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This picture summarizes prospect theory by Daniel Kahneman.

prospect theory plot

Looking at the gains part: The slope of the graph is getting smaller. I can understand this: If I own a million, then adding 100 euro's isn't as impactful as when I own only 1 euro.

My question is about the losses part: Here also the slope of the graph is getting smaller away from the reference point. This implies that if someone would either lose 100 euro or have a 50% chance of losing 200 euro, he would go for the gamble and become risk seeking.

But to me this doesn't make intuitive sense for two reasons:

  1. If I am loss-averse, which I am, then why would I take a gamble with my second 100 euro's? I would look at it as if I already lost 100 euros and then I can take the gamble of 50% of winning 100 euro or 50% losing another 100 euro. Since I am loss-averse I would not take the bet.

  2. Let's say I only own 200 euro in total: in that case I would definately want to hold on to my last 100 euro, since then I can at least pay for the rent. In other words, the utility of my last 100 euro is way bigger than the utility of my second-last 100 euro. But this is not represented in the slope.

Can anyone explain to me why according to Kahneman the slope of the losses-part diminishes away from the reference point?

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Prospect theory states that people make decisions based on the potential value of losses and gains rather than the final outcome, and that people evaluate these losses and gains using certain heuristics (risk potentials) - Source.

When you look at Prospect theory graphs, you need to remember that it is all about perceived potentials. (Perceived potential gains/losses against the perceived potential value).

Let's look at the logic to start with. If the potential value of the prospective task is negative, it is perceived that the outcome result has a higher potential to be negative (loss); and the opposite is true also. If the potential value of the prospective task is positive, it is perceived the outcome result has a higher potential to be positive (win or gain).

Now with the logic in place, more potential loss perceived will result in a perceived potential of a more negative outcome and more potential gain perceived will result in a perceived potential of higher gains.

The line crosses the $0,0$ $x,y$ axes because it is perceieved that a zero potential value will result in zero loss or gain and the potential losses increase as you move nagatively away from the $0,0$ reference point, and the losses diminish as you move positively away from the $0,0$ reference point.

Now you also have to factor the probability of win or lose into the equation. With low expactation of any gains (low perceived value) it doesn't matter if you win or lose, it is perceived that you are going to lose overall. With high expectation of gains, (high perceived value), you need to have a win in order to achieve the gain perceived.

If you also rotate the graph, you get this

original graph rotated

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