A Dollar Loss Is 2&1/2 Times As Painful As A Dollar Gain Is Pleasurable.

Daniel Kahneman and Tversky are two Nobel price winning economist. Their most important contribution is called prospect theory which describes individual behavior in the phase of risky situations where there are prospects of gains and losses. Below is an insightful abstract from one of my favorite book “Thinking, fast and slow“.

In general financial economist models where individuals made decisions based on the likely fact of those choices in the persons final wealth.

Perspective theory challenge that assumption. People’s choice are motivated instead by the values they assign to gains and losses. Losses are considered far more undesirable than equivalent gains are desirable.

Moreover the language used to present the possible gains on losses will influence the final decisions that is made.

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Loss Aversion

For example, you are told that a fair coin will be flipped and that if it comes up heads you will be given $100. If the coin comes up tails, however, you must pay $100. Would you accept such a gamble?

Most people would say no even though the gamble is a fair one in a sense that in repeated trials you would end up even. Half the time you would gain $100 and half the time you would lose $100. In mathematical terms, the gamble has an expected value of zero.

Kahneman and Tversky then tried their experiment with many different subjects, varying the amount of the positive pay off to test what it would take to induce people to accept the gamble. They found that the positive payoff had to be about $250. Note that the expected value of the gain from such a gamble is $75, so this is very favorable bet.

Kahneman and Tversky concluded that losses were 2 &1/2 times as undesirable as equivalent gains where desirable. In other words a dollar loss is 2 1/2 times as painful as a dollar gain is pleasurable. People exhibit extreme loss aversion and even though a change of $100 of wealth would hardly be noticed for most people with substantial assets.

Risk-Seeking Behavior

Loss aversion leads many investors to make costly mistakes. Interestingly, however, when individuals faced with a situation where sure losses were involved, the psychologist found that they were overwhelmingly likely to take the gamble.

Consider the following two alternatives.

  1. Sure loss of $750.
  2. A 75% chance to lose $1000 and a 25% chance to lose nothing.

Note that the expected value of the two alternatives are the same – that is, a loss of $750. Almost 90% of the subjects tested chose alternative (2), the gamble. In the face of sure losses people seem to exhibit risk seeking behavior

Framing Effect

Kahneman and Tversky also discovered a related and important framing effect. The way choices are framed to the decision maker can lead it to different outcomes. They posed the following problem.

Imagine that the US is preparing for the outbreak of an unusual Asian diseases, which is expected to kill 600 people. Two alternatives programs to combat the diseases have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows:

  1. If Program A is adopted 200 people will be saved
  2. If Program B is adopted there is 1/3 probability that 600 people will be saved and a 2/3 probability that no people will be saved.

Note first that the expected value of the number of people saved is the same 200 in both programs. But according to prospect theory people are risk averse when considering possible gains from the two programs. and, as expected about 2/3 of the respondents to this question picked program A as the more desirable.

But suppose we framed the program differently.

  1. If program A* is adopted, 400 people will die.
  2. If Program B* is adopted, there is a 1/3 probability that nobody will die and a 2/3 probability that 600 people will die.

Note that the option A and A* as well as B and B* are identical. But the presentation in the second problem is in terms of the risk of people dying. When the problem was framed in this way, over 75% of the subjects chose program B*. This illustrated the effect of “framing” as well as a risk-seeking preference in the domains of losses.

When doctors are faced with the decisions regarding treatment options for people with cancer, different choices tend to be made if the problem is stated in terms of survival probabilities rather than mortality probability.

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