The Mystery of the Fourth Cell
We are a story telling people. Stories encapsulate a large amount of information and pass it on efficiently, more efficiently than mere logical or rational justification can. Our ancestors sitting around on the savanna plain did not have the luxury to engage in deep machinations of logic and so devised stories, parables or allegories as the method for passing on social wisdom. Rational decision making is incomplete because it ignores the power of stories, myths or parables as method of delivering important information.
In fact, one recent author, Christopher Booker, the Seven Basic Plots, claims that there are really only seven basic wisdom stories.
As neatly summarized over at onlyagame,
"Booker believes we tell stories as a mechanism of passing a model for life from generation to generation; that in essence, all stories are archetypal family dramas, and that their core message is that we must resist selfish evil (Booker doesn't use this term, preferring 'ego-centred', according to his Jungian framework). I find this a lovely belief system, although it will likely be quite unpalatable to those who idolise testability." (my emphasis)
Are the above paragraphs ture, just a story, false but important, or something else? I don't know. Did story telling develop in tandem with the ability to count in different ways? Did story telling evolve from stock stories to variants in which it wasn't possible to tell what the plot was before the final paragraphs ended? Is rational decision making just a hard skill to learn in the same way being a concert pianist is hard? Again, I don't know. I don't know because I have no idea what evidence would count against the hypothesis being true, stories being more efficient than rational decision making.
But I do know that there is a tremendous amount of poor reasoning about correlations because we don't employ on a regular basis a simple analysis, what academics would refer to as a two by two covariation table.
When we ask whether A's are related to B's there are two distinct questions that we could be asking. First, in a world full of A's, what is the ratio of B's to non B's? Second, in a world full of B's what is the ratio of A's to non A's? These are distinct questions.
Let's take a concrete example. Let A = statements I believe, and B = statements that are true. Consider only 20 statements. We can diagram the relation as follows:
| True Statements | False Statements | ||
| I believe the statement. | A | B | A+B |
| I don't believe the statement. | C | D | C+D |
| A+ C | B+D | 20 |
Now, how do we tell if I am an oracle? The usual focus is on the first cell, how many of my beliefs are true. Surely if A is high, then I am an oracle. My beliefs are true. But that is not true. Suppose that C = 3, D = 5, while A = 7 and B = 5. Then in the world only of true statements, I believe A/A+C or 7/10 and incorrectly disbelieve 3/10. Similarly, in a world only of my beliefs, A/A+B or 7/12 of my beliefs are true, while 5/12 are false. So in this case, I am pretty good at detecting a true statement, but almost half of my beliefs are false. That is if something is true, there is a 70% chance I will believe it, but if I believe something, it only has about a 60% chance of being true.
We don't have to limit the table to belief versus truth. There are a number of other interesting dichotomies, attractiveness of belief versus truth, social consistency versus truth. Basically, we want to use these tables when we are dealing with the interaction between the way the world is reported and the way the world is.
Now what makes using these tables hard is that we don't focus on all four cells, and usually completely ignore D, something explored in great detail by Thomas Gilovich in "How We Know What Isn't So." In discussing why bad interpersonal strategies persist, Gilovich considers someone who thinks that is necessary to push at all costs. We have a table like the following, using the dichotomy be pushy versus personal gain.
| Individual Gain | Individual Loss | ||
| Be Pushy | A | B | A+B |
| Don't Be Pushy | C | D | C+D |
| A+C | B+D |
It isn't that I hate stories; I read them to my three year children. As a result of reading the cat book, my young son now says he has three cats, black, pink and purple that he has to feed. But let's leave the stories to children and move on to evidence based business making decisions.
