Risk Policies: Framing and Rationality
A classic demonstration of how framing concurrent decisions in terms of gains versus losses leads to inconsistent risk preferences, where the logical rule of dominance is violated due to narrow bracketing. Based on Kahneman and Tversky's prospect theory experiment.
THE IDEA
SPEAKING OF RARE EVENTS
“Tsunamis are very rare even in Japan, but the image is so vivid and compelling that tourists are bound to overestimate their probability.”
“It’s the familiar disaster cycle. Begin by exaggeration and overweighting, then neglect sets in.”
“We shouldn’t focus on a single scenario, or we will overestimate its probability. Let’s set up specific alternatives and make the probabilities add up to 100%.”
“They want people to be worried by the risk. That’s why they describe it as 1 death per 1,000. They’re counting on denominator neglect.”
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RISK POLICIES
Imagine that you face the following pair of concurrent decisions. First examine both decisions, then make your choices.
Decision (i): Choose between
A. sure gain of $240
B. 25% chance to gain $1,000 and 75% chance to gain nothing
Decision (ii): Choose between
C. sure loss of $750
D. 75% chance to lose $1,000 and 25% chance to lose nothing
This pair of choice problems has an important place in the history of prospect theory, and it has new things to tell us about rationality. As you skimmed the two problems, your initial reaction to the sure things (A and C) was attraction to the first and aversion to the second. The emotional evaluation of “sure gain” and “sure loss” is an automatic reaction of System 1, which certainly occurs before the more effortful (and optional) computation of the expected values of the two gambles (respectively, a gain of $250 and a loss of $750). Most people’s choices correspond to the predilections of System 1, and large majorities prefer A to B and D to C. As in many other choices that involve moderate or high probabilities, people tend to be risk averse in the domain of gains and risk seeking in the domain of losses. In the original experiment that Amos and I carried out, 73% of respondents chose A in decision i and D in decision ii and only 3% favored the combination of B and C.
You were asked to examine both options before making your first choice, and you probably did so. But one thing you surely did not do: you did not compute the possible results of the four combinations of choices (A and C, A and D, B and C, B and D) to determine which combination you like best. Your separate preferences for the two problems were intuitively compelling and there was no reason to expect that they could lead to trouble. Furthermore, combining the two decision problems is a laborious exercise that you would need paper and pencil to complete. You did not do it. Now consider the following choice problem:
AD. 25% chance to win $240 and 75% chance to lose $760
BC. 25% chance to win $250 and 75% chance to lose $750
This choice is easy! Option BC actually dominates option AD (the technical term for one option being unequivocally better than another). You already know what comes next. The dominant option BC is the combination of the two rejected options in the first pair of decision problems, the one that only 3% of respondents favored in our original study. The inferior option AD was preferred by 73% of respondents.
When to use it
Strategic Management: Evaluating a portfolio of R&D projects as a group rather than individually to counteract the bias of risk aversion in gains.
Public Health Messaging: Understanding the impact of framing (e.g., survival rate vs. mortality rate) helps craft messages that accurately convey risk without triggering systematic biases.
Negotiation: Recognizing when the other party is framing the negotiation as a series of individual gains to exploit your risk aversion, instead of a broader exchange.
Personal Finance: An investor holding a losing stock faces a choice between a sure loss (selling) and a gamble (hoping to recover). Recognizing this as a 'domain of losses' helps explain the inclination to hold losing positions too long.
FROM THEORY TO EVERYDAY LIFE
In practice
Original Kahneman & Tversky Experiment (Gains and Losses)
73% of subjects chose a sure $240 gain over a gamble with a higher expected value, and chose a risky loss over a sure loss. The combination of their choices (A and D) was strictly dominated by the rejected combination (B and C), highlighting the perils of narrow framing.
Comparing Concurrent Decisions Together
A team evaluates a small guaranteed gain and a separate possible loss. Before choosing, it compares the combined outcomes of its preferred pair with those of the rejected pair. This can reveal that choices appealing in isolation produce an inferior overall result.
A MOMENT TO REFLECT
Put it to work.
When evaluating a risky investment, do you look at the individual bets in isolation (narrow framing) or as part of a larger portfolio? How does your frame change your willingness to take risks?
Think of a time you avoided a 'sure loss' by taking a bigger gamble. Did the framing of the situation as a 'loss' territory cause you to make a riskier choice than you normally would?
How can you force yourself to 'broad bracket' decisions to avoid the kind of dominated choice demonstrated in the $240/$750 problem?
References
- Prospect Theory: An Analysis of Decision under Risk — Daniel Kahneman, Amos Tversky (1979)
- The Framing of Decisions and the Psychology of Choice — Amos Tversky, Daniel Kahneman (1981)
CONTINUE THE CONVERSATION
Source texts
- Thinking, Fast and Slow (Daniel Kahneman)