Prospect Theory - A Lesson

An educational post - Prospect Theory: A Framework for Understanding Cognitive Biases; must read:

"Imagine a prospect theory agent - let's call him Prospero - trying to decide whether or not to buy an hurricane insurance policy costing $5000/year. Prospero owns assets worth $10,000, and estimates a 50%/year chance of a hurricane destroying his assets; to make things simple, he will be moving in one year and so need not consider the future. Under expected utility theory, he should feel neutral about the policy.


Under prospect theory, he first sets a frame in which to consider the decision; his current state is a natural frame, so we'll go with that. 


We see on the left-hand graph that an objective $10,000 loss feels like a $5,000 loss, and an objective $5000 loss feels like a $4000 loss. And we see on the right-hand graph that a 50% probability feels like a 40% probability.


Now Prospero's choice is a certain $4000 loss if he buys the insurance, versus a 40% chance of a $5000 loss if he doesn't. Buying has a subjective expected utility of -$4000; not buying has a subjective expected utility of -$2000. So Prospero decisively rejects the insurance.


But suppose Prospero is fatalistic; he views his assets as already having been blown away. Here he might choose a different frame: the frame in which he starts with zero assets, and anything beyond that is viewed as a gain.


Since the gain half of the value function levels off more quickly than the loss half, $5000 is now subjectively worth $3000, and $10000 is now subjectively worth $3500.


Here he must choose between a certain gain of $5000 and a 50% chance of gaining $10000. Expected utility gives the same result as before, obviously. In prospect theory, he chooses between a certain subjective gain of $3000 and a 40% chance of gaining $3500. The insurance gives him subjective expected utility of $3000, and rejecting it gives him subjective expected utility of $1400.


All of a sudden Prospero wants the insurance."