The “either/or” fallacy of believing in discrete models: an example of folk statistics

This is quite an interesting take on issues around our lives. The following post was by 
Andrew Gelman, and the term BDA refers to highly readable book “Bayesian Data Analysis”

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The “either/or” fallacy of believing in discrete models: an example of folk statistics

Psychologists talk about “folk psychology”: ideas that make sense to us about how people think and behave, even if these ideas are not accurate descriptions of reality. And physicists talk about “folk physics” (for example, the idea that a thrown ball falls in a straight line and then suddenly drops, rather than following an approximate parabola).

There’s also “folk statistics.” Some of the ideas of folk statistics are so strong that even educated people–even well-known researchers–can make these mistakes.

One of the ideas of folk statistics that bothers me a lot is what might be called the “either/or fallacy”: the idea that if there are two possible stories, the truth has to be one or the other.

I have often encountered the either/or fallacy in Bayesian statistics, for example the vast literature on “model selection” or “variable selection” or “model averaging” in which it is assumed that one of some pre-specified discrete set of models is the truth, and that this true model can be determined from the data. Or, more generally, that the goal is to estimate the posterior probability of each of these models. As discussed in chapter 6 of BDA, in the application areas I’ve worked on, such discrete formulations don’t make sense to me. Rather than saying that model A or model B might be true, I’d rather say they can both be true. Which is not the same as assigning, say, .3 probability to model A and .7 probability to model B; rather, I’m talking about a continuous model expansion that would include A and B as special cases. That said, any model I fit will have its limitations, so I recognize that discrete model averaging might be useful in practice. But I don’t have to like it.

Since I’ve been primed to see it, I notice the either/or fallacy all over the place. For example, as I discuss here, cognitive scientist Steven Sloman writes:

A good politician will know who is motivated by greed and who is motivated by larger principles in order to discern how to solicit each one’s vote when it is needed.

I can well believe that people think in this way but I don’t buy it! Just about everyone is motivated by greed and by larger principles! This sort of discrete thinking doesn’t seem to me to be at all realistic about how people behave–although it might very well be a good model about how people characterize others!

Later in his book on causal reasoning, Sloman writes:

No matter how many times A and B occur together, mere co-occurrence cannot reveal whether A causes B, or B causes A, or something else causes both. [italics added]

Again, I am bothered by this sort of discrete thinking. I’m not trying to pick on Sloman here; I’m just demonstrating how the either/or fallacy is so entrenched in our…

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