Counter-intuition (warning - not really cycling related)

In the course of the threads about bicycle helmets, many people have made comments based on their intuition. It just seems impossible that forcing people to wear helmets hasn't made cycling safer. It just feels wrong that helmets don't seem to make any difference in terms of injury severity or crash survival rates.

People often feel so strongly about their feelings that they flatly deny the observed facts. This isn't unusual; indeed many bicycle helmet researchers do the same; I don't have the link to hand, but I have a great piece of research where the researcher found that helmet wearing (or not) had no statistical bearing on the injury severity of cyclists (whereas being drunk did; the study looked at both). However, the report concluded that helmet laws would be a good thing! That's a bit like a drug company admitting that a new drug showed no benefit in a trial, but that people should take it anyway.

However, intuition is very often wrong. I've become quite interested in this, and in fact it almost now seems to me that pretty much everything in the modern world is counter-intuitive! Our intuition developed tends of thousands of years ago, and clearly conferred evolutionary advantages when we lived in caves. However, it is very poorly suited to the modern world.

The following is a very good demonstration of this. If you have the time, read through the following and see what you think...

The Monty Hall Problem

You have been invited onto a TV game show, and excitingly have reached the final round. in front of you are three doors, all different colours. Behind one of the doors is the star prize - your dream bicycle, coupled with the bike holiday you've always wanted to go on. However, two of the doors have no prize behind them.

'Well, now's the time to make your decision!' says the host. 'Behind one of the doors is the star prize! Which door will you choose?'

You ummm and ahhh, and plump for one of the doors.

'You chose the red door!' says the host. 'Lets hope you chose wisely!'

The lights dim, and a gentle drum-roll starts. 'We can open the red door,' says the host. 'However, before we do that, I'm going to remove one of the doors you didn't choose - and it's one of the dummy doors!'

"It's a good job you didn't choose the green door, as there's no prize there!'

The audience let out a collective gasp, and the spotlight on the green door goes out, leaving just your red door and the other door illuminated. "Thank goodness!" you think, "I didn't choose the green door! Perhaps I did choose the right one, as it's either 'my' door, or the other one!"

"Now,' says the host, 'as you've been such a great contestant, I'm going to give you another option. If you want to, you can change from the red door to the other one. Or you can stick with your first choice. You've got five seconds to decide - change door, or not?'

What should you do to have the best chance of winning the prize? Stick with the red door, or switch? Think quickly, and stick your thoughts down below!


Views: 42

Comment by Colin on March 21, 2010 at 11:22am
Switch.
Your original choice had a 1 in 3 chance of being right. The other door has now been shown to have a 1 in 2 chance, but that doesn't apply to your original choice, it's still 1 in 3.
Comment by Colin on March 21, 2010 at 11:25am
If I'm right (maybe I'm not?), I don't think this is about intuition, it's about people's reluctance to change their mind once they decided something, and the anticipated embarrassment they'd feel if they switched and were then wrong.
Comment by Peter H on March 22, 2010 at 6:10am
The mathematical solution shows that if you chose the remaining door you have a 66.6% chance of winning. Which is counter intuitive. The maths is very interesting.
1. The first choice represents a 1/3 chance of winning
2. The remaining two doors represent a 2/3 chance of winning (ie a 66% chance the prize is behind either one)
3. One of the remaining doors are removed (note that the presenter would not remove the door with the prize behind)
4. This leave the odds as:
1/3 for the door you picked originally
2/3 for the remaining choices (which is now only one door)

Therefore, you have a 1/3 chance that the door you originally picked has the prize, or 2/3 chance of the remaining door has the prize.
Comment by Colin on March 22, 2010 at 7:13am
2/3 for the remaining choices (which is now only one door)

Ah, yes, I think you're right here, where I said 1/2 for the remaining door.
Comment by Dan on March 22, 2010 at 12:26pm
The answer to the gameshow question is that you should switch doors. As Peter H points out, your chances of winning actually double if you change doors, compared to staying with the same door. Well done everyone!

I daresay by setting this up as a ‘trick’ in a blog about counter-intuition, people were more wary about jumping in on this one. However, the vast majority of people will stick with the same door. I have actually run this demo at a conference in full game-show mode (I even wore a spangly jacket; if anyone wants a powerpoint deck with gameshow graphics, music jingles etc and a script to run this let me know; it’s quite a fun thing to do). All 50 people in the audience wanted the contestant to ‘stick’ (I got them to call out advice). I then went into the audience and asked a few of them why, and they all felt it was better to stick; when pushed it was because the odds were now ’50:50, so you might as well stay with the first choice’.

If that’s what you thought too, don’t feel bad. I thought it when I first saw this problem; indeed even after working through the maths I was still sufficiently unconvinced that I wrote a computer program to simulate the two scenarios, ran it thousands of times and observed the outcome. If you switch, you win twice as often as if you stick. It really happens! So why are people so adamant that you should stick? I think it stems from two reasons:
- our ‘intuition’ or ‘dead reckoning’ is actually extremely poor at judging odds. However, we still tend to trust it – in some cases even when people have been shown the maths and the computer output for the above problem they ‘don’t believe it’, and continue to think you should stick.
- people are very averse to changing their behaviour. This is seen all over the place; in politics, for example, pollies who change their views are seen as ‘weak’. This is all topsy-turvy; changing your views in the light of new evidence should be seen as evidence of a strong character. However, we value ‘pushing through’ more than this; it is this tendency that also leads people to throw ‘good money after bad’ – we tend to just keep doing things, even when they are not working.

My hypothesis about why this is answers Kylie’s question. There are times when it is more important to make a fast decision and stick to it than to make the best decision. For example, if you are being pursued by a sabre-toothed tiger and need to escape, you two options might present themselves – to climb a tree, or attempt to jump over a fast-flowing river. Now, you could stop, consider the two options, look at how likely you are to be able to climb the tree (considering other trees you have climbed, and how quickly you can climb), vs looking at the river; (how far is it to jump, how tired are your legs etc etc). However, you’d probably be eaten during the evaluation! Similarly, if you were to start climbing the tree, but then change your mind and go for the river instead, you’d also probably get eaten. In this kind of scenario, making a quick decision, and then sticking to it, is going to produce the best outcome – even if your actual choice is not the optimal one. In evolutionary terms, in prehistoric times this type of situation was much more common than a situation where there was lots of time to weigh up and consider each possibility before acting – so evolution tended to favour individuals capable of fast decision making, rather than those who took lots of time to consider everything.

However, in the modern world, what used to be an advantage perhaps becomes a disadvantage. It’s now rather rare that we need to make rapid life-or-death decisions based solely on our own judgement, but rather common that we need to make considered decisions based on lots of information, and we also need to be alert to the need to change our minds if the situation changes or new information becomes available. However, we find that hard to do; as a species we are wired up to prefer rapid, intuitive decision making to slow, considered decision making. We are also very averse to changing our behaviour once we have decided to do something a certain way.

And this is why the gameshow example works the way it does. People plump for a door at the beginning, and want to stick with their first choice. When pushed, they justify this by saying the new odds are 50:50, so you might as well stick. But in reality, they are using this justification to post-rationalise a decision they have already made based on intuition; even if the new odds were 50:50, you might as well switch as not, so you might expect half the people to switch. Or even some of them. But they don’t. They all stick! And as a result, they are only half as likely to win the prize…
Comment by Dan on March 22, 2010 at 2:36pm
Around 1991, in Australia, cycling participation levels suddenly changed. Dramatically. This massive change happened against a background of other comparable trends (eg in pedestrian safety, sports participation, transportation modal share, road conditions, etc etc) remaining constant.

If you want to show it wasn't MHL, you are going to have to demonstrate a different significant, one-off factor that caused this effect to happen that was not MHL (and the associated helmet promotion). From an epidemiological perspective, we need to locate something that caused:
- cycling participation to suddenly drop
- a previously rising trend to be reversed, and cycling to go into decline
and pinpoint the start of this thing / effect to around 1991.

What changed for cycling in 1991? It defies all logic to suggest that MHL was not the primary cause of this change. Especially when exactly the same effect has been seen in their places where MHL has been introduced, but those other factors would have been somewhat different. And when many of the sub-factors that contribute to those declines have also been seen in other places (for example the decline in cycling in areas of the UK where helmet promotion has been undertaken). It is simply the best fit for the data, supported by international experiences.

I truly fail to understand your position on this, BB.

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