Passport Prices

I recently went through the process of getting a new passport and was interested to see the government using some price discrimination: different prices for different people. People self-selected into the different pricing categories. Why? Because the government charged different prices according to how quickly you wanted your passport:

4 weeks - £72.50
1 week - £103
1 day - £128

Thus those who are in a rush and thus prepared to pay more, pay more. While those who are in no hurry and thus prepared to pay less, pay less. Clever. Much cleverer than just one standard price. And it is used by firms/governments all the time. Price discrimination by time is ubiquitous because there will always be some impatient people.

The Confirmation Trap

Example taken from Bazerman and Moore (2009) based on Wason (1960):

Imagine the following sequence of numbers follows a rule, and that your task is to diagnose that rule. When you write down other sequences of three numbers, your instructor will tell you whether or not your sequences follow the rule.

2-4-6

What sequences would you write down?

Commonly guessed patterns include "numbers go up by two" and "the difference between the first two two numbers equals the difference between the last two numbers". In fact, the rule was much broader: "any three ascending numbers". But people had only tried sequences that tested their hypothesis by accumulating evidence that confirmed it, but didn't test for wider rules. They fell into the confirmation trap by just seeking to confirm their suspicions by trying sequences like 1-3-5 and 22-24-26 instead of trying, for example, 1-2-3 or 1-2-10.

This is called the confirmation bias. In all walks of life, from politics to business, people seek to confirm their beliefs rather than really test them.

People ask "May I believe it?" rather than "Must I believe it?"

Econitus

The following problem is adapted from Bazerman and Moore (2009) Judgement in Managerial Decision Making:

Lisa is worried about her health. Her doctor tells her not to worry too much as there is only a 1 in 1,000 chance that women of her age has the dreaded Econitus virus. Nevertheless, Lisa remains anxious about this possibility and decides to obtain a test that can detect Econitus. The test is moderately accurate: When someone has Econitus it delivers a positive result 86% of the time. But there is, however, a small 'false positive' rate: 5% of people produce a positive result despite not having Econitus. Lisa takes the test and obtains a positive result. What are the chances that she has Econitus?

0-20 percent chance
21-40 percent chance
41-60 percent chance
61-80 percent chance
81-100 percent chance

The correct answer is 1.7%!

If you answered 86% then you fell into the common trap of ignoring 'base rates'...

If 1,000 women like Lisa take the test, 999 will not have Econitus. But the false positive result means 50 will be told they have Econitus. Therefore there is only 1.7% chance that Lisa has Econitus (trust me!).

What this demonstrates is that people ignore background information in favour of more salient information about a specific case.

Hopefully this will be useful the next time you are given statistics by a doctor...

Boy Or Girl??

The following problem is taken from Bazerman and Moore (2009) Judgement in Managerial Decision Making:

You and your spouse have had three children together, all of them girls. Now that you are expecting your fourth child, you wonder whether the odds favour having a boy this time. What is the best estimate of your probability of having another girl?

6.25% (1 in 16), because the odds of getting four girls in a row is 1 out of 16

50% (1 in 2), because there is roughly an equal chance of getting each gender

A percentage that falls somewhere between the two estimates (6.25-50 percent)

The answer is 50%. (The sperm that determines gender of the child does not know the gender of previous children! In other words, the gender of each child is independent of that their siblings.)

So what explains our potentially wayward intuition here?

According to Kahneman and Tversky (1974) "Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not corrected as a chance process unfolds, they are merely diluted."

So there you go, hope this helps when you're expecting your fourth child...