The Drunkards walk: Chapter 2

Tl;DR

I love how much this book refers back to Thinking Fast and Slow. One of the first examples of how complicated it is for people to think about probability is the somewhat famous Linda problem aka the Conjunction Fallacy. Essentially: If you give a person two options, one of which has additional detail, more people will chose the option with the details rather than the one without. Logically this is impossible since something with more detail is at most as likely as the option with fewer.

Example:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.

Most people choose option 2. There are a variety of conditions that moderate this kind of fallacy, but it reproduced quite reliably even when people are given incentives to get it right (like betting money).

It also goes on to discuss Availability Bias, another trick where things that are easier to think of seem more probable than things that are harder.

But maybe my favorite part of this chapter is on: mathematical notation. Mr. Mlodinow wonders: why didn’t the ancient greeks make a theory of randomness. He’s got some interesting theories (cultural notions of fate might preclude thinking of something as random), but what’s fascinating is that the Greeks lacked robust arithmetic – essentially the basic kinds of things you can do with numbers: Add, subtract, multiply and divide.

Ancient Grecian math was done using numeral notation that lacked order – they had different symbols for 1-10 and 100, 200, 300 – but those numbers could appear in a random order: (100 and 3, or 3 and 100). And.. they lacked the concept of Zero. I am looking forward to reading The Nothing That is: The natural history of zero someday. Apparently the ‘adding/subtracting by zero results in the same number’ rule came to Greece in ~300 BC from the Babylonians, and the ‘multiplying a number by zero leaves zero unchanged’ rule came from India in ~900 from the mathematician Mahavira

Apparently it was the Romans who made a start in understanding probability – Cicero seems to have coined the word Probabilis. While they made a start, the still ended up in trouble in their legal system with the concept of Half Proofs – the idea that when evidence was doubtful, additional evidence could boost the overall credibility of the judgement. Today I think we call this circumstantial evidence – not concrete proof, but things that seem to make the allegation more likely. For example: for the allegation that Johnny committed the a crime – a ‘half proof’ is that he was in the area when the crime was committed. Or that his DNA was found at the crime scene.

The Romans thought of these as Half Proofs – and thought that two half proofs made a Full Proof. This ‘additive’ conception isn’t right though (How many proofs is 3 half proofs?). The 2nd law of probability is:

If two possible events, A and B, are independent, then the probability that both A and B will occur is equal to the product of their individual probabilities

Honestly – I have a very hard time figuring out how to apply the 3 laws correctly. Maybe writing will help.