### Allais paradox - a choice problem

Okay, I have a hypothetical situation for you – and you need to make a choice. Listen carefully. You’ve just visited the doctor and she told you you’re going to die unless you get treated immediately. There are two treatments - The blue pill would give you a 100% chance of living another 12 years before dying, and the red pill would give you an 89% chance of living another 12 years, a 10% chance of living another 18 years and a 1% chance of sudden death. Which do you choose? Now remember your answer, and imagine a slightly different scenario. Your regular doctor is out that day so you go to the slightly dodgier one next door, who offers you two other treatments: The green pill gives you an 11% chance of living 12 years before dying and an 89% chance of sudden death, and the yellow pill gives you a 10% chance of living a full 18 years before dying, with a 90% chance of sudden death. So, which one of these do you choose? So what did you base your decisions on? Behavioural economists think we make decisions based on something called expected utility – it’s how much we expect that something will satisfy our wants and needs. If you like chocolate ice cream more than vanilla, you’ll feel more satisfied if you choose chocolate (in the animation both ice creams have cherries on top (I’ll come back to this)). So for you, chocolate ice cream has more expected utility. Studies show that in the previous question most people choose the blue pill in the first scenario, giving them a guarantee of living another 12 years, and the yellow pill in the second scenario, giving them a 10% chance of living another 18 years, and a 90% chance of death. But what if instead we write the options out like this: Now the options have something in common. In the first scenario, in both cases you have an 89% chance of living 12 years, so if we remove that, your decision shouldn’t change, right? Kind of like how removing a cherry from both ice creams won’t change your favorite flavor. In the second scenario, both options have an 89% chance of death in common, so we should be able to cancel those too without changing your decision. Hold on, now both scenarios are exactly the same. But studies showed that most people chose the blue pill in the first scenario and the yellow pill in the second one, which doesn’t make sense. Both the blue and green pills give you a higher chance of living over the chance of a longer life, and the red and yellow pills give you a chance of a longer life but with the drawback of a lower chance of living. So for people who chose the blue and yellow pills, what do they want? A higher chance of living or a longer life? This is called the Allais Paradox – it was first outlined by Maurice Allais, a Nobel-Prize winning economist in a 1953 article. The paradox undermines the theory of expected utility because it shows that we don't always make decisions that align with our wants and needs. We tend to make decisions based on how much we think we have to gain or lose now, rather than on the final outcome. And we also tend to choose certainty over risk, even if the riskier option is closer to what we really want. Psychologists who have studied the Allais Paradox found that people dislike risk in general. When questions are framed in terms of gains or losses, people are far more likely to consider the losses first and try to minimise them – it’s a phenomenon called loss aversion. It’s similar to regret theory, which says that when we’re making decisions, some of us try to minimise the amount of regret we feel afterward. Humans are pretty complicated! And not everything is as simple as ice cream. So, what did you decide?

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