(This section is a modified excerpt from my book Down to Earth)

Cost-benefit analysis is a logical way of making decisions based upon the probable outcomes of various courses of action. A cost-benefit analysis can be divided into five steps:

  1. Specify the possible options for action. These must be mutually exclusive; that is it must be impossible to choose more than one.
  2. List all the possible outcomes (i.e. sets of consequences) for each option. The outcomes on this list must be mutually exclusive and exhaustive. The list of outcomes is mutually exclusive if the outcomes cannot overlap (that is, no more than one of them can occur), and it is exhaustive if it includes everything that can happen (that is, the list is so complete that at least one of the outcomes on it must occur).
  3. Determine the probability of each outcome of each option.
  4. Assign a value (positive or negative) to each outcome of each option.
  5. The sum of the values times probabilities for each option is the expected value of that option. Select the option (or, in case of a tie, any one of the options) that maximizes expected value.
It is instructive to compare cost-benefit analysis with sort of simple consequentialist reasoning discussed in the previous section. Recall that this simple consequentialist reasoning also consists of five parts:
  1. A listing of all the possible options for action
  2. A listing of all the important consequences of each option
  3. A judgment concerning which set of consequences is best (or least bad)
  4. An assertion of the principle that we should choose the option with the best (or least bad) consequences
  5. The conclusion
 These, however, do not correspond point-for-point to the five steps mentioned above. The first item in each list is essentially the same. But in the simple consequentialist reasoning discussed in the previous section, each option for action is assumed to lead with certainty to a given outcome (which may consist of several different consequences, both positive and negative). In cost-benefit analysis there may be several different outcomes (each perhaps likewise consisting of a variety of consequences). These we list in step 2 of the cost-benefit analysis. Since which of these possible outcomes will occur is uncertain, we can at best assign to each a probability (step 3 of the cost-benefit analysis). Another difference between simple consequentialist reasoning and cost-benefit analysis is that in the latter we do not merely list and judge the consequences; rather, we assign to the complete set of consequences for each outcome a number that represents its total value (step 4). The conclusion is then drawn, not by logical inference, but by numerical calculation (step 5).

Suppose, to give a specific example, that we are designing a storage tank for some hazardous substance and are faced with the decision of making the tank double-walled or single-walled. These two choices constitute our options. (Of course, in a real situation, there would be other options, such as varying the thickness of the walls or other design features of the tank, but we are simplifying.) For each option, several outcomes or consequences are possible with regard to the tank's performance. In setting up the decision problem we must decide on a useful way to categorize these outcomes. Suppose we categorize them this way:

These outcomes are mutually exclusive; that is, each must rule out the others (for example, if the tank develops only a small leak, that means that it doesn't not leak and it doesn't develop a major leak). And the list of outcomes is also exhaustive; that is, it covers all the possibilities (necessarily, one of the three outcomes on our list will occur; there is no fourth possibility). These requirements are prerequisites for the calculation by which we make our decision.

Having defined options and possible outcomes, we must next determine the probability of each outcome, given each option. This we set out in a decision table, or decision matrix, as follows:

OPTIONS Never leaks Minor leak Major leak
Single wall 0.9 0.09 0.01
Double wall 0.99 0.009 0.001

According to this table, for example, the probability of a single walled tank never leaking is 0.9, the probability that a single-walled tank will develop a minor leak is 0.09 and so on. In practice, these probabilities would be derived from field studies on similar tanks, from engineering considerations, or from computer models. Their accuracy is crucial to a good decision.

Notice that the sum of the three outcome probabilities for each option (horizontal line) is 1. This is a result of the fact that the outcomes are mutually exclusive and exhaustive. One and only one of them can happen, so that, given a particular choice of option, the probablity of one of another of them happening adds up to certainty, i.e. 1.

We must incorporate one more element into our decision table before it will yield a decision: an estimate of the cost or benefit of each possible outcome. Quantifying costs and benefits is generally the most difficult aspect of formal decision making. Since we are keeping things simple, let's suppose we can put a dollar value on each outcome for each option: namely the profit or loss to our company resulting from the outcome, given the option. These profit or loss figures are calculated from the total set of consequences for each option and outcome. In our example, these consequences would probably include: the cost of installing and maintaining the tank, the profit gained from using the tank over a specified time period, and the repair and cleanup costs, if any, that we might have to pay if the tank leaks. If the tank never leaks, we expect to make a profit. But if it leaks, the cost of repairs and cleanup will cut into our profit and may result in a net loss. The loss will be greater the more serious the leak. I have made up some figures that represent a summing up of the consequences for each option and outcome. We place these profit or loss numbers next to their respective probabilities on the decision table (losses being indicated by negative numbers):

OPTIONS Never leaks Minor leak Major leak
Single wall 0.9        $20,000 0.09        $0 0.01        -$90,000
Double wall 0.99      $10,000 0.009     -$1,000 0.001      -$100,000

Thus, for example, this table indicates that if we built the single-walled tank, we would (over some specified period of time) realize a profit of $20,000 if it never leaked, break even if it developed a minor leak and lose $90,000 if it developed a major leak.

If we built many such tanks, we would expect to realize the $20,000 profit 90% of the time, break even 9% of the time and lose $90,000 1% of the time. Thus, on average, we would expect to realize a profit of (0.9 ´ $20,000) + (0.09 ´ $0) + (0.01 ´ -$90,000) = $17,100 per single-walled tank. This "average profit" is called the expected value or expected utility of the option (in this case, the option of building the single-walled tank). Similarly, if we built many double-walled tanks, we'd expect to make an average profit of (0.99 ´ $10,000) + (0.009 ´ -$1,000) + (0.001 ´ -$100,000) = $8,891. This is the expected value of the double-walled option.

Since, on average, we'd expect to make more money with the single-walled option, our best choice is to build the single-walled tank. That is the decision which the table yields.

The general idea governing such choices is the principle of maximizing expected value -- that is, of choosing the option that on average produces the greatest positive value or (if loss is unavoidable) the least loss. The ultimate justification of this procedure lies in utilitarian ethics: we are attempting to maximize happiness (understood as satisfaction of desire) under conditions of uncertainty. The probabilities represent the uncertainty. The values represent the desirability to us (either positive or negative) of various outcomes. To maximize expected value is thus to select the option that is most likely to maximize satisfaction of desire.

In general, decision problems may consider any number of options and any number of outcomes. For each option-outcome pair, we must, as in our example, estimate a probability and a value (i.e., cost or benefit).

It might be supposed that cost-benefit analysis provides a purely logical and objective means of making decisions. But, though logical (assuming the correctness of the utilitarian ethical tradition), it is by no means objective. The subjectivity of cost-benefit analysis is most glaring in the use of numerical quantities for values. These numbers always represent somebodyís judgement of value. In our example these quantities were monetary, and we assumed that we were making the choice on behalf of a firm whose sole concern was maximizing profit. Cost and benefit were measured in dollars gained or lost by the firm. Our decision ignored the environmental and human costs of a leaky tank, except as these might result in costs to the firm. Thus, while it may have been a rational decision given a value system in which this firm's bottom line is the only thing that matters, it might well have been an irrational decision given different concerns.

It is possible to include environmental costs and benefits in a cost-benefit analysis. Indeed, most of the cost-benefit analyses actually done by government agencies attempt to do so. Letís see how this might work with respect to our example. Suppose that the storage tank was to be located near a sensitive wetland and also that a serious leak might result in human injury or death. Then if we ascribe value to human beings and wetlands over and above their possible impact on the firm's profits, we would need to include injury to either in evaluating losses. As a result, we might well regard the $90,000 and $100,000 figures as gross underestimates of the loss caused by a serious leak.

But how could we improve these figures? The sorts of losses we are now considering are not readily quantifiable in monetary terms. If a dangerous leak occurs and someone is killed, how could we quantify the losses to that person and those who care about her? Is a human life worth $1,000,000? $10,000,000? Various suggestions have been made. Some have argued that the worth of a human life is equal to that person's earning power over a lifetime. Others have held that the worth of a life can be calculated from the amount of risk a person is willing to accept in order to earn a given salary. Both suggestions and others like them, are obscene. Is a retired person who will henceforth earn nothing therefore worth nothing? Is a rich person who is willing to accept little risk to earn more money thereby worth more than a poor person who has to accept a high risk job to support a family?

And how do we quantify potential injury done to a wetland? Is it simply the loss of dollars due to decreased hunting and fishing in the area? Or should we include the "scenic" value of the wetland as well? Should we count dollar loss just to people now alive, or dollar loss to all future generations affected by the damage? And what about injury to the plants and animals in the wetland themselves? Should their losses be part of the equation, or don't they count? What about the wetland ecosystem? Is it an entity capable suffering loss over and above the losses of the individual organisms that comprise it? If so, should its losses count in the decision?

The answers to these questions will always, once again, reflect somebodyís judgment. The practice of assigning monetary figures to values that are not normally expressed monetarily is called shadow pricing. Though nonmarketed goods, such as water quality or human life, have no standard monetary values, we may attempt to assign them "shadow prices" by various methods of comparison with things we do value monetarily. I mentioned and dismissed some suggestions for shadow-pricing human life a couple of paragraphs back. There are methods, some of them quite sophisticated, for shadow pricing all sorts of environmental values. We will not consider the details here, since all these methods are controversial. Regardless of how we assign shadow prices, their effect on the outcome of a cost-benefit analysis may be profound.

To illustrate how different values can produce a different decision, suppose we include shadow prices for the threat to both humans and the environment from a serious leak. We assume that a minor leak will not significantly harm humans or the environment, but a major leak would on average do damage in the range of $1,500,000 to humans and the ecosystem. Then, adding this loss to the previous figures for a major leak, the decision table would look like this:

OPTIONS Never leaks Minor leak Major leak
Single wall 0.9       $20,000 0.09        $0 0.01      -$1,590,000
Double wall 0.99     $10,000 0.009     -$1,000 0.001     -$1,600,000

The expected value of the single-walled option is now (0.9 ´ $20,000) + (0.09 ´ $0) + (0.01 ´ -$1,590,000) = $2,100 and the expected value of the double-walled option is (0.99 ´ $10,000) + (0.009 ´ -$1,000) + (0.001 ´ -$1,600,000) = $8291. Given this quantity of concern for human health and the environment, the double-walled tank is the better option.

To obtain this new table, we assumed that we could accurately shadow price damage to health and the environment. This assumption is, in most real applications, a pure political convenience. Numbers are needed, so numbers are found. But there is no independent reality against which to check them; no matter how sophisticated the method by which they were derived, they merely represent somebodyís (or some groupís) subjective judgment. But because this judgment is expressed numerically, it can make cost-benefit analysis seem a more exact and rigorous procedure than it really is.

It should be noted, however, that money values are not essential. Cost-benefit analysis can proceed with other measures of value as well. We might, for example, adopt an arbitrary scale of desirability from -1 (maximum undesirability) to 1 (maximum desirability) and use these figures instead of dollar figures in our calculations. But the numbers will be just as subjective.

In theory -- humanistic utilitarian theory, to be specific -- the best decision is one that uses a value scale that somehow "averages" the ranking of desirabilities for each individual. But how can we determine the desirability of something for even one individual? Suppose we simply ask the person. If she understands how the value scale is to be used, then she may exaggerate her values in ways that bias the outcome in her favor. But even if she tries to answer honestly, she may have little idea of where her values fall on our arbitrary scale. Moreover, we as interviewers might bias her response by the way we word our queries. Thus while this idea of averaging the desriabilities for all individuals with respect to a given value scale might be good in theory, it is largely unworkable in practice.

And who is to count as an individual? Do our descendants get a "vote"? How about crows? These questions go to the heart of the presuppositions of utilitarian ethics. Averaging the value scales of living human beings is a good procedure even in theory only if the only beings whose values count are humans who are alive today. That is a short-sighted theory.

Moreover, since the scale of value represents desirability, at bottom this whole procedure is based on the assumption that the best course of action is to maximize satisfaction of desires. It is based, in other words, on utilitarianism. But utilitarianism is not the only ethical theory. According to other ethical traditions, there are often good reasons to change or eliminate some of our desires, rather than trying to satisfy them.

There are still other difficulties. To perform a cost-benefit analysis, someone must first define both the options for action and the possible outcomes (the categories listed to the left and at the top of the decision table). These category definitions will affect the way we perceive the problem. The outcomes we considered in the case discussed above all had to do with leakage of the tank. This way of conceptualizing the problem may lead us to overlook other distinctive outcomes, such as a tank explosion. Presumably, this would fall under the category "Major Leak". But if we had considered it as a separate category, our decision table might have been quite different. Explicit consideration of this possibility may have led us to revise values or probabilities and, ultimately, to make a different decision.

Substantial reconception of the problem may also result from redefining the options. Perhaps the best option is one we never even considered: not building any storage tank and changing the whole manufacturing process so that the chemical it was to contain is no longer needed. Thus the way we limit or categorize the options can also affect the final decision.

Performing a cost-benefit analysis with all these limitations clearly in mind can sometimes be enlightening, particularly if the participants represent a wide spectrum of views. The process never yields a purely rational or neutral decision, for all the reasons elaborated above, but it can be a systematic way to compare the assumptions and desires of the various participants. It can be this, however, only if the various points of view are represented competently and articulately.

But because of their fundamental subjectivity and veneer of exactitude, cost-benefit analyses are frequently misleading. Many cost-benefit analyses are just technical sleights-of-hand for disguising foregone political conclusions as rational decisions. Institutions often use cost-benefit analyses to intimidate the unsophisticated, politicians frequently call for lengthy cost-benefit analyses in order to entangle and delay regulation (especially environmental regulation), and decision-makers may use them to depersonalize responsibility for judgments that are ultimately theirs.