# Your Money or Their Life?

How do you put a dollar value on a human life? It's not something anybody likes to do, but when faced with a decision as to whether to spend money to reduce some risks, it's what you have to do ...

It is December, 1789. You are riding in an stagecoach.

A masked man appears at the roadside. He orders the coach driver to stop. He draws out a flintlock pistol, and waves it threateningly at you and the other travelers in the stagecoach. “Hand over some money”, he growls, “or I may kill someone tonight…” Out of the corner of your eye you can see what may be another highwayman, perhaps with the same strange proposition, waiting patiently further up the road.

Knowing that you may need more information to make your decision, the highwayman draws out a parchment and hands it to you. The document explains that he is a very inaccurate shot. Every evening he draws out his gun and tries to shoot someone. However, on average he only actually hits one person per year. He is a reasonable fellow and as honest as a highwayman can be. If everyone who travels the road pays him \$5, he will spend his evenings studying the violin instead. He notes (parenthetically) that he is a very busy and efficient highwayman and that he stops and threatens exactly 1,000 people a year. So if everybody pays him \$5, he will receive \$5,000 and an average of one life per year will be saved.

Do you pay?

It's a lot more difficult valuing other people's lives than it is your own. The highwayman's proposition is not dissimilar to the difficulty faced by a government in deciding policy, or a company incorporating a safety feature into a product: a change might cost everybody \$50 a year, but is expected to save one life per 100,000 population per year. Should it be adopted?

One approach to this is called Willingness To Pay (WTP). It's title describes it well: simply ask people how much they would be willing to pay. Such studies have indeed been done, and the answer typically arrived at is that saving a “statistical life” — that of a random individual &mdash is worth somewhere between \$1.6 million to \$7 million.

The highwayman has offered you and your fellow travelers the opportunity to save one statistical life for \$5,000 (in 1789 dollars). You decide you are willing to pay this amount. You each give the highwayman \$5 and continue on your journey.

As you suspected, a second highwayman was loitering further along the road. He stops the coach. His proposal is similar, but he is clearly a nastier fellow. If you don't pay he will try and shoot one of the children at the local orphanage. He asks for \$10. You decide that you care more about children than you do about adults, so saving on average one child's life per year is worth \$10 to you. You pay the demand and continue your journey.

This is consistent with many studies: an unknown child's life is worth more to us than an unknown adult's life. We will also pay more if the death is considered slow, painful, or gruesome. We will pay more to prevent cancer than car accidents.

An expert negotiator boards the coach. You explain what has happened. She looks at you and laughs. “Did you ever stop to think that the highwayman might be willing to settle for a lesser value if you can justify it? Or that the highwayman will demand more money the richer you are? You need a different approach to valuing human lives.” An economist, who is traveling with you, agrees. “The value of a human life”, he suggests, “is no more or no less than the sum of all the person's earnings over their life time. We must, of course, place a value on any work they did for other people which they could have done for money. The fact that my cooking is done by my wife, rather than by my maid, does not decrease its value”. You murmur in agreement.

Fortunately one of your fellow travelers is a tax inspector who just happens to have with him an anachronistic laptop with exactly the right data on it. He calculates the net present value of current lives, estimating future income, taking into account all unpaid work, and using current interest rates. He also estimates future inflation, and so arrives at a figure of between \$15,000 and \$2,000,000 (1996) dollars, depending upon the age of the person being considered. You decide to call this the Human Capital approach, and you and your fellow travelers agree to use this figure to try and negotiate with the next highwayman.

Just then another highwayman stops the coach. He proposes that you each give him \$10 dollars. You propose \$4 dollars, based upon your new method of valuing human life. “Wait a minute”, he says, “although I can agree with your argument that since a human life is worth \$4,000 it does not make sense for you to pay me more than \$4, you are forgetting about the people I don't kill. I wound quite a few. In fact, I seriously injure 1 in 10 of the people I shoot at. On average, it takes them five years to fully recover from their wounds and they end their days a full seven years earlier than they would otherwise. Surely preventing that is worth an additional \$3 to you?”

You look at each other and realize your mistake. You should have taken into account both the quality and the quantity of the lives saved. You decide on another approach. You will value each life-year saved at a figure of \$100 (in 1789 dollars) when the person is healthy. You will call such a year a Quality Adjusted Life Year (QALY). You decide that a person who is seriously wounded enjoys his years only half as much as someone who is healthy. Crunching his demographic models, and discounting all the values using the current long term interest rate, you decide that the highwayman has a point. You haggle and agree a figure of \$5. You pay and move on.

The economist looks worried. “This road may have many highwaymen,” he points out, “each using this new Your Money Or Their Life approach. We only have a limited number of dollars: we can only be willing to pay the highwayman if we have money left to pay him with. Indeed, if we respond to every demand we receive we will make ourselves so poor that we will no longer be able to afford a doctor or an apothecary if you become sick. In effect, by giving money to the highwayman we are slightly increasing the risk of our own deaths.”

The economist suggests that instead you all agree on a total amount you are willing to pay to save other people's lives. Perhaps this should be limited to 10% of your income. Each highwayman will be asked to submit a demand, and at the end of the journey you will send payments to those highwaymen whose propositions will result in the greatest saving o f Quality Adjusted Life Years. There will be highwaymen whose demands won't be met, and lives that won't be saved. But at least you will have made the best possible use of the money you spent.

The above story illustrates some of the methods that are in current use for making decisions where a risk to human life must be balanced against dollars and cents. Many things can be made safer if they are more expensive. Governments can always spend more money on reducing risks and saving lives, but at some point the public is no longer willing or able to pay the cost.

Different governments (and even different agencies of the same government), use different methods to determine the value of lives saved, and thus make different decisions about when risks should be addressed, and when they should be ignored. For example, the US EPA uses Willingness to Pay (WTP) as a criteria, the USDA uses a hybrid Human Capital/Willingness To Pay approach, and the US FDA uses a Quality-Adjusted Life Year (QALY) approach.

There is no one right answer in valuing a statistical life. There is, however, one answer that may be wrong. Do not use the size of possible damage awards as a method of valuation. The courts do not like to be used this way — and in the past have awarded punitive damages as a result.

If you want to delve into this topic more deeply, Donald Kenkel's summary paper on this topic is a good starting point.

27 May 2005

To get notified when new articles appear, subscribe to the Risky Thinking Newsletter. It's low volume: we don't send out an issue unless there is something interesting to say. You can also subscribe to our RSS Feed

Recently published articles can also be found here.

Agree or disagree? I'd like to hear your thoughts. Please initially use the contact form to get in touch.