If we take a closer look at the choices that people make in Part 1 of Risk and Rationality we can see that something seems to have gone wrong. The dominant option BC is exactly the same as the combination B and C in the first set of decisions, that around 97% of people reject. And the inferior option AD is exactly the same as the combination of A and D in the first set of decisions, that around 73% will have chosen. How can it be that we are so poor at making decisions, that in decisions (i) and (ii), 73% of people make a choice that is so obviously inferior once we have seen the same choice r ..read more

In our everyday decision-making, it is probably the case that we use inductive and abductive reasoning far more than we use deductive reasoning. However, there is a good use that we can make of deductive arguments; we can use them to draw out hidden assumptions in our reasoning. For example - take the following line of reasoning:             Premise: The grass is wet             Conclusion: It has rained. This seems to be a straightforward example of abductive reasoning - reaching a co ..read more

Sometimes the beliefs we hold can be very stubborn; sometimes we continue to hold on the belief even when faced with evidence that shows the belief to be false. In the literature of psychology, this is called belief perseverance. Belief perseverance happens in three domains. 1) Self-impressions - that is, beliefs about ourselves. I am convinced that I am a good pool player, and this is despite the fact that although I play regularly against a variety of opponents, I never win. 2) Social impressions - beliefs about another person. I believe my work colleague to be not very generous. I have rece ..read more

This example is taken from Daniel Kahneman Thinking, Fast and Slow You face two concurrent decisions. First examine both, and then make your choices:               Decision (i): Choose between             A. sure gain of £240             B. 25% chance to gain £1,000 and 75% chance to gain nothing               Decision (ii): Choose between     &nbs ..read more

Plot spoiler: Many of us are familiar with the premise of the film The Matrix. In the 21st century, intelligent machines and humans wage war against each other. Humans have tried to stymie the machines by stopping them getting access to solar power. The machines responded by enslaving the humans; their minds are now hooked-up to the Matrix - a simulation of the real world in the 20th century - and the bioelectric power they generate while they 'interact' in this virtual world is harvested to power the machines. Neo - the main protagonist of the film - is such a human. Everything that his mind ..read more

These examples are taken from Daniel Kahneman Thinking, Fast and Slow Example 1 A cab was involved in a hit-and-run accident at night. Two companies, the Green and the Blue, operate in the city. You are given the following data 85% of the cabs in the city are Green and 15% are Blue A witness identified the cab as Blue. The court tested the reliability of the witness under the circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the colours 80% of the time and failed 20% of the time. What is the probability that the cab in ..read more

Now, both examples in Part 1 of this post give you two pieces of information. The first is a base rate, which is a fact about the population to which a particular case belongs. The second is information specific to the case. In fact, in terms of the calculation of probability, the two examples are mathematically identical. The correct answer in both cases is 41%. (Very roughly, suppose the eye witness saw 100 accidents, 85 Green cabs and 15 Blue, calling it with an accuracy rate of 80%. Of the 15 Blue accidents, they would call it Blue 12 times. Of the 85 Green accidents, they would call it Bl ..read more

It is tempting to answer b) to the question regarding Jimmy's current situation. After all, we can imagine that while he will want to be in employment - and perhaps may take an office job because that is what is on offer - we can also imagine that such a job on its own would not fulfil all his wants. It is easy to imagine that his teenage love of team sports will carry on into his twenties. The second option, that given that Jimmy has a desk-bound job, he would also spend his spare time playing basketball with his mates, just sounds more plausible. But is it more probable? To answer that, we n ..read more

Writing in 2019, the term 'echo chamber' is a familiar one, used in respect to social media. Take the case of George. George loves his mobile phone, and looks at it on average every 12 minutes. He signs up to news feeds that  report in a way that reflects his  world view, and does not look at the ones which say things he disagrees with. On all the rest of his social media, he friends or follows people who seem to share his opinions on all kinds of social and political issues, and does not link up with people whose views oppose his. So George has put himself in an 'echo chamber' - the ..read more

In many ways, Jimmy was an average pupil at school. He did OK in the academic subjects - he always ended up around the middle of the class in the end-of-term results for geography and history, for example. However, he both enjoyed and excelled in sports. He represented the school in the basketball team, and trained with the county's youth cricket squad. Jimmy is now in his mid twenties, still fit and healthy. Which of the following scenarios do you think is more probable: a) Jimmy has a desk job as a cleric in a solicitor's office. b) Jimmy has a desk job as a cleric in a solicitor's office, a ..read more