Wednesday, February 04, 2004

Human Life - How Cheap Is It?

I thought this calculation was a bit shonky but, since reading Strawman's "Value Judgments - The cost of a human life" at the Australian (Self-Styled) Libertarian Society site, I've realised that I have a lot of practice to put in to match Ozblogistan's true masters of shonky mathematics and spurious logic. Strawman poses the question: "How much is your life worth in dollars?" By way of an answer, he presents this equation:

For the maths nerds, VOYL (the Value Of Your Life) is given by

[sic] = Maximum Payment (the most you would be willing to pay)
PSYL = probability of saving your life.

For the mathematically challenged, he presents this simple example, showing how easy it is to derive the monetary value of your life:

For instance if buying an airbag had a 0.1% chance of saving your life ** and you were willing to pay up to $1,000 for it, you have just valued your life at $1,000,000. Not a bad sum, and probably realistic for most people in Australia.


** Note this is not 0.1% chance of saving your life in an accident, but of saving your life. For instance, you had a 1% chance of having a accident, and it had 10% of saving your live in an accident, then it would have a 0.1% chance of saving your life. Don't let the lefties confuse you on this issue.

I doubt whether it would be possible to confuse Strawman on this subject; his cognitive functions appear to operate in a state, or at a level, beyond confusion. Still, it's possible that I might manage to confuse a few of the rest of you, so it's worth a try.

The first thing to note is that Steawman doesn't provide any of the theoretical underpinnings of his "VOYL" equation. There is a link to Strawman's extensive glossary of philosophical, political and technical terms, but nothing in the gloss linked to "life worth" explicitly supports the "VOYL" equation. Perhaps Strawman had one of those late night, ethanol induced epiphanies or, like Archimedes, he discovered it while he was relaxing in the bath. So my first task, before I go on to confuse you utterly on the issue is to attempt to make sense of this "VOYL" equation. To do this, I'll be considering the airbag purchase as a bet.

An obvious objection to this treatment of the subject is that the "VOYL" equation, despite its questionable philosophical rationale, assumes rational choice in relation to costs and probabilities and betting is an inherently irrational activity. Perhaps so, but betting examples provide a way to explain issues involving probabilities in terms that most of us can understand. In addition, while it may be irrational to take your weekly pay packet down to the gee-gees on a Saturday expecting to leave with enough money to retire on, once you've made the decision to bet there are some strategies for maximising your returns (or minimising your losses) which work better than others. To the extent that you are irrational, you'll regularly put all your earnings on the horses or the dogs; to the extent that you are rational you'll try to ensure that the horses you back aren't complete donkeys.

Buying an airbag for $1,000 when there's a 0.1% probability that it will save your life is roughly equivalent to laying out $1000 on Potentially Fatal Road Accident which is running at odds of 999:1 in Race 5 at Eagle Farm. If you laid such a bet, and Potentially Fatal Road Accident won, you can be confident of two things; firstly that there would be a stewards' inquiry and secondly that the bookie with whom you laid the bet wouldn't be there when you turned up to collect your winnings (plus original stake) of 1 million dollars. Unless he'd laid the bet off on someone else, of course, in which case the entire bookie's ring would be empty for the rest of the day.

This presupposes that the 999:1 odds posted on Potentially Fatal Road Accident were in fact fair odds and that the horse had only a 1 in a 1000 chance of winning. "Smart" punters don't back horses on this basis; they look for horses where the bookies are paying out at odds which are above their (the punters') own estimate of the fair odds. Bookies, in turn, adopt a simple strategy to ensure that no matter which horse wins, they come out ahead of the punters at the end of the day; the initial odds are set below the fair odds (so Potentially Fatal Road Accident would only start the day quoted at 180:1) and shorten the odds on horses that are especially favoured by the punters.

This points to a necessary modification to Strawman's theory; "PSYL" represents not an objective measure of the probability that some measure will save your life, but a subjective one. The higher your subjective estimate of the probability that an airbag will save your life, the more willing you will be to shell out $1,000 for one. Suppose, for example, I believe that the probability that an airbag will save my life is only 1 in 10,000 (bookie odds of 9999:1). If I shell out $1,000 dollars for an airbag, by Strawman's logic, I have just valued my life at $10,000,000. On the other hand, if I rate the probability at 1 in 100 (99:1), the valuation is only $100,000. This is starting to look a little nonsensical.

The nonsense gets worse if we substitute a somewhat cheaper life preserver into Strawman's example. The unit price of a condom is, roughly, $1.50. Like Strawman's airbag, it's a one use item. Let's assume that your chance of catching a fatal dose of AIDS is 0.1% (as in Strawman's example, it's the product of your chance of getting a root and your chance of getting a dose in the process). If you're sensible, and use the condom, by Strawman's logic you've just valued your life at $1500. Allowing for inflation, that's probably about the going rate for human life in Casablanca, circa 1942.

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