But it’s not about sex.
This post may contain scenes of a sporting, educational or mathematical nature.
I was a competitive kid.
No, I don’t mean there is an annual ‘kid of the year’ competition; I meant that I played a lot of sports. I enjoyed winning (and was remarkably gracious for a child), but I absolutely hated losing. I mean, like really, really hated it.
At times, probably too far into my teens to admit publicly, I would cry at the end of football matches because of the pain of losing. As games drew to a close, I used to feel the tears well; anger borne from complete frustration.
It wasn’t every game I lost, but enough for it to be noteworthy. As the game progressed, I would work harder and harder to drag my team to a positive result. I would give everything I could, physically and mentally, so when it didn’t work, sometimes I just couldn’t control it. Being told ‘it’s just a game’ was like a red rag.
Now, although I enjoyed some success in sport during my teenage years, I knew early on that I was never good enough to make it professionally as either a footballer or rugby player, so sport should have been recreation.
But it wasn’t. The pain of losing was still there, it was intrinsic.
I was brought up in a very competitive school environment, you knew exactly who was the best in the class. Assessments like the 11plus, SATs and GCSEs were pitched as ‘you won’t get a good job if you don’t do well [i.e. better than your peers] at these’. At university, your marks were posted on the wall for all to see. And compare. They may as well have ranked them like a league table.
In all aspects of my life, I prayed to the church of competition. Competition was good; it was the drive to improve, it was the reason for doing anything. Be the best.
Around my 19th birthday, my collarbone was broken in a rugby training accident. It never healed properly and I never played rugby again. I went months without sport (and about 3 years before I could sleep on that side again). Once I was fit, I resumed playing football, but there was one incident that changed everything.
It was the last few minutes of a game. We were losing 4-3. We were defending a corner; I cleared the ball and started a break. There was an opportunity for my team to break and score an equaliser. There were three of us against two defenders. The ball was loose. A defender jumped in. I jumped in. We both got the ball, but there was a horrific noise. The force of our challenge broke my opponents’ ankle, tibia and fibula. As I sat with him on the pitch, waiting for the ambulance, I knew that I had to change something. I knew that I hadn’t intentionally hurt someone, but that meant nothing. Speaking to him afterwards, I found out he had complications, including a blood clot that lodged in his lungs and he spent weeks in hospital and months rehabilitating.
How could I cause such a serious injury just because I didn’t want to lose? If competition could cause this pain, I didn’t want to be part of it anymore.
If not competition, what?
Around this time, I had started training as a teacher. When I stood in front my own classes, it became very clear that the culture of competition is not helpful. In fact, I would suggest that bar a small minority, it is a hindrance. When I talked about the negativity of competition in education I used to hear “but the working world is full of competition and we need to prepare them for that”.
All that tells me is that competition is a cultural thing, and we can’t change it overnight. So, what can we do?
We can look somewhere different for an answer: Mathematics.
It all adds up
I’ve always liked maths. A slightly different set of choices at school and I might now be a mathematician rather than a educator and scientist.
The branch of maths that is most interesting here is Game Theory. This is not the same as Gamification, which is the use of techniques borrowed from games to increase motivation for, and engagement in, learning tasks. Game Theory is the study of the strategy of games.
The most famous ‘experiment’ in Game Theory is the Prisoners’ Dilemma. Although there are a number of variations, one version (Davis, 2003) goes like this:
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:
- If A and B each betray the other, each of them serves 2 years in prison
- If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
- If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get, and that their decision will not affect their reputation in the future.
The possible decisions can be summarised by the following table (a payoff matrix):
|Prisoner B stays silent (cooperates)||Prisoner B betrays (defects)|
|Prisoner A stays silent (cooperates)||Each serves 1 year||Prisoner A: 3 years
Prisoner B: goes free
|Prisoner A betrays (defects)||Prisoner A: goes free
Prisoner B: 3 years
|Each serves 2 years|
Because betraying a partner offers a greater reward than cooperating with them (freedom or 2 years versus 1 year or 3 years), all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them to betray each other.
Doing it again
However, things change when we repeat the scenario multiple times. This variant, called the Iterated Prisoner’s Dilemma, provides an opportunity to reward or punish their partner. Robert Axelrod’s (2006) book, The evolution of cooperation is a must read on this subject.
If a rational, self-interested prisoner could only betray when asked once, then what is the best strategy if there is a second, third or hundredth round? Well, if the prisoners know how many repetitions of the game there will be, the best strategy is to defect. The reason for this is that, logically, the last round is worth defecting on because you have the best payoff. From there you can work back round by round until the optimal strategy is to defect for all.
When the prisoners don’t know how many rounds there will be, then there is a different choice. If both prisoners continue to defect, they will both get two years in prison. However, if they both cooperated, they would only get one year in prison each. By offering the opportunity for reward/punishment and learning, we change the game completely. Suddenly defection is not the de facto ‘best choice’. Previously it was logical for both to defect as it was individually the ‘least worst’ option, now there is the opportunity to cooperate to achieve a more positive result.
There is risk that if one prisoner chooses to cooperate, the other could defect and go free, leaving the cooperator with a three year term. However, the next round, the cooperator could punish the defector by defecting themselves, this leaves the defector with an option of either two or three years in jail.
Over the course of two rounds, cooperation becomes a lot more attractive.
Game Theory allows us to look at the strategies we can use to get the optimum result. The rational course of action is still to minimise your jail time, however, how you do it is not so straight forward.
The optimum theoretical choice is for both prisoners to cooperate. We can assume that as they are potentially guilty of misdemeanours, that they may not be trustworthy; there is always the chance one may defect for instant benefit.
So, what is the best strategy? After a lot of work (and a lot of asking prisoners), the best strategy was found to be ‘tit-for-tat’. Tit-for-tat assumes cooperation, but punishes defection by defecting in the following round. Basically a player using tit-for-tat copies whatever their opponent did in the previous round.
The tipping point
Now, here is the key point: if you use tit-for-tat, you will not win. If you added up all the ‘sentences’, you would do slightly worse than your opponent. However, as a pair, you will do better than any other strategy on average, including trying to win.
This is a big thing: you will not win, but you will do better than if you tried to win.
I’ll let that sink in…
That’s a pretty big thing: cooperation is mathematically beneficial. Coming second isn’t a bad thing if it means we all succeed.
Yes, I know this is for one limited, theoretical scenario, but the Iterated Prisoner’s Dilemma is a pretty good facsimile of many of our interactions when they are deconstructed.
I’m in the ‘education is a social activity’ camp and I propose that the optimum outcome from education is that everyone to succeed. I suggest that the optimum strategy for an individual is not to win (i.e. great grades, job, house), but for us all to win.
Cooperation and collaboration trumps competition. The order we end up doesn’t matter, what matters is where we came from and how much better we did together.
So what the f— is the point in league tables?
Coming second is definitely the way forward, especially if the other option is playing on your own.
I still play football, but only for recreation. I don’t care about winning or losing, I much prefer ‘just playing’ and enjoying the little parts of the game – I never keep score anymore (embarrassingly so at times). Maybe I was different from proper sports people, in that I hated losing, whereas they talk about winning.
Where does ‘sport’ fit into this? I have nothing against sport, and even competitive sport. I think it is invaluable in many ways. However, it is the culture that surrounds it that causes the problems. For example, I respect Arsene Wenger, the manager of Arsenal (I am a Spurs fan, so this is probably rare). Wenger has built his team around the ideas of cooperation, collaboration and integrity. Jose Mourinho has built his teams on winning at all costs. Yes, Mourinho has a bigger trophy cabinet, but the how it is achieved that is more important.