”.  Thus, if I say that I think it “not likely” that I will be killed while crossing the road, I mean that I would be very much surprised indeed to hear I had been killed while crossing the road.

Available data indicate the rate of recidivism of the kind covered by Chapter 841 is  less, perhaps much less than 50%.  [The present analysis doesn’t take into account the meaning of the word “that” in the legal criterion]. Expert witnesses for the defense cite the common-usage meaning of “likely”, but prosecutors and juries use a meaning closer to “more likely than not likely”.  This observation suggests that citizens use a flexible definition of “likely”.

If a neurologist finds that a patient “might  experience paralysis” and “will likely regain cognitive function”, one  “might” interpret this to mean that paralysis is something less than “likely but more than “unlikely”; and that is “more likely than not” to regain cognitive functions.  However, it is clear that students reading this scenario are, like prosecutors and juries [based on this reporter’s personal experience, and the very high rate of commitment in the Texas court], likely to interpret this using a non-standard definition.

The non-standard definition might be seen as ad hoc but also might be seen as “context-dependent”:  if the risk is very high, the mathematical value of the  informal probability assessment of the term “likely” might decrease.  Thus, we might deny that one is likely to be struck by lightning ( in general; the lifetime chance of being hit is ~1/10,000)  but we might agree  that it one is “likely” to be hit by lightning when standing outside in a thunderstorm, even if the chances of being struck in a storm  are judged less than 50%.

I am unaware of any study testing the hypothesis that the average person adjusts their sense of “likely” according to perceived risk.

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