Black Swans, the “Ludic Fallacy”, and Bayesian inference

June 28, 2011

A few days ago, I finished reading The Black Swan by Nicholas Taleb, which goes in-depth on topics such as judgment under uncertainty and the issues relating to unrealistic models which deliberately ignore unlikely but possibly highly influential phenomena in order to stay simple. Taleb emphatically argues against the use of the Gaussian bell curve, or the GIF (“great intellectual fraud”), as he likes to call it, pointing out that it forecasts events several standard deviations from the norm as extremely unlikely. He points out that an event 4 SD away is twice as likely as 4.15 SD, and that “the precipitous decline in odds of encountering something is what allows you to ignore outliers. Only one curve can deliver this decline, and it is the bell curve (and its nonscalable siblings). Nassim instead expounds scalable “Mandelbrotian” curves, which, like all things Mandelbrotian, are fractal – The speed of the decrease of odds as one moves from the mean is constant, not declining. So the odds of having a net worth of over 8 million pounds is 1 in 4,000, for higher than 16 million pounds it’s one in 16,000, for 32 it’s 1 in 64,000, etc. So not only does the Mandelbrotian curve put more importance on outliers (“Black Swans”, or unpredictable but highly influential events such as stock market crashes that Gaussian models miss), but any small portion of the graph resembles the larger curve in a fractal sort of way.

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The Allais Paradox and Misunderstanding Probability and Randomness

June 4, 2011

The Allais Paradox:

Suppose you are given two gambles to choose from, 1A and 1B:

1A: 1 million with 100% certainty
1B: 89% chance of 1 million, 1% chance of nothing, and 10% chance of 5 million

Later, you are given two more gambles to choose from, this time 2A and 2B:

2A: 1 million with 11% probability, nothing with 89% probability
2B: 5 million with 10% probability, nothing with 90% probability.

Which combination do you choose? The “paradox” is not logical but rather just highlights a quirk in human reasoning. Most people, for some reason, choose the combination 1A-2B. I can see why. I really have to fight the inner urge not to, but this is completely inconsistent.

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On the title of this blog

May 24, 2011

Some of you might be wondering, what does he mean by “Boundless Rationality?” Does he think that this blog is a Fountain of Truth and Objectivity? Well, let me explain.

Once upon a time, economists made their models based on the assumptions that humans made rational choices with perfect information and attempted to always maximize utility. In other words, they would have their utility function laid out to them with the sum of the products of the expected utilities and their respective probabilities. But alas, it was not so.

It turns out, most humans don’t really think that way. Some of the reasons:

1) Incomplete information and incorrect methods of reasoning lead to highly inaccurate inferences.

2) People have an inconsistent set of beliefs about the world around them.

3) People are emotionally attached to certain choices.

4) People are more likely to remain close to previously proposed solutions than to propose completely new ones.

etc, etc. So somewhere along the way, Herbert Simon proposed a new kind of model, bounded rationality, which took into account all of those aforementioned problems. Therefore, rather than looking for optimized rational models, bounded rationality theory searches for more realistic models on how humans make choices. But you’ll see more on that later.

So essentially, the title is a kind of a joke, or play on words. Boundless Rationality is an irrational thing to hope for. It doesn’t exist, because we can never actually have perfect information about the world around us, and even if we did, it would be far too costly to compute and make sense of it all.

Nevertheless, there are mathematicians and researchers who manipulate inductive probabilities (ie. weather forecasting, “There’s a 70 percent chance of rain tomorrow”) according to mathematical laws. The fact that I’m stating that might seem a bit surprising because it seems obvious. But it’s not. People continue to treat inductive probabilities in a sort of wishy-washy way which ends up in sub-optimal decision-making.

But it doesn’t have to be that way. There are and have been a number of researchers – Harsanyi, Jaynes, Tversky, Kahneman… – who have specialized in studying the ways that we treat incomplete information and try to come up with coherent and consistent ways to makes sense out of it. And they’ll be discussed a lot here

So that’s basically the idea of boundless rationality. It’s a practically and theoretically impossible ideal but it’s the right direction to look towards.

NB. But don’t worry, that’s not ALL this blog’s about!

Further Reading:

Bounded Rationality – Bryan D. Jones, U Washington

A Perspective on Judgment and Choice – Daniel Kahneman, Princeton University