OddThinking

A blog for odd things and odd thoughts.

Estimated Value of Passenger Airbags

I don’t buy cars on impulse. I am one of those people who gets angsty about such a big purchase, and I come over all analytical to overcome my fear.

How can I rationally choose between different cars? Well, I list all the different features, come to a personal judgement about what they are worth to me, rate all the cars being evaluated, and decide which one gives the best value for money.

Some items are moderately easy: I can judge how much more I will pay for a car with a built-in CD player by looking at the price of an aftermarket CD player, plus the installation cost.

Some items are pretty subjective: How much happier (or sadder) would I be with 10 more kilowatts of engine power, measured in dollars.

Some take a bit of calculation: Every time I drive during fog, I would pay $1 to have fog-lights turned on. Now, how often will I drive during fog during the life of this car?

During such a purchasing process, I stumbled over one item that posed a tricky dilemma: How much more would I be willing to pay for an equivalent car with a passenger-side airbag?

How could I possibly put a dollar value on human life? Let me show you!

First, I estimated the probability that the car would be involved in a horrific accident that – but for the passenger airbag – would have killed the passenger.

That was a tough calculation. I had to take into account the expected time that I would own the car, the probability that I would be involved in a serious accident each year (given my normal driving style and risk-profile), the percentage of those accidents that would be on the borderline where an air-bag would mean the difference between life and death for the passenger, and the percentage of time that I was involved in such an accident that I would actually have a passenger in the front seat.

Then I came to the hard part: how much was it worth to me for my passenger (probably a family member or friend) to not be (certainly) killed by my driving? Tough question. A lot, clearly! In fact, all of it! All of my money to save that life! There’s the solution! I substituted in my net worth for the value of a human life.

So multiplying the probability of a passenger air-bag saving a life by my net worth that I would sacrifice to prevent a (certain) death, gave me the expected value of a passenger air-bag.

I ignored the expected residual value (i.e. that the unused airbag would increase the re-sale value of the car when I sold) and the expected cost of replacing airbags that fired in non-life-versus-death situations – they are both trivial and probably pretty much cancel out.

What was the result? What was a passenger air-bag worth to me?

Fifty measly cents!

I felt a little ungenerous, but I couldn’t argue with my logic. Can you?

p.s. For the record, yes, my current car has a passenger airbag.


Comments

  1. Just out of interest, what model car are you looking at that has an optional passenger airbag? I didn’t think there were any.

  2. This is an historical story. I think the calculations were done in 1999.

  3. I guess you didn’t put the cars COLOR into consideration…? A friend of my family (his name is Ferenc) bought his first car in 1978, a black Ford Capri that was run over by a lorry the very next day. The Ford was parked outside his own garage. He then had to look for a new car for the insurance-money.

    He came home with a dark green Saab 99. On his way home from the car-dealer, waiting for green light at an intersection, a guy on a moped crashed into his passenger-door. Ferenc kept the car for 3 years in wich time it never experienced any 6 months period without an accident.

    In 1981 he started working as a car mechanic at the local BMW-store and felt obliged to by one of their models. He was glowing with pride, cruisig along on his way home with his brand new, dark-blue Beemer. Until a taxi tried to overtake another car in the opposite lane. Do I need to say anything else than HEAD ON…? Luckily they all climed out of the wrecks with minimal injuries and Ferenc could go buy himself a new car.

    Ferenc still works at BMW and is a proud owner of his third YELLOW 5-series. None of these 3 cars have ever been hit by so much as a fly…

    Safe driving

  4. I am one of those people who gets angsty about such a big purchase, and I come over all analytical to overcome my fear.

    Research shows that humans suck at making big decisions rationally. Best to obsess over the small stuff and listen to your gut on the big stuff; that gives you the biggest chances of making the right moves.

    I have to say Scott Adams’ approach to the problem seems intelligent, though.

  5. Ferryman,

    That’s a funny anecdote, but it didn’t affect my decision for two reasons.

    One is that hypothesis that car colour affects accident rates has had little scientific support.

    The other is that I was choosing between several models of car rather than several instances of cars. The colour choices between the car models were effectively identical.

  6. Aristotle,

    Can you recommend any further reading there? I don’t doubt that humans are crap at rational decisions, but I would be interested in hearing how they’ve shown that attempts at carefully-considered “rational” decision-making turns out to be less effective than “gut feel”.

    Thanks

  7. Ugh, I wish I had a citation! I read it somewhere semi-reputable a while ago (a bit over a year ago, I think, maybe a little longer), but I can’t for the life of me remember where, and my handful of attempts to tease a citation out of a search engine have been less than successful – as you can imagine for a query with no obvious strong keywords.

  8. Julian,

    I don’t think you should discounting the replacement cost of airbags which fire accidentally or in non-life-vs-death situations as trivial – according to research, the 2001 cost of replacing a single airbag was NZ$1320, so if my car had 4 such airbags (driver+passenger, front+side), one good 16km/h jolt would effectively write off the vehicle (NZ$5280).

    However, the same research shows both that there is subtantial benefit in the non life-vs-death case, and that you are also seriously undervaluing the dollar worth of the human life (unless your personal net assets are rather more substantial than they look). The paper puts a single life (death) at AZ$2.47 million dollars, based on “willingness to pay” settlement figures in legal claims.

    The summary of the paper is (roughly) that it’s economically viable to retro-fit or replace airbags on vehicles in NZ up to 14 years old, but that it’s also far more cost effective if they come as standard on a new car….

  9. I remember reading something similar, although I think it was implying something different: that people will try and optimise the easy variables, which are often the less important ones (but because they’ve optimised them, they “feel” like they’re more important), whereas “gut feel” would give them a much better indication of the value of the item.

    The study (IIRC it was a scientific study done somewhere) wasn’t designed to show that we’re bad at maths, but our gut feel is actually very good at solving problems with tons of variables, which is very difficult with “real maths”. — you can keep about 3 numbers in your “head”, but have a feel for many many numbers in your “gut”.

    If you used the analysis of the air bag in your purchasing decision, you may optimise on that value rather than something else which may have a far greater impact on how safe the car is (like perhaps colour).

  10. I know you’re not really interested in a normative cost of human life here, but I just found Peter Martin blogging about a research paper that used speed limit changes and road mortality rates to estimate the value of a human life. Could be useful next time it comes up at trivia…

    Turns out it’s (1997) US$1.54 million.

    The reference is in the blog post.

  11. The book Hagakure was written by a samurai a couple of hundred years ago, and is a collection of his thoughts and opinions on how to be a samurai – effectively it’s meant to be a manual. (The book is central to the movie Ghost Dog btw)

    One of the best ideas (imo) in it is: any critical decision should be made in the space of seven breaths.

    Authoritative-sounding support for that say that your first instinct, after a bit of time thinking about important factors, is generally pretty good, and that any amount of time after that you just spending second-guessing yourself and going around in circles.

    The classic logic/instinct problem suddenly occurs to me here. How did it go? $100 is under one of three cups. You pick one. You’re shown that another is empty. Do you now want to change your choice? And there’s some dodgy probability calculations to rationalise changing. Classic example of getting yourself into a lather of second-guessing, when you know full-well that your first guess was as good as any other. Better probably, since the guy running the scam probably knows you’ve guessed correctly and is trying to convince you to change so he keeps the money.

    I’m sure I have heard of psych experiments where they’ve actually tested this second-guessing syndrome (possibly in the same conversation) that returned some sort of quantitative result supporting first guess vs second, but it was third-hand – can’t give you any references.

    In my personal experience though, it seems to have been borne out to some extent, and it “feels right” – in the gut, you know?

    😉

  12. The classic logic/instinct problem suddenly occurs to me here. How did it go? $100 is under one of three cups. You pick one. You’re shown that another is empty. Do you now want to change your choice? And there’s some dodgy probability calculations to rationalise changing.

    You are probably thinking of the Monty Hall problem. Actually, the probability is not dodgy at all. If the person lifting the cups plays according to the rules (i.e. they always lift an empty cup, regardless of whether your initial choice was right or wrong), then changing your choice is provably the correct action, in terms of expected outcome.

  13. There are studies about second-guessing, and they show it is a good thing!

    Here is a non-peer-reviewed summary:

    The most well known test-taking strategy advises students to never change an answer to a multiple-choice item. The justification of this theory is that the initial impression is usually correct. In fact, many faculty members advise their students not to change answers (Kussler, 1988). The literature states that, although most students believe in this theory, it is more common to see students change answers (Haase, Riley, Dunn, & Gaskins, 1992). In fact, not only do most students change at least one answer to a multiple-choice question, the overwhelming majority of these changes are from incorrect to correct answers (Benjamin, Cavell, & Shallenberger, 1984).

    For peer-reviewed, try:

    Effects of Student Confidence and Item Difficulty on Test Score Gains Due to Answer Changing, Philip H. Ramsey, Patricia P. Ramsey & Michael J. Barnes, Teaching of Psychology, Volume 14, Issue 4, 1987, DOI:10.1207/s15328023top1404_3

    Significant gains, even for changes based on low confidence, were intepreted as suggesting previous cautions about answer changing are not warranted.

    To quote Carl Sagan: “I try not to think with my gut. If I’m serious about understanding the world, thinking with anything besides my brain, as tempting as that might be, is likely to get me into trouble.”

Leave a comment

You must be logged in to post a comment.