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A mathematical approach to understanding the diversity of ethical decision making.

Society judges the competence and the liability of engineers by their adherence to commonly accepted standards of behavior such as the National Society of Professional Engineers' Code of Ethics or a professional societys' more specific code of ethics. Professional practice, and therefore control of the profession, is dictated by the acceptance of these codes.

Yet, often, when engineers are confronted with the subject of professional ethics, they have one of two negative reactions. The first is to downplay the importance of the topic because of its subjective nature. Ethics do not have the hard facts of mathematics or the structure of the scientific method as a basis for the determination of the correct answers. For this reason alone, ethics are often dismissed as not being worthy of serious study by engineers, who are, by nature, hard facts oriented.

A corollary response is that since there are no formulae or procedures that lead to "right" answers, the study of engineering ethics is best relegated to philosophers and social scientists, individuals who do not do "real" engineering. The opinion of many engineers seems to be that only when one is able to develop a set of guidelines for ethical decision making will the field be appropriate for engineers to study.

The fact is that ethical standards are a basis by which most engineers are evaluated. Not knowing these standards would be like a student being required to get an "A" in a course without having any knowledge of the grading criteria..

In spite of the opinion of many engineers, ethics' apparent lack of mathematical content has nothing to do with the importance of the subject: ethics are the foundation for the evaluation of the engineer and thus actually play a pivotal role in the decisions which, by the nature of his/her education and expertise, the engineer is called upon to make every day.

Of greater concern for ethical engineers is that many engineers, especially in their early years, are conditioned to solve problems "by the book." While the selection of appropriate formula, say, for calculating the stresses and strains for a bridge, is acceptable in most cases, the correct procedure alone is not enough. The ultimate test of the bridge will be its capability to withstand the weight of traffic without collapsing. Adequate strength in real life is more important than appropriate procedure.

The study of engineering ethics is different from the study of other engineering subjects in that ethics do not necessarily have one right answer for each problem that engineers face. This lack of correctness is unsettling for many engineers, who would prefer to leave such nebulous questions to philosophers and lawyers. This abdication is tantamount to allowing people with little or no background in the engineering thought process, let alone technical understanding of an extremely diverse set of disciplines, to determine the means by which engineers will be evaluated.

In this article, the familiar language of mathematics, specifically the nomenclature of naive set theory is used to explain the importance and diversity of ethical decision making to the engineering professional. It is hoped that, by using familiar terms to explain unfamiliar concepts, both the engineering professional and soon-to-be practicing engineer will understand the relevance of ethics to their professional lives.

Set theory

Before beginning the discussion of engineering ethics, a brief review of the fundamentals of set theory will be useful.

The underlying concept that will help in the understanding of engineering ethics is that of a set (Figure 1a). While there may be some discussion on what actually constitutes a set, for the purposes of this article, a set will be defined as "a collection of objects, called members or elements of the set." These objects need not be tangible; objects may be thoughts or ideas or even sets containing other objects. The elements in a particular set are usually related in some fashion. For example, the set of interest may include all possible outcomes of an experiment, the names of all registered voters in a geographic region or all possible actions in a response to a certain stimulus. The objects need not be capable of enumeration; it is sufficient to be able to describe the elements themselves or their relation to each other. For all practical purposes, sets are assumed to be finite, but, in theory, most sets are assumed to be infinitely large.

In addition, a set may be defined that contains all the sets that are of interest. This set is referred to as the universal set or universe. It is denoted by U and is important because it limits the number of sets that are under discussion at any given time.

Subsets can be also defined. These are important because many times only the elements of a larger set that meet very specific criteria are of interest. Mathematically, subsets are defined in the following manner: Let A and B represent sets. Then A is a subset of set B if and only if either of the following is true: (a) each element of A is a member of B; (b) no element of A fails to be a member of B.

It should be obvious that both conditions set forth in the previous definition will be met if either condition is met. In simple terms, in order for A to be a subset of B, all the objects in set A must be with in set B. A is a proper subset if all of its elements are also elements of B but not all the elements of B are contained in A (Figure 1b).

It is not necessary for A to be a subset of B. If none of the elements in A are present in B, then A and B are called disjoint sets (Figure 1c). If some of the elements in A are present in B but not all the elements in A are in B and some of the elements in B, but not all, are present in A then the sets A and B intersect. The common elements of the sets A and B are the intersection of A and B (Figure 1d) while all the elements of both A and B make up the union of the sets A and B (Figure 1e).

Set B is not limited to having only A as a subset. In fact, every set has [2.sup.n] subsets where n is equal to the number of elements. This is defined as the power set of B. The power set P(B) includes all possible combinations of elements to form all possible subsets as well as the null or empty set. Assuming there are n elements in B, then the number of elements in the power set ([2.sup.n]) can be thought of as representing the number of options that the decision maker has when he or she is told to select as many of the elements as is necessary to solve the problem. In other words, P(B) represents the entire decision space for a particular problem.

With this brief review of set theory as a background, it is now possible to move on and explore some of the issues facing engineers as they study the field of professional ethics.


Although the importance to the engineer of understanding professional ethics has been already addressed, the term ethics has not been properly defined. In simple terms, ethics is usually regarded as the implementation of an individual's set of values. A more strict definition is..."the system or code of morals of a person or group that sets standards as to what is good or bad or right or wrong in one's conduct." Engineering ethics are defined as "the study of the moral problems confronted by individuals and organizations involved in engineering."

Therefore, it is obvious that the term ethics does not refer to only one set of behaviors and beliefs, but to a myriad of sets that are appropriate for different individuals, organizations and societies. For example, in a hypothetical world, there may exist only three values: value 1, value 2 and value 3. In this imaginary world, all moral codes are based solely on these three attributes and every action is judged by some combination of these attributes. Therefore, there exist eight possible value systems ([2.sup.3]) in this hypothetical world. That there is overlap between the various value systems can be seen in Figure 2. The eight value systems would be: * value 1; * value 2; * value 3; * value 1 and value 2; * value 2 and value 3; * value 1 and value 3; * value 1, value 2 and value 3; and * The empty set or no values.

The empty set, or amoral condition (having no moral values), would introduce broad complications in regard to an individual's behavior, so, for purposes of this discussion, the possibility of the empty set will be ignored, reducing the set of viable value systems to seven.

With the hypothetical three value system shown in Figure 2, the possibility of different individuals proposing different solutions to an ethically ambiguous situation in which all proposals are morally correct solutions can be discussed. By ethically ambiguous, it is meant that the right solution to the dilemma is not obvious; in fact there may be several right answers. For example, individual 1 who possesses value system 1 may chose a solution that is consistent with value 1 but may or may not be consistent with values 2 and 3. In like manner, individual 2, possessing value system 2, may chose a solution that is consistent with value 2 but may or may not be consistent with values 1 and 3. The same pattern would continue for each individual possessing a different value system ending with individual 7 whose action would have to be consistent with all three of the values in order to be ethically consistent.

At this point, additional clarification may be required to increase its usefulness for engineers. In order to make it more understandable, substitute actual values for values 1, 2 and 3 Figure 3). Let value 1 be the underlying value justice. This means that if value 1 is an element in an individual's value set, then any decision made must be consistent with the tenets of justice. Equality and disinterest are some of the primary characteristics in individual 1's value system. Decisions are also characterized by the cliche, "You get what you deserve." Individuals are rewarded and/or punished in accord with their actions. Rewards and punishments are consistent and constant across individuals and situations. In our example, let value 2 be mercy. In any value system containing mercy, the decisions made must be consistent with mercy. Decisions made by individuals having mercy as a value would be characterized as exhibiting compassion and sympathy. Therefore, individuals having both justice and mercy as core values would be expected to make decisions that had the characteristics of both justice and mercy. That is, the decisions would be equal and disinterested at the same time as being compassionate and sympathetic. Punishments and rewards would be consistent; but punishments may be less severe and rewards more easily attained in a system containing both mercy and justice as opposed to one that contains only justice.

To continue the example, let value 3 be honesty. Once again, if the value system of the individual contains honesty as a core value, all decisions made must be consistent with the characteristics of honesty. For our purposes, these would include sincerity and truthfulness. Individuals who had honesty as well as justice and mercy as core values would be required to make decisions that were sincere and truthful as well as equal, disinterested, compassionate and sympathetic. It can be seen that the more core values that are present in a particular value system, the more constrained the set of actions that individual has to choose from if he or she wishes to remain ethically consistent and make moral decisions that reflect the values in his or her value system.

To help us understand the diversity of ethically consistent actions that may arise from a single situation, let us consider the following potential dilemma facing a manager in a manufacturing company. It must be recognized that failure will occur; the manager must be able to cope with the failure in an ethically consistent manner.

The company has been in the business of designing and manufacturing widgets for several decades. Just recently, evidence has come to management's attention that reveals that the widgets have a potentially fatal design flaw. While by no means a certainty, if the widgets are installed incorrectly, they could fail, possibly causing the entire sub-assembly of which they are a part to fail. If the sub-assembly fails, the entire assembly could explode killing the operator. However, failure is not a certainty; in fact, it is very unlikely. But should all three failures occur, lives will certainly be lost.

Figure 4 is an event tree that depicts the scenario. In an additional effort to make the scenarios easier for the reader to understand, probabilities have been assigned for each possible occurrence.

Before one can decide on which action to take, it is necessary to evaluate the situation in light of individual value systems. The probabilities of fatalities and non-fatalities are presented at the far right of the exhibit. All possible outcomes have been defined as the sum of the various probabilities is one. It is now possible to determine that the probability of the motor exploding and resulting in a fatality is .0001. Whether or not this probability is too high is not part of this discussion; how the manager will deal with the situation given various value systems is. The underlying assumption in most decision alternatives that will be presented in this example is that the loss of lives is undesirable and should be minimized. It is not, however, a necessary condition for any of these value systems to exist.

A manager with only the value justice in his value set may respond to the dilemma by deciding the flaw must be rectified regardless of cost or impact on either the company or the consumer. Because disinterested and equitable decision making is a trademark, justice demands that an ethical decision on the manager's part affect all parties to the same extent. One possible solution may be that all widgets must be recalled and replaced. Who is affected or how much it may cost them is of no concern; what is important is that all customers are treated the same and that the situation is corrected. The manager still may have a variety of options: recalling the motors after the sub-assembly has failed and replacing the motor; repairing the sub-assembly after the widget has failed but before the motor fails; recalling and repairing all the widgets before they fail; or removing the product from the market entirely. The issue is that all impacted customers are treated alike; no preference is given for size of the customer's business or for the fact that the president knows the customer's father. Equality of treatment is essential.

In fact, an ethical decision in this value system may be to not repair any widgets or sub-assemblies or motors for any one. This is difficult for conscientious engineers to fathom but it is necessary to remember that in this moral system justice is the only value; professionalism and regard for life do not play any part in this manager's decision making.

An individual with value mercy as the sole primary value may agree that the situation needs to be corrected but take compassion on the customers for whom recall is expensive. An ethical solution may involve some sort of cost sharing based on ability to pay or even complete absorption of the costs by the manufacturer. The set of ethical decisions for this individual may also include recompense for expenses incurred by the customer that are not directly attributable to the manufacturer. For an example of this behavior, note the recent decision by Johnson and Johnson to settle out of court with regard to the Tylenol poisonings of 1982.

Honesty as a core value may result in a completely different solution. Here, the ethical decision may be to inform the customer of the potential risk and the costs involved in correcting the situation and allowing the customer to make an informed decision with regard to replacement. Presentation of accurate and unbiased information to the extent that it is known is of chief importance. The needs of the customer or the fair treatment of all of those people involved are not important in this particular value system.

What if the value system is not singular but contains two or more values? The solutions may become more complex. For instance, a person sharing the values of the mercy and honesty may allow the customer to make an informed decision but will offer to share or absorb costs to ease the financial burden. They may even suggest the establishment of a fund to research alternatives to recall and replacement.

For the person who adheres to all three values in this hypothetical system, the decision may involve recalling all widgets at no cost to the customer while informing them of the inherent danger. hi this example, it can be seen that the fulfillment of the requirement for justice may dominate the requirement for allowing the customers to make informed decisions. Thus it is possible, that given particular decisions, a morally right decision for one value or set of values will contain the morally right decision for other value systems as well. Figure 5 shows honesty as a proper subset of the justice and mercy value systems as an example.

The inclusion of only three possible values in this hypothetical morality space is certainly not realistic. Most individuals have many values. Certainly some values dominate others, but on a daily basis, one juggles the relationship between multiple values to determine one's actions. People are excellent practicing ethicists given their individual value systems; many times however, they can not articulate or identify their own individual moral code.

Sometimes, individuals must make their own decisions. Other times, however, society provides the guidelines on the acceptability of various behaviors. Laws have been established, codes of ethics written and traditions passed through generations that for the most part shape behaviors in both one's public and private lives. These guidelines are usually beneficial, but sometimes they can make difficult and conflicting demands.

Not only do various value systems cause one difficulty, but so do the demands of the legal system. For example, many individuals have difficulty distinguishing between legal behaviors and ethical behaviors. In a recent class on engineering ethics, students were asked why a certain action was "wrong." The overwhelming response was it was wrong because it was illegal. When pushed to try to determine if a behavior could be legal and unethical at the same time, the class looked at the instructor in a puzzled fashion as if she had lost her mind. The idea that legislated behaviors might not be right was a new concept for many. To explain this apparent paradox, the set theory can be re-examined.

In Figure 6, a universe of all the possible actions for a given stimulus is represented. From this Venn diagram, it can be seen that an individual has only four options with regard to the nature of the action he or she takes. The action can be neither legal nor ethical, it can be both legal and ethical, it can be legal but not ethical, or it can be ethical but not legal. The set of all possible actions in this particular universe that are legal are represented by the set L while the set of all possible actions that are ethical, according to a particular moral code, are represented by the set E. The intersection of the two sets (L E) represents the actions that are both legal and ethical. The complement of the two sets, or the entire universe minus the two sets [U - (L E)], represents all the actions that are neither legal nor ethical. Usually, actions are contained within the intersection of L and E in that they are both legal and ethical. Occasionally, however, dilemmas are encountered where the desired solution is only one or the other. This conflict occurs most often when actions are legal but are not ethical. All examples of these conflicts must be presented in the light of particular value systems. Therefore, an example of legal yet unethical behavior can be found in the cosmetics industry if the individual is an animal rights activist. The use of animals for the testing of various cosmetics is deplored by many is inhumane and unnecessary. Others counter with the argument that animal testing is the least expensive way to go and that they have a fiduciary duty to their stockholders. Both sides will agree that animal testing is legal; however, one of the sides will argue that it is completely unethical and should be halted.

When a large group believes that a presently legal behavior is unethical, pressure is placed on society and government to revise the laws. Prohibition and its repeal are examples of the pressure society can place on the legislative bodies to change the legal status of unethical behaviors.

Situations this nature where actions are considered legal yet unethical usually arise when the "behavior" is not expressly forbidden by law. However there are instances when behaviors are mandated by law and are considered to be unethical by some members of society. A well known example includes mandatory registration for the draft. Once again, the conflict between the legal system and the value system of the individual becomes quite apparent.

A third set of possible behaviors are those that are not legal but are ethical. Many times, these behaviors are related to the instances where certain behaviors are mandated by law and are considered to be unethical by certain members of society. Using the previous example of mandatory registration for the draft, failure to comply with the laws is illegal. But to refuse to register or to protect a target minority would be regarded by many to be the ethical, and therefore the more desirable, behavior. Other examples may include the distribution of illicit but pain alleviating drugs to terminally ill patients, and the refusal to obey a court injunction to return to an unsafe workplace. As in the second instance, where behaviors were legal yet unethical, behaviors that are illegal yet ethical must be determined in accordance the particular value system. For example, in the area of assisted suicide for the terminally ill, just as many people believe it to be ethical as unethical. Some would claim that when an individual is no longer experiencing a certain level of quality in his life and wishes to end it, it is ethical for them to do so. Others, just as adamantly, claim that no one has the right to play God and determine when a life should end. Presently, it is illegal to assist a suicide; but some would argue that it is ethical under certain situations.

The final set of mutually exclusive behaviors in which an individual may participate are those that are both illegal and unethical. For the most part, these behaviors have a detrimental effect on both the individual and the society, and, therefore, such decisions are rarely chosen. But, when such decisions are chosen, justification for these decisions is attributed to the behaviors really being in the second or third category rather than the fourth. For example, "I shoplifted the Rolex because society has unjustly denied me the ability to pay for one."

Engineering ethics

How then does this previous discussion affect engineers? Like other professionals, engineers are in the unenviable position of having to abide by not only their own individual codes of morality but also that of their profession. Each individual is expected to make decisions based on at least two value systems. The ideal situation would be that the professional code of ethics is a proper subset of the individual's moral code (Figure 7a). It should be expected, however, that the professional code of conduct at least intersects the personal code of conduct (Figure 7b). The greater the intersection, the less conflict in decision making the individual will experience. Conversely, the lesser the degree of intersection, the greater the conflict in ethically ambiguous decision making until the two sets are disjoint. At this point, the agreement between the professional and the personal value systems will be nonexistent and the individual will be in a high state of tension. In this instance, there can be no resolution, save the acceptance of one value system and the denial of the other. Fortunately for engineers. this is a rare occurrence as most professional codes of ethics deal with issues such as "confidentiality, industrial secrets and proprietary interests in invention." These issues are usually not of primary interest in conventional codes of morality.

The difficulty with conflicting ethical values that is more likely to plague an engineer is the conflict between the value systems of various individuals within the same organization (Figure 8). When the conflict is between individuals of like status, the resolution is usually one of compromise - finding some area of intersection between the various value systems. However, when the conflict involves individuals of varying positions within the organization and compromise is not an alternative, the dominant player's value system many times determines the course of action.

Engineers are unlike many professionals in they do not all subscribe to the same organization's code of ethics. They are different in the sense that their loyalties are usually associated with the organization that employs them rather than with the profession. As a result. engineers find themselves in situations where the best interests of all parties involved can not be obtained. There are certain to be different right answers to the same dilemma because of the perspectives and the values of the individuals associated with the situation.

Codes of values are both private and public. The very existence of multitudes of ethical codes must result in more that one morally correct answer to ethically ambiguous situations.

Although engineers are by nature uncomfortable with issues of this nature, perhaps a brief journey into the realm of ethics and set theory can help the engineering professional understand that there are times when different individuals can have different answers to the same problems and yet still all be correct.

For further reading

Dunham, W., Journey through Genius: The Great Theorems of Mathematics. New York: John Wiley & Sons. Inc., 1990. Freudberg. D., The Corporate Conscience, New York: American Management Association. 1986. Hardy. F.L. Finite Mathematics, New York: Harper & Row, Publishers. 1977. Hays. W.L., Statistics (Third Edition). New York: Holt. Rinehart, and Winston. 1981. Kelley. R.E., The Gold Collar Worker: Harnessing the BrainPower of the New Workforce. Reading, MA: Addison-Wesley Publishing Company, Inc., 1985. Kischuk, S. and M. Anderson, "The Enigma of Engineering Ethics: A Historical Perspective." Florida Engineering Society Journal, 1991. Lin. Y.F. and S.Y.T. Lin. Set Theory with Applications (Second Edition. Revised and Expanded). Tampa. FL: Mariner Publishing Company, Inc., 1981. McCarroll, T., "Creativity: Whose Bright Ideal?" Time. 1991. Martin. M.W. and R. Schinzinger, Ethics in Engineering, New York: McGraw-Hill Book Company. 1983. Miller. I.R., J.E. Freund and R. Johnson, Probability and Statistics for Engineers (Fourth Edition), Englewood Cliffs, NJ: Prentice Hall, 1990. Reidenbach. R.E. and D.P. Robin, Ethics and Profits: A Convergence of Corporate American's Economic and Social Responsibilities, Englewood Cliffs, NJ: Prentice Hall. 1989. Schermerhorn, J.R. Jr., Management for Productivity (Third Edition), New York: John Wiley & Sons, 1989. Spiegel, M. R., Schaum's Outline of Theory and Problems of Probability and Statistics, New York: McGraw-Hill Book Company, 1975. Stewart, T.A., "Brainpower", Fortune, 1991. Tuleja, T.F., Beyond the Bottom Line: How Business Leadersare Turning Principles into Profits, New York: Facts on File Publications. 1985. Walpole, R.E. and R.H. Myers. Probability and Statistics for Engineers and Scientists (Third Edition), New York: MacMillan Publishing company. 1985.
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Title Annotation:Decision Making
Author:Callahan, Anita
Publication:Industrial Management
Date:Jul 1, 1992
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