Remember Remember...

If we are rational creatures then we need to be able to remember accurately. Interestingly, however, our memory is as complex as a Rubik's cube in a maze.

One rule of thumb initially discovered by Daniel Kahneman is the peak-end rule. He got patients undergoing a painful operation to note down the amount of pain (out of ten) they were in, minute by minute. Thus he was able to create graphs of the sum total of pain patients experienced. For example (my data):

The patients were then asked after the operation to remember how much pain they went through. To be consistent they should have given the average amount of pain they recorded during the operation (here 5.5). But they didn't. Instead they tended to report the average of two points: the most memorable (the peak) and the end of the operation (here 5).

Thus our memory tricks us. We do not remember a how a whole experience (good or bad) was, instead averaging the best/worst bit and the end. This is a challenge to those who defend human rationality. If we do not remember accurately, then how can we make decisions that maximise our personal benefit/satisfaction/goals?

Kahneman then decided to prove the peak end rule (using, in my opinion, ethically dubious methods). He asked the surgeons to extend the operations subjects went through by leaving their instruments in the patient at the end for a couple of minutes. This increased the length of the operation. It also meant that the pain experienced in the final couple of minutes of the operation fell. In accordance with the theory, although the total amount of pain experienced went up, the amount of pain patients remembered fell. Gruesome but true.

Risky risky...

I am about to toss a fair coin. If heads you win £100. If tails you lose £100.

Do you want to play this gamble?

If yes, then you are risk-preferring.

If no, then you are risk-averse.

If you are indifferent, then you are risk-neutral.

That is because the expected value of the gamble is £0 (100x0.5 + -100x0.5 = 0).

Personally I would not like this gamble, which makes me risk averse. The extent of my risk averseness would have to be revealed by considering different gambles, but as long as I am consistent in my attitude to risk an economist could call me rational.

Here are a copuple of other interesting gambles which may shed light on your attitude to risk:

I am about to toss a fair coin. If heads you win £100. If tails you lose £75. Do you want to play?

I am about to toss a fair coin. If heads you win £1000. If tails you lose £50. Do you want to play?

If you would not like to play these gambles then you highly risk averse... Personally I think I would probably play both, definitely the latter one.

Russian Roulette

Scenario 1: There is a gun pointed at your head. It has six chambers. There are four bullets inside. The chambers will be spun randomly before the gun is fired once.

Scenario 2: There is a gun pointed at your head. It has six chambers. There is only one bullet inside. The chambers will be spun randomly before the gun is fired once.

In which scenario would you be willing to pay more to have one bullet removed from the chambers?

Interestingly, according to economic theory you should be willing to pay more to reduce the bullets from 4 to 3 than from 1 to 0. Is this the case for you?


For those who are economically inclined, here is a brief sketch of the proof of the theory:

Where u(.) is a von Neumann-Morgenstern utility function, p1 is what you are willing to pay in Scenario 1, p2 is what you are willing to pay in Scenario 2 and Y is your income.

In Scenario 2:

u(alive, Y - p2) = 1/6u(dead) + 5/6u(alive, Y)

In Scenario 1:

1/2u(dead) + 1/2u(alive, Y - p1) = 2/3u(dead) + 1/3u(alive, Y)

Re-write Scenario 1:

u(alive, Y - p1) = 2/6u(dead) + 2/3u(alive, Y)

Comparing scenarios:

u(alive, Y - p2) > u(alive, Y - p1)

Therefore:

p1 > p2

QED

Weight In Gold

Much thanks to Pete Everson for this nugget:

Gold is priced £32,845.67 per kg.

The average professional footballer weighs 73.5kg.

So that means that any footballer earning £2,414,156.75 a year, or £46,426.09 a week is being paid their weight in gold.

Some of professional footballers get paid multiples of their weight in gold!

Meanwhile the average annual salary in the UK is £26,500, less than one kilogram of gold.

Does this strike you as fair?

If you are concerned about fairness then you run this risk of being considered irrational by economists...