Heston

You are called Heston. You need to make a bar of chocolate. The process to make this bar of chocolate uses three machines, one after the other. All three need to work for the chocolate bar to be made. Each machine has a success rate of 90%. What is the probability that the whole process is a success and the chocolate bar gets made?

Answer = 73%. (0.9 x 0.9 x 0.9 = 0.73)

People often guess a higher success rate than that. This is an example of the confirmation heuristic, whereby people overestimate the probability of conjunctive events. A 'heuristic' just means a rule of thumb, we use them all the time and mostly that's okay, but sometimes they lead us to make systematic mistakes just like the one above.

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...

Why Three Options?

I'm going to start with a confession: Over the course of my time as a student I have spent a lot of time in coffee shops. Starbucks. Costa. Nero. You name it, I've been there. One of the things which intrigues me about said coffee shops is that they tend to offer three different sizes of hot beverage. Small, Medium, Large. Tall, Grande, Venti. Primo, Medio, Massimo.

Why three?

 

Could it be that there are precisely three different types of people who buy coffee, each preferring their own exact drink size? 

Given that the actual sizes of mugs differ between the franchises, I think not.

Could it be that the manufacturers of mugs only do precisely three sizes?

Unlikely.

Or, could it be that coffee shops know some behavioural economics?

When offered three options we are likely to prefer the middle one. This is because we are risk-averse and regret-averse; we want to avoid being on an extreme. If offered two sizes of drink, we'll choose whichever one we like. If offered ten, we'll be overwhelmed by the choice. If offered three, we're likely to choose Medium; Grande; Medio.

Of course the thirsty will still go for the Large, and the thrifty for the Small. But by offering three options Starbucks, Costa and Nero maximise their revenue. They cater for all and simultaneously nudge people who would have bought Small into purchasing more coffee. 

So there you go: not all my time in coffee shops was wasted...

Turn it up to 11

A problem for economists who think that people are rational is that we are sometimes influenced by things that we really shouldn't be. Much thanks to the friend who recently showed me this clip from the comedy Spinal Tap which parodies human irrationality:

Beyond Own Brand

As we perused the soup section of my local Tesco recently, it was obvious to my friend and I that Tesco were pushing their own brand soup (Tesco Everyday Value). A lot of shelf space close to other cheap soups was dedicated to it. However, the vast majority of the soup category was taken up by Heinz - a brand known mainly for its quality rather than price. It would appear that Tesco was not directly competing with Heinz, especially as Tesco Everyday Value soup was not placed directly next to the Heinz soups.

We were wrong.

Upon closer inspection (and a little light research) we discovered that Crosse & Blackwell, a high end brand placed next to Heinz, is owned by Tesco.

So what?

Tesco is clearly wanting to gain market share in the world of quality soup (who wouldn't?). However, they've realised that consumers see Tesco Everyday Value as an inferior option to brands like Heinz. If you wanted a really nice soup, you would look at Heinz, Campells or Baxters. Not Tesco Everyday Value.

People are very good at creating rules of thumb; seeing Tesco on the packaging usually means low price, not high quality. Thus when we quickly (and we're always in a rush) scan shelf after shelf of similar looking soups, we narrow down the options using rules of thumb. (This isn't a criticism of consumer behaviour; rules of thumb are necessary to survive in this complicated world.) We quickly rule out Tesco own brand soup as inferior (correctly or not).

So what do Tesco do?

They create (or buy) a brand that consumers will not immediately write off as low quality. Crosse & Blackwell are the method Tesco are using to squeeze market share out of Heinz. Instead of fighting the rule of thumb and re-branding Tesco Everyday Value, they simply create a new brand. Simples.

Rules Of Thumb - Superstition

My parents recently went on a short trip to a Eurozone country (for those reading this in the future, the Euro was the currency which collapsed thus causing the Second Great Depression). My advice beforehand was to take Dollars or things you can easily barter (jewellery or livestock), but in the end they went with Euros rather than greenbacks, earings and chickens.

Upon their return I aksed my mum what the exchange rate was, only to hear the reply that she didn't know exactly, but she thought of it as "about £1 to €1". This is a rule of thumb. It is also clearly wrong (actually about £1 to €1.2, as of the 11th June 2012). However, people are constantly using similar (incorrect) rules of thumb in their everyday lives. So why do we do it?

http://cdn.theatlantic.com/static/mt/assets/steve_clemons/euro1.jpg

Well, while the diference between €1 and €1.2 per pound might be life or death for a currency trader, it is close enough for an ordinary person. It's a very easy way to remember a potentially complex ratio. And frankly my dad may well have been pleased this rule of thumb was in operation, as if anything the 'adverse' effect would only to have made things look more expensive than they really are, thus reducing purchases!

Two famous psychologists called Amos Tversky and Danny Kahneman famously coined the term 'heuristics' to describe rules of thumb, and show that they can occassionally lead us into serious errors. All of this is a challenge to traditional economic theory which assumes that we are rational beings that don't need to resort to crude rules of thumb to solve everyday problems. An important part of behavioural economics over the last 40 years has been the attempt to explain how exactly we use rules of thumb, and therefore how they need to be incorporated into our big important economic models.

Recommended listening:
Superstition by Stevie Wonder

Anchors – The Chain

• Is Wayne Rooney 45 years old?

• How old is Wayne Rooney?

http://i.telegraph.co.uk/multimedia/archive/01837/wayne-rooney_1837352b.jpg

The answer is... 

26 (b. 1985), hair transplant aside.

It’s very likely (although you may struggle to believe it) that your guess was affected by the number 45 in the first question. The number 45 acted as an ‘anchor’.

The theory goes as thus: in your thinking you started by briefly considering whether Rooney is 45 (clearly not). Then you adjusted down until you reached a reasonable figure, and settled on that being your guess. If the age in the first question was 15 you would have started by considering whether Rooney is that young (again, clearly not). You would then have adjusted up until you reached a reasonable figure.

In 1974 two Israeli psychologists named Amos Tversky and Daniel Kahneman published an article called ‘Judgement under Uncertainty: Heuristics and Biases’ (a heuristics is just a ‘rule of thumb’). It was a seminal work which demonstrated how people make systematic errors.  One of their key findings was that when people estimate something unknown, they start at an initial point and then adjust their answer. But people systematically use insufficient adjustment from that starting point: thus there is a ‘bias’ towards the initial point.

Even if we are made aware of the fact that anchors have an effect, and even if the anchor is plainly ridiculous, we are unable to completely rid ourselves of this bias. For example, anchoring may have an effect on your following answers

• Has Wayne Rooney scored 10,000 goals for Manchester United?

• How many goals has Wayne Rooney scored for Manchester United?

Aside from the obvious own goal that is his hair, he’s scored (as of April 2012) 180 goals for Man U.

Given that you are probably not reading this while on a TV quiz game show you would be forgiven for thinking ‘so far, so irrelevant’. 

But it might interest you to know that shops have been using anchors for years. Ever wondered why the most expensive car is the first thing you see when you enter the showroom? Or why the most expensive house is on the cover of the real estate magazine?

They’re trying to influence your estimate of what a reasonable price is by anchoring your mind at their highest price (i.e. an expensive convertible makes everything else look like a bargain). That way, you buy more expensive stuff. Clever eh?

So the next time you shopping don’t be influenced by the highest price in the shop. It's just a trick!

Footnote: 

Confusingly, in a chandlery an anchor may not be an anchor while literally anything that clearly isn’t an anchor could be an anchor. Funny old world.

Recommended listening:

The Chain by Fleetwood Mac