probability by stories, a four point scale

when the narrative fallacy isn't a fallacy

I probably ought to do an occasional series of “ideas for novels that will never be written”.  Among the works from which my finance career has saved the reading public is a science fiction murder mystery, set in a world in which time travel is in wide use.

In such a world, obviously, there is no fixed set of historical facts, so conventional techniques of deduction don’t work.  Consequently, society has had to gradually abandon the whole concept of causation and explanation.  The detectives investigating the case are actually literary critics – their job is to find the person whose guilt makes the most satisfying narrative.

I think we can all be glad that book didn’t happen; some of us might say that the paragraph above was a bit too long.  But the reason it’s stuck in my mind (unlike so many more sci-fi pitches, I used to go through a period of regularly daydreaming them) is that I actually quite like the idea of “narrative probability”, and would defend its use in a lot of applications.

These would be cases where you’re trying to express subjective probabilities.  Trying to get people to do this with a percentage number is always a disaster; if you have more than two or three options, you’ll almost always get a set of probabilities that doesn’t add up to 1.  People don’t think about probabilities in this way, and forcing them to give a number is just putting pressure on them to make something up.  That’s how you get phenomena like the “bluffer’s 40%”, a number which basically means “I think this will happen, but I am not confident and so want to give myself an easy out if I’m wrong”.

One way to address this problem might be by respecting the actual degree of granularity in people’s perception of probability, and reformulating the question.  “What is the subjective probability?” in a lot of important contexts means “to what extent is this consistent with your information set?” or roughly “how much sense would this outcome make to you?”.

If you ask the question “how much sense does this make?”, I’d argue that there’s roughly a four point scale:

• “This version of events makes no sense”

• “This version of events makes sense”

• “This version of events makes more sense than any of the others”

• “No other version of events makes sense”.

This scale is implicitly the one used by the legal system.  The last two points on it correspond to “on the balance of probabilities” and “beyond reasonable doubt”, the civil and criminal standards of proof and the first two are the logical building blocks of the second two.  Some legal reformers (mainly because they’ve recently seen a bad decision that’s happened because of the base rate fallacy) want courts to extract numerical subjective probabilities and have a seminar on Bayes’ Rule, but I think their actual scale is more likely to be useful.