Fireman Mortality, Behavioral Finance, and the Conjunction Fallacy

According to a new NEJM study, fireman are more likely to die from a heart attack running up the stairs to a fire, than from the fire itself.

Firefighting is known to be a dangerous occupation. What is less appreciated is that the most frequent cause of death among firefighters is heart disease rather than burns or smoke inhalation. Cardiovascular events, largely due to coronary heart disease, account for 45% of deaths among firefighters on duty.

Many people might find this conclusion surprising. Why? Because in thinking about firefighter mortality, and the riskiness of the occupation, it might seem reasonable to imagine that firefighters die so disproportionately often from fighting fires that it is the primary cause of death.

That is incorrect. It is an example of what is in behavioral finance usually called a conjunction fallacy, when it is assumed that “specific conditions are more probably than general ones”. Here is a well-known example from Dan Kahneman and Amos Tversky:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more likely?

  1. Linda is a bank teller.
  2. Linda is a bank teller and is active in the feminist movement.

Most people answer the question with 2), that Linda is in a bank teller and a feminist. The more probable answer, of course, is that Linda is simply a bank teller: It is more general, and therefore more likely.

It is easy to make a similar mistake in thinking about fireman mortality. Given that they fight fires, and that is a well-known hazardous occupation, you might think that the mortality risk from fire-fighting would dominate the risk from other causes of death. The trouble is, literally, that coronary disease is so widespread in the population that the incremental increased risk from it is not sufficient to make it more likely that firefighters die fighting fires than from heart attacks.

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Comments

  1. Brian says:

    they are also characteristic of the work performed by police officers, military personnel, and persons in various other occupations.
    The work is similar but the people are not.
    Guys in the military tend to be younger – and when you’re older the physical fitness thing is not, generally, an optional deal. You stay fit or they will make you – and they can initiate ‘unfit for service’ if you refuse to stay in shape.
    I don’t know firefighters but they seem to run all the way from ‘kid’ to ‘middle-aged guy’. Likewise I don’t know about their PT routine but I doubt it would be as intensive as most units would enforce on their troops.

  2. Phil says:

    good catch kadroo!

  3. Regret says:

    Possible typo: “specific conditions are more probably than general ones”. Probably s/b probable?

  4. worth says:

    Read the book Fooled By Randomness, by Nicholas Nassim Taleb. Overflowing with theories, studies, and truths (though he himself may not acknowledge them as “truths”, anti-dogmatic skeptic that he appears to be), it’s a stunningly insightful and informative read. He’s a financial trader-philosopher who cites Kahneman and Tversky, as well Greek historical figures such as Solon, extensively, and it WILL change your perspective on just about everything you stumble upon in your daily walk through life. You’re welcome.

  5. lanceypoo says:

    worth you reading that 5 years too late is like vic’s having a painting of the titanic

  6. worth says:

    lanceypoo, your comment is an excellent illustration of the case of presumptive error with incomplete data: because I commented on a book today, you presume that I read it recently. Au contraire – I read it when it was published, and I refer back to it whenever I get the chance. Also looking forward to his next work, due out in April! Thanks for your assistance.

  7. Speaking of Taleb’s new book, I recently read it in galleys. It is maddening, smart, discursive, and generally a must-read.

  8. Andy Nelson says:

    I recently completed a study that shows that investing in stocks consistently provides annual returns in excess of 25%. Of course I ignored October 1929, the six months around the dot com collapse, and a few other inconvenient data points.
    I had an emotional reaction to this study. It is worse than statistically flawed. I think it is immoral to ignore the 9/11 deaths.