05 July 2018

When 2 + 2 = 5

Imagine you have to score student performance in a Grade 10 algebra test(1). Looking at one student's step-by-step calculations you discover that at one step she calculated that 2 + 2 = 5. Obviously, for a Grade 10 student this is a very basic arithmetic mistake.

Now, because this is a very basic mistake, would you dock more or fewer points for it than for an advanced mistake? Why? Why not? Would you dock more points if the algebra problem were framed in terms of serious consequences(2)? Would you dock "a good student" the same number of points as you would "a bad student"? Would you dock a female student the same number as a male student, a white student the same number as a black student?

How about a mediocre male student who protests every self-perceived act of injustice inflicted upon him? Would you deduct the same number of points from his test as from a mediocre meek female?

Making performance judgements on math problems is relatively easy(3). Consider judgements on more important things. All other things being equal: In an election, do you interpret dishonesty or stupidity in "your candidate" with the same gravity as you do for a rival candidate? In a job competition, do you judge experiences and accomplishments of a local candidate with the same rigour as those of an outside candidate. In court, do call for the same sentence for an offender born in Switzerland as you do for an offender born in Nigeria?

It is hard work to develop and stick by good rules of judgment. And it is easy to dress up prejudice in a mantle of objectivity(4).

My favourite example comes from an Israeli parole board where cases were randomly assigned to judges, and yet the proportion of decisions in favour of the prisoners declined in the course of the sessions and reached a minimum just before the scheduled breaks(5).

Image: Danzinger et al. (2011)

Of course, the first step towards improved judgement is a correct judgement of our judgement apparatus. Unfortunately, we aren't good at that either. Consequently, as a family member, as a good friend, as a professional, as a citizen, what are your obligations to alert someone to their faulty judgement?

NOTES AND REFERENCES

(1) For example: Solve the following equation for x: -2 (x + 2) + 2 (-x + 2) + 2 (2 + 2) = 0
(2) Say: "Determine the amount x (in millilitres) of midazolam that can be safely administered in preoperative sedation." "Calculate the number of battalions required to secure the border."
(3) Given these axioms and these rules and these particulars, these results must follow.
(4) "My decision sexist? Oh god, far from it. His publication record just wasn't as impressive." "My decision racist? It couldn't be further from the truth. She just wasn't a good team-fit." "My decision age-ist? Oh my god, never. His coding skills just weren't up to par."
(5) Danzinger et al. (2011), Extraneous factors in judicial decisions: www.pnas.org/cgi/doi/10.1073/pnas.1018033108 (Accessed: 5 Jul 2018)

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