Actuarial work is demanding..., so you're arriving late at your hotel that night. The hotel manager has only two rooms left. These two rooms are exactly the same, except for one aspect: The fire alarm.....
The manager tells you that in the event of a nighttime fire due to the usual causes, guests in Room 1, equipped with Alarm 1, have an actuarial calculated 2% chance of dying. Guests in Room 2, equipped with Alarm 2, have only a 1% chance of dying.
However - things in life are always complicated - there's a slight problem.....
According to the manager...... The wiring of Alarm 2 is such that it sometimes causes electrical fires that increase the risk of dying in a nighttime fire by an additional 0.01%.
In other words, Alarm 1 is associated with a 2% risk of death and Alarm 2 is associated with a 1% + 0.01% (betrayal) risk of death.
Outcome
According to a study by Gershoff and Koehler, most participants choose the room with Alarm 1. This, even though this room 1 has double the increased risk of fire death, according the researchers. Reason: most participants found the tiny risk of "betrayal" (product malfunction) much more frightening than the much larger risk of actually dying. When people get upset by a tiny risk, they often paradoxically choose the much larger risk.
Personally I think a more imaginable risk 'weighs' stronger than a non-specific abstract risk and in general people are unaware of conditional probability effects......
Conclusion
This simple example proofs that emotion has a strong influence on risk decisions.
Just like in our actuarial profession, risk decisions are often irrational.
It is our duty as actuaries to demystify and to rationalize risk. However, sometimes we're victim of the same emotional bias....
Read more about this interesting subject on:
- Vaccination and betrayal aversion (2011)
- Safety First? The Role of Emotion in Safety Product Betrayal Aversion (2011)
However - things in life are always complicated - there's a slight problem.....
According to the manager...... The wiring of Alarm 2 is such that it sometimes causes electrical fires that increase the risk of dying in a nighttime fire by an additional 0.01%.
In other words, Alarm 1 is associated with a 2% risk of death and Alarm 2 is associated with a 1% + 0.01% (betrayal) risk of death.
What room do you choose as a professional actuary?
Outcome
According to a study by Gershoff and Koehler, most participants choose the room with Alarm 1. This, even though this room 1 has double the increased risk of fire death, according the researchers. Reason: most participants found the tiny risk of "betrayal" (product malfunction) much more frightening than the much larger risk of actually dying. When people get upset by a tiny risk, they often paradoxically choose the much larger risk.
Personally I think a more imaginable risk 'weighs' stronger than a non-specific abstract risk and in general people are unaware of conditional probability effects......
Just like in our actuarial profession, risk decisions are often irrational.
It is our duty as actuaries to demystify and to rationalize risk. However, sometimes we're victim of the same emotional bias....
Read more about this interesting subject on:
- Vaccination and betrayal aversion (2011)
- Safety First? The Role of Emotion in Safety Product Betrayal Aversion (2011)
Posts
LinkedIn Actuary-Info Group
It seems you completely forgot to multiply the 1% and 2% values by P(fireOccursDueToTheUsualCauses). Since this is very small, you'll find the decision rational.
ReplyDelete-Andrew
1% and 2% are the P(fireOccursDueToTheUsualCauses | Room X)...;-)
ReplyDeletePersonally I wouldn't choose any room and look for another hotel!!!
Anonymous - I agree with Andrew
ReplyDelete"IN THE EVENT OF a nighttime fire due to the usual causes, guests in Room 1, equipped with Alarm 1, have an actuarial calculated 2% chance of dying. Guests in Room 2, equipped with Alarm 2, have only a 1% chance of dying."
Dear Sirs Actuaries,
ReplyDeletemeticulous actuarial remarks as comments on this blog, and so true!
Nevertheless..., it states 'The wiring of Alarm 2 is such that it sometimes causes electrical fires that increase the risk of dying in a nighttime fire by an additional 0.01%.
This probability is therefore also 'intended' to be a 'conditional probability', just like the 1% and 2% probabilities IN THE EVENT of a nighttime fire.
As this aspect is clearly not 'smart' formulated in the 'Safety First?' research of Koehler/Gershoff, this misunderstanding - at first site - probably accounts more for the choice for the 2% risk room (with 0% unconditional 'wire fire' death risk) than other factors mentioned in the research.
In a way you could say that - unlike actuaries - average people don't perceive conditional (Bayesian) risk as conditional.....
Remains, the additional conclusion by Koehler/Gershoff their paper:
When the 0.01% betrayal risk associated with Alarm 2 was replaced by a mathematically identical nonbetrayal risk, namely, an elevated risk of structural collapse, most guests selected the alarm that was associated with the lower overall risk of death (1.01%).
Which 'proves' with more certainty that participants in the test probably don't choose on a mathematical basis, but on 'perception'.
Conclusion
All this proves (again) that statistical research questions have to be formulated and interpreted in a critical and sound way.
Try to avoid questions that depend on 'conditional probabilities' in surveys, questionnaires as much as possible. This also count for board room investigations in case of defining risk appetite.
Most people will not understand those questions and your actu(ari)al interpretation of e.g. risk appetite might - how well interpreted- be completely wrong.