Thinking More Clearly About Cost-Benefit Analysis
Brian Gongol

The disaster in New Orleans after Hurricane Katrina represents a titanic failure of cost-benefit analysis. Much has been said about the fact the city's levee system was only designed for a Category 3 hurricane. The system was designed to accommodate a 50-year storm -- that is, it was ready to withstand everything up to the worst storm every 50 years.

This decision, like all engineering decisions, was reached after performing a cost-benefit analysis. Unfortunately, too many cost-benefit decisions are undertaken using the wrong evaluation method.

The simplest form of cost-benefit analysis multiplies the probability of a hazard by its estimated impact. This is performed routinely in determining where to place stoplights and railroad crossing signals. Some people would prefer that a signal and gate be installed at every railroad crossing. But at an average cost of $150,000 per gate, that's simply not economically feasible. Instead, engineers and economists assign some estimated dollar value to the value of a human life -- say, $1 million.

The decision whether to install the crossing signal, then, is based on comparing the costs and benefits -- in this case, the "benefit" is the likely value of the life saved by the signal:

Probability of One Death at Crossing in 30 Years that Could Be Prevented By a Signal Value of One Life Estimated Benefit Cost of Signal Decision
1 in 1,000,000 x $1,000,000 = $1 $150,000 Don't Install Signal
1 in 1,000 x $1,000,000 = $1,000 $150,000 Don't Install Signal
1 in 10 x $1,000,000 = $100,000 $150,000 Don't Install Signal
1 in 2 x $1,000,000 = $500,000 $150,000 Install Signal

Of course, some people will object to this kind of analysis, suggesting that no cost is too high to save a life. But, in fact, we can spend too much to save a single life. Suppose that a train-crossing signal were installed at a site where the chance of a fatal accident were only one in a million. In that case, society would have invested $150,000 with only a very slight chance of a valuable return. That $150,000 would probably have been better spent on early childhood education or cancer research or CPR training -- all of which would have a very good chance of earning a very valuable return. Cost-benefit analysis is socially responsible and economically sound.

In general, a very simple evaluation of costs and benefits (like the decision where to place a train crossing signal) is adequate. It's a simple measurement of expected values.

However, expected-value breaks down as a cost-benefit analysis tool at a certain level. For instance, the Secret Service goes to extraordinary lengths to protect the life of the President of the United States, because a President's death is considerably more catastrophic than the death of most other individuals -- not because the President's life is intrinsically more valuable than a mechanic's or a preacher's, but because the violent death of a President can set off a chain of consequences that could lead to financial panic, political instability, and social unrest.

When simple expected-value analysis breaks down, engineers, economist, politicians, and other planners are obligated to consider minimax (alternatively called "maximin") solutions. A minimax solution seeks the best-possible outcome from the worst-case scenario. (The nomenclature difference between "minimax" and "maximin" depends on whether we're looking at the outcome as "cost" or "benefit"; the basic point is the same, that we are trying to make the best of the worst situation.)

Flood protections based on an expected-value estimate will probably be inadequate under a minimax approach. London, like New Orleans, is at high risk for catastrophic flooding, but London's defenses have been designed to handle a flooding that is only expected once in a thousand years.

In the case of New Orleans, it's evident that the worst-case scenario (or something close to it) has come true. But the risk has been clearly known for years, and it's clear that major hurricanes are bound to strike virtually every part of the US Gulf and Atlantic coasts.

The expected-value method breaks down for events of this magnitude. If we insist on inadequately preparing major cities for catastrophic events by using minimax preparations, then we can expect disaster when another hurricane hits New York, or when another massive power failure blacks out a quarter of the country, or when the big earthquake finally hits Los Angeles.

When an event is certain in the long run, there's no excuse for not using the minimax approach.