## The riddle of induction and why economists assume linearity in their models

30 September, 2013 at 21:23 | Posted in Theory of Science & Methodology | 1 Comment

Recall [Russell's famous] turkey problem. You look at the past and derive some rule about the future. Well, the problems in projecting from the past can be even worse than what we have already learned, because the same past data can confirm a theory and also its exact opposite …

For the technical version of this idea, consider a series of dots on a page representing a number through time … Let’s say your high school teacher asks you to extend the series of dots. With a linear model, that is, using a ruler, you can run only a single straight line from the past to the future. The linear model is unique. There is one and only one straight line that can project a series of points …

This is what philosopher Nelson Goodman called the riddle of induction: we project a straight line only because we have a linear model in our head — the fact that a number has risen for 1 000 days straight should make you more confident that it will rise in the future. But if you have a nonlinear model in your head, it might confirm that the number should decline on day 1 001 …

The severity of Goodman’s riddle of induction is as follows: if there is no longer even a single unique way to ‘generalize’ from what you see, to make an infernce about he unknown, then how should you operate? The answer, clearly, will be that you should employ ‘common sense.

Nassim Taleb

## 1 Comment »

1. My experience is that people are pretty good at ‘joining the dots’ and persuading themselves that the resulting picture is unique in some sense. Further, people in groups often fall prey to group-think, so that there really is a uniquely accepted picture, which is regarded as uniquely rational.

If by ‘common sense’ one means accepting group-think, then that is a problem. An alternative is to recognize all reasonable pictures. Sometimes we can operate so as to avoid a crisis, whichever picture holds. At other times we need to make a choice. In science it is conventional to use Occam’s razor: keeping it simple. Group-think tends to agree. But is this wise?

Taleb’s discussion seems to be of context-free induction which, as he says, is ill-advised. More often, we have some over-arching theory (such as Newtonian mechanics) that assists us in drawing the picture. In such a context, induction can be quite reasonable.

A classic example is two people who are trying to predict the time of sun-rise tomorrow. Suppose that neither has evidence that there has ever been a full eclipse of the sun. The first extrapolates from the times of previous sun-rises. The second has observed some partial eclipses and works out that sun-rise will be delayed by a full eclipse. The first prediction is very simple, the second very complicated, introducing seemingly extraneous factors. It is obviously ‘better’, but I have not seen anyone articulate a general principal that would favour it.

I speculate on two possible tests:
1. A theory that can explain more ‘dots’ is to be preferred as ‘the big picture’, from which may select those elements that are relevant to the question at hand. Thus we apply Occam’s razor to the presentation of the result, but not to the derivation of it.
2. We should question a picture if there is an equally well-founded but contradictory picture.

Either way, we are left with two problems:
1. Keeping our eyes open to enough dots, and minds open to enough pictures.
2. Being able to collaborate effectively to share dots, picture elements and pictures.

We need to better if we are to avoid more fiascos like Iraqi WMD or the financial crisis.

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