We Are All (Lousy) Witnesses

So . . . it's coming up on exam time for my students, and I just did our course review and exam prep in class earlier this week.  The exam is for my business case course, which has the students read a business case (a story about a business and the problem they are facing).  They then must use the available information to come to a defensible decision about what the company in the case should do.  One of the skills involved is to be able to sort out useful information from useless (or in some cases, incorrect) information.  Which brings me to what I'm talking about today - how we can use information provided to us.  Examples and clarification after the jump.

Imagine you're talking to a friend who volunteers at a local school.  She's talking about the kids and mentions that she's noticed a pattern with regard to which kids seem to get into trouble the most.  According to your friend, this can be based on the relative number of times she hears the teacher calling out a child's name in a stern tone.  The pattern that she has uncovered is that the students who are Lablish (a made-up ethnicity so that we don't get into specific stereotypes) are the most trouble.  It's always Lablish names that are being called out sternly.

What can you ascertain from your friend's story?

Most of you would probably have come to one of two conclusions: either Lablish kids are poorly behaved, or the teacher is prejudiced against the Lablish.  And one of those might be true.  But to limit the analysis to that would ignore a viable third alternative, which is that your friend only notices or remembers when the teacher calls out a Lablish name (this could be due to your friend's prejudice, or the fact that your friend is Lablish herself, or just because Lablish names tend to be unusual). 

Another example (from Fooled By Randomness by Nassim Nicholas Taleb): two people are playing a game.  They flip a fair coin and if it's heads, person A wins a dollar, and if it's tails, person B wins a dollar.  The game begins and it's heads ninety-nine times straight.  What are the odds that it will be heads on the next flip?

Most people will either say 50/50 (which is the mathematically correct answer) or surely tails (playing into what is called the gambler's fallacy, when someone believes that an outcome is "due").  The correct answer, however, is that it is almost certainly going to be heads again.  Why?  Because it is far more likely that the assumption that the coin is fair is a faulty one than that heads would come up by chance 99 times in  a row (flipping the coin every 10 seconds, it would take 200,000,000,000 billion millenia before it was likely to happen).

In both cases, the source information is faulty.  And we know this type of thing happens, because we have axioms (axia?) like "take it with a grain of salt" and "don't believe everything you read."  Yet we often take information at face value, and believe it.  The whole reason that the movie The Usual Suspects works (spoiler alert in case 15 years wasn't long enough for you to get around to seeing the movie) is because we believe the narrator, who we know is a character in the story with a motive for presenting himself well.  We shouldn't believe him, but we do. 

There is endless proof that eyewitness testimony is faulty, but they are still strong evidence in court.  And not just in court - we tend to rely on eyewitness accounts  as incontrovertible, whether the witness is someone else or ourselves (and we would never lie to ourself, now would we?).  So doubt the source.  Question the account.  There doesn't have to be an apparent motive (e.g. our friend in the first story doesn't have to be openly racist) for it to be untrue; it may just be regular biases at play.

And if any of my students are reading this, know when to question the data in a case.