A statistician friend once told me that he believed mathematics to be the true universal language. Time, space, and most of the circumstances of our lives can be measured by numbers. The English philosopher Bertrand Russell once said that “mathematics, rightly viewed, possess not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture.”
One need not have any special competence in mathematics to enjoy its benefits in the houses we build, in the cars we drive, in the most simple and most complex aspects of everyday life. That being said, what about morality? Can mathematics help the many of us who essentially want to be decent people but cannot always figure out how? If math is the universal language, shouldn’t there be equations that could help us distinguish between right and wrong at those many trying moments of life when we find ourselves without any other guidance?
The relationship between numbers and morality is intriguing. By definition numbers are relative while morality deals with absolute values. The relatively new term ethical calculus refers to using numbers and mathematics in making difficult ethical decisions. How do numbers play a key role in the process of making moral choices?
In war, where life and death decisions are constantly made, numbers can play a catastrophic role. During World War II, the decision was made to use the nuclear bomb against Japan in Hiroshima and Nagasaki. The bomb killed an estimated 330,000 Japanese citizens. Military officials estimated that an invasion of Japan would have caused the death of one million U.S. soldiers and possibly the death of another million Japanese. Did we make the right decision by potentially “sparing” close to two million lives?
The Steven Spielberg movie Saving Private Ryan tells the story of the rescue of one man by a squadron of eight U.S. rangers. At one point, one of the Rangers asks: “Why is one man’s life worth risking eight, why is the life of this private worth more than ours?” In William Styron’s bestseller, Sophie’s Choice, a mother of two is faced with an unbearable and tragic decision. In a concentration camp, a Nazi officer forces her to choose which of her two children he will kill. At first she refuses to make the decision, but when the officer threatens to kill both children, she makes a devastating choice between which of her two children will live and which will die.
The concept that one life should be sacrificed in order to save the life of others is not new. In Greek mythology, Iphigenia, the daughter of Agamemnon, leader of the Greek forces at Troy, is ready to give her life to save her country:
O my father, here I am; willingly I offer my body for my country and all Hellas, that you may lead me to the altar of the goddess and sacrifice me, since this is Heaven's ordinance. May good luck be yours for any help that I afford! And may you obtain the victor's gift and come again to the land of your fathers. So then let none of the Argives
lay hands on me, for I will bravely yield my neck without a word.
- Iphigenia, Euripides
The notion of sacrifice is at the heart of Christianity, the voluntary sacrifice of one for
the redemption of the world. According to the Gospel of John, Caiphas the High Priest
says, "You do not realize that it is better for you that one man die for the people than that the whole nation perish." (John 11:50)
Numbers and mathematics influence us when we make moral decisions about the production, distribution and consumption of goods and services. The English philosopher Jeremy Bentham (1748-1832), in his Introduction to the Principle of Morals and Legislation, developed the concept of utilitarianism on the idea that “the greatest good for the greatest number of people” is the fundamental principle of morality. We believe that “life is a pearl beyond price,” however we have limited financial and human resources. How should we allocate these resources? Can we do a costbenefit analysis of a situation when dealing with human life? The question is very pertinent in healthcare. Should we allocate more resources in order to benefit the maximum number of people and engage in preventive medicine, or should we allocate great sums of money to individuals for high-cost treatments?
Numbers play a crucial role in our justice system as well. In sentencing a criminal, the severity of the crimes often determines the number of years a convict will have to serve. Theft is universally condemned in principle, yet judged differently depending on the value of the stolen property. In the old common law, the difference between simple larceny and grand larceny was determined by whether the value of the stolen object was more than 12 pence. The difference in punishment was draconian. In New York, grand larceny is punishable by more than one year in prison, while a fine is imposed for petty larceny. Opponents of the death penalty make the argument that it is better to spare the life of nine guilty persons than to execute one that is innocent. Would the argument still hold with a different ratio? How about the life of one innocent against the lives of 3,504? (Number of inmates on death row in the U.S. today.)
The issue of reparation for historical injustice and war crimes is often reduced to a money equation. Following the September 11th attacks, the Federal Government created the Victim Compensation Fund with approximately six billion dollars to be divided among the families of the victims. Kenneth Feinberg, appointed by Congress to preside over the fund, developed a complicated mathematical system based on life expectancy and loss of future earning income to determine how much each family should receive. In 1996, Ruder·Finn represented the Swiss government in the issue of the Swiss “dormant accounts” that belonged to holocaust victims, survivors and heirs. The Swiss banks were accused of making it very difficult for more than 50 years for claimants to take possession of those funds. It was a major crisis for our client. The Swiss government took the right steps to correct the injustice, and a settlement was reached with the payment by the Swiss banks of $1.25 billion to survivors and heirs. That amount far exceeded any money that was found in the dormant accounts. Nobel Peace Prize laureate Elie Wiesel, author and a Holocaust survivor himself, wrote in the forward of Stuart Eizenstat’s, book Imperfect Justice: Looted Assets, Slave Labor, and the Unfinished Business of World War II, that he was reluctant to define the greatest tragedy in Jewish history in terms of money. To him the issue was not about financial evaluation but about morality and theology. He writes:
I remember a little girl, a beautiful innocent little girl with golden hair and blue eyes, who had taken her most cherished possession with her, a beautiful scarf she had received as a Passover gift. Are there enough funds in the world to compensate her brother for that stolen scarf?
Thane Rosenbaum, author of The Myth of Moral Justice: Why Our Legal System Fails to Do What Is Right, believes that legal remedies should not be limited to jail sentences and cash settlements but should offer moral and spiritual relief to the victims. Victims should be given a forum and allowed to speak about what they have endured and the pain that is theirs. Rosenbaum believes that “civilization is always more civilized when the truth is unhidden…truth is part of the healing process of what it means to seek and receive relief.” In cases of medical malpractice lawsuits, juries have awarded astronomical amounts of money to victims in compensation for pain and suffering. Canadian legislators, recognizing that it is impossible to truly measure pain and suffering in a just way, have imposed a cap of $200,000. In the U.S. legislators are trying to reform the system as well, by imposing a cap on the total amount that can be paid for punitive damages.
Right and wrong
Numbers can also be indicative that something is right. According to Giving USA, an annual survey of charitable contributions published by the American Association of Fundraising, Americans gave an estimated $240.72 billion in 2003. This amount is approximately 2.2 per cent of the nation’s gross domestic product. America gives more of its GDP to charity than any other western democracy. The UK, for example gives only .5% of its GDP to charity.
Numbers can also be good indicators that something is terribly wrong and unjust. James Wolfensohn, chairman of the World Bank, recently said that of the 5 billion inhabitants of the world, 20% own 80% of the world resources. According to Vernellia Randall, professor of law at the University of Dayton, 1% of U.S. citizens own 40% of the total property in the country while 80% of U.S. citizens own 16%. A U.S. Department of Agriculture study showed that almost 10% of American families do not have enough food. America has the highest prison population per capita in the world. According to a study of the U.S. Department of Justice, 6.7 million Americans were either in jail, on probation or on parole in 2002.
Sometime numbers can become irrelevant because of their magnitude. Josef Stalin once said, “A single death is a tragedy, a million deaths is a statistic.” It is hard to grasp, for instance, that in the Middle Ages, one third of the population in Europe died during the Black Plague. In Africa there are 28.5 million infected with HIV/AIDS. In Zimbabwe, approximately 33% of the population is infected.
Time magazine reports that the typical CEO now makes $301 for every $1 paid to the typical employee. In 1982 it was only $42 to $1. Dick Grasso, former head of the NYSE, had to resign when his compensation package of over $200 million became public knowledge. Eliot Spitzer, New York State Attorney General, decided to sue him to recover at least $100 million. Can excessive executive compensation be morally wrong? If so, how can we determine the criteria for what is acceptable and what crosses that fine line into moral impropriety?
Numbers involved in financial relations with employees and clients could also pose some ethical concerns. Ruder·Finn, like most consulting firms, charges its clients on an hourly basis. The hourly rates are based on the experience and expertise of the consultant as well as on what other similar firms charge. The value of what we do is not always related to the number of hours we spend. Sometimes one hour of work brings a significant financial return to the client. At other times, many hours can bring little results. Ruder·Finn estimates that for a consultant to be profitable, he or she has to be billable at the ratio of 2.5. This allows the firm to pay for the overhead costs such as rent, insurance and other unidentified expenses. Some groups at the firm perform very well and have a higher ratio than 2.5; others do not perform as well and have a lower ratio. Yet, the clients are billed at uniform rates. The whole system is arbitrary but we think it is fair. We believe we are treating our clients and ourselves in a just manner. Are we right?
Does ethics impact the bottom line? The recent examples of Enron, WorldCom and Arthur Andersen attest to the fact that unethical conduct does have a negative impact on the bottom line. Such behavior has ruined companies, defrauded employees and sent top management to jail. Is there, however, a correlation between behaving well and doing well? Does integrity, honesty and trust impact profits, earning per share and stock prices?
Some studies have established a definite link between principles and profitability. Roman Hayibor and Agle conducted a study of 52 research projects on ethics and profits. They found that 63% showed a positive link, 27% showed minor or no significant relations, and 10% actually impacted the bottom line negatively.
A survey conducted by Roper Starch Worldwide found that 54% of respondents would pay more for a product that supports a cause they care about, 66% said that they would switch brands, and 62% said they would switch retailers to support socially responsible behavior.
In mergers and acquisitions, goodwill, based on intangible criteria such as a happy workforce, loyal customers and a good general reputation, is used in determining the value of a company. It is sometimes calculated to be worth as much as 50% of the tangible assets of the company. Kevin T. Jackson, professor at Fordham University and author of Building Reputational Capital, argues that “integrity and fair play have tangible and profitable benefits. His study of 40 of the largest U.S. corporations, including Hewlett Packard, Northrop Grumman and Levi Strauss, demonstrates that the annual loss of their reputational capital was greater than their profits combined. Two Harvard professors conducted a study over an 11-year period and found that companies that have a stakeholders-balanced approach in conducting their business have four times the sales growth than companies that focus solely on shareholder value.
Making the right ethical decisions is often very hard and challenging, particularly when dealing with issues that affect people’s lives. Mathematics is a science that deals with facts while ethics deals with conscience and ideals. In one of Ruder·Finn’s “Thoughts and Images” series, Rabbi Tarfon is quoted saying: “Do not keep away from the measure which has no limit, or from a task which has no end.” Numbers can enhance our consciousness of realities and give us more than a superficial assessment of the probabilities and causalities of new realities that we would have to evaluate. While never a substitute for good values and hard thinking, numbers and the ability to make the best use of them as provided by mathematics and statistics can certainly help us better confront our ethical dilemmas and make more ethical choices.