Broad framing

Let’s start with a question, would you accept a gamble on the toss of a coin in which you could lose $100 or win $200.

I wouldn’t go for the gamble, the loss of $100 weighs more than winning $200 for me. I will take the gamble if it can be repeated 100 times. The question is taken from Thinking fast and slow, as always my judgment was correctly predicted in the book. I’m not surprised, as most of my judgments are predicted accurately in the book.

There is no reason to reject the gamble if it can be repeated 100 times. The expected return is $5000 with a very low probability of losing any money(1/2300). The one who rejects the single gamble is also prone to reject similar other gambles too. Because each gamble is evaluated separately and rejected, like the decision we made at the beginning. This is narrow framing, the decisions are taken separately.

Consider three tosses of the above gamble, let’s check the possible outcome and probabilities

• 12.5% loss $600
• 37.5% win $0
• 37.5% win $300
• 12.5% win $600

I will take the deal as there is only 12.5% chance of losing something. But the human are naturally narrow framer and If I was encountered with gamble independtly at different occussion I will turn down. We need paper and pen to calculate probabilities, our monkey brains are not good at this. We can reduce the pain of lossing the gamble by having a broader frame, for favourable gamble the probability of losing reduces rapidly.

The author have a sermon for you If you still haven’t convinced for taking a favourable gamble.

“I sympathize with your aversion to losing any gamble, but it is costing you a lot of money. Please consider this question: Are you on your deathbed? Is this the last offer of a small favorable gamble that you will ever consider? Of course, you are unlikely to be offered exactly this gamble again, but you will have many opportunities to consider attractive gambles with stakes that are very small relative to your wealth. You will do yourself a large financial favor if you are able to see each of these gambles as part of a bundle of small gambles and rehearse the mantra that will get you significantly closer to economic rationality: you win a few, you lose a few. The main purpose of the mantra is to control your emotional response when you do lose. If you can trust it to be effective, you should remind yourself of it when deciding whether or not to accept a small risk with positive expected value. Remember these qualifications

• It works when the gambles are genuinely independent of each other; it does not apply to multiple investments in the same industry, which would all go bad together.
• It works only when the possible loss does not cause you to worry about your total wealth. If you would take the loss as significant bad news about your economic future, watch it!
• It should not be applied to long shots, where the probability of winning is very small for each bet.

If you have the emotional discipline that this rule requires, you will never consider a small gamble in isolation or be loss averse for a small gamble until you are actually on your deathbed and not even then.”