Kaveh Behbahani's article 'Rational Decision-Making, Expected Utility, and the Value of Human Life'

Dedicated to all the doctors, nurses, paramedics, and healthcare workers who, through their self-sacrifice, make a mockery of the dignity of viruses.

Rational Decision-Making, Expected Utility, and the Value of Human Life[1]

Kaveh Behbahani

Abstract

In this article, we first discuss unstable situations about which we lack sufficient knowledge and explain the nature of rational decision-making in such situations based on decision theory and the concept of expected utility. We then address the various errors and biases that hinder our estimation of the expected utility of choices. Next, we turn to the subject of the "value of human life" and refute, with arguments, the mistaken notion that "the value of human life is infinite." We also demonstrate the function of the concept of expected utility in important decisions concerning human lives. Finally, we arrive at the discussion of allocating scarce medical resources for the coronavirus disease, and, considering the criterion of expected utility along with other ethical considerations, we offer points and recommendations on this matter.

Decision Theory and Expected Utility

Our world is a world of instability and a lack of certainty. Hence, we are always grappling with situations about which our information and knowledge are insufficient. Nevertheless, we usually gain information about phenomena through trial and error and with the help of experience, and we try to overcome this instability somewhat.

However, sometimes acquiring information is very costly and perhaps impossible. We want to know with certainty what will happen in the future, but it cannot be known. It is here that we are compelled to make predictions and, based on them, make decisions and accept their risks. We have a coin and want to flip it. We also know all the necessary information about it: the weight of the coin, the amount of force we apply to the coin, the wind speed, the coin's bounce rate after hitting each surface, and so on. Yet, we still cannot say with certainty whether it will land on heads or tails when we flip the coin. Even if we flip the coin thousands of times and collect data, we may still err in our prediction. The reason is that prediction is fundamentally a probabilistic matter.

Our decisions all inherently contain some kind of risk. In this situation, our minds sometimes become paralyzed in analysis. Many options lie before us, and we do not know which to prefer or how to make a rational decision. We are bewildered as to what the optimal decision is. Moreover, when the decision we are about to make is important and our ignorance is great, the task becomes more difficult. In this state, we do not know which of the possible choices to turn to, and with each choice, whether the situation will get better or worse.

Decision-making in the absence of certainty, that is, in a situation where we are not sure of the consequences, is anxiety-inducing. But humans are compelled to make decisions. Therefore, it is appropriate to ask: In the absence of certainty, how does a rational person make a decision? How is rational decision-making possible in an unstable, uncertain, and volatile situation?

Decision theory[2] addresses precisely this subject. This theory is a branch of logic that clarifies the impact of probabilities on action in uncertain situations;[3] a field of knowledge where bridges are built between philosophy, economics, and other disciplines, and questions are asked about what constitutes a rational decision in a situation where we lack sufficient information and there is no certainty. This branch of knowledge also teaches us how to analyze based on benefit and cost to choose among various options and make rational decisions.

When various options lie before us, we must calculate how much each choice will cost us and how much benefit it will bring; that is, the potential benefits and potential costs of each choice must be calculated. In this situation, the option that yields the greatest benefit and incurs the least cost is the rational one. Decision theory, by drawing on probability, addresses precisely this.

One of the fundamental concepts of decision theory is expected utility[4]. The utility of something comes down to how much we like it. When we prefer "A" to "B" , it means the utility of "A" is greater for us than the utility of "B". Every decision naturally has consequences that distinguish it from other decisions. In life, one cannot turn back events. What is past is past. But the concept of expected utility takes shape by asking ourselves what would happen if we could repeat our decisions over and over and over again. If we repeatedly made a certain decision and repeatedly saw its consequence, what would the average outcome be? To calculate the expected utility of each outcome, we must know the percentage probability of its occurrence, and we must also know how much each outcome is worth and desirable to us.[5] Then we must multiply these two values together, and finally, sum the products we have obtained for each individual outcome.

But what is the efficient, formal definition of probability? The simple definition of the probability of any event occurring is the result of dividing the outcome of that specific event by the total number of all possible outcomes. According to decision theory, a rational person, when deciding under conditions of uncertainty, does what "maximizes expected utility." We will clarify the matter somewhat by examining a few simple examples.

Example One

Someone decides to give you a lottery ticket for your birthday. They give you the choice between two tickets they have brought: Ticket 1 and Ticket 2. If you choose Ticket 1, you have a 2 percent chance of winning 100 Tomans. If you choose Ticket 2, you have a 1 percent chance of winning 150 Tomans. Which choice is rational?

Decision theory says choosing Ticket 1 is more rational. Why? If you choose Ticket 1, you have a 2 percent chance of winning 100 Tomans. Multiply these two numbers together:

This 2 is the expected utility of choosing Ticket 1.

Now let us turn to Ticket 2 and calculate its expected utility:

The expected utility of Ticket 2 is 1.5.

Since the expected utility of Ticket 1 is greater than the expected utility of Ticket 2, and since a rational person seeks to maximize expected utility in decision-making, choosing Ticket 1 is more rational.

Example Two

Let us set up a hypothetical game. Suppose I flip a coin. If it comes up heads, you must give me 100 Tomans, and if it comes up tails, you must give me 50 Tomans. If we repeat this over and over and over again, in half of all the coin flips I will win 100 Tomans, and in half of them, 50 Tomans. Now the expected utility can be calculated: the probability of each option (heads or tails) is . The value of the heads option is 100 Tomans, and the value of the tails option is 50 Tomans:

The average of my winnings and your losses per coin flip is 75 Tomans. It is obvious that this game yields nothing but loss for you. Of course, this was apparent from the very beginning and required no calculation.

But let us change the rules of the game. I give you 80 Tomans to flip the coin, and the rest of the rules are the same as before; that is, if it comes up heads, you must give me 100 Tomans, and if it comes up tails, you must give me 50 Tomans. Is the game to your detriment this time or not?

Again, we must calculate the expected utility:

But since you receive 80 Tomans for each coin flip, this time, on average, 5 Tomans come to you with each coin flip: . So the game is rational.

Example Three

Lottery tickets always have buyers around the world. But is buying them rational? Should we buy a lottery ticket or not? Here we have two options that must be compared: buying a ticket and not buying a ticket. We must estimate the probability of each option's outcome to obtain the expected utility of each decision. Suppose the price of a lottery ticket is $1. In this case, the available options are as follows:

Option one (not buying a lottery ticket):

If we do not buy a ticket, the money we have stays in our pocket and is not spent. There is a 100 percent (or close to 100 percent) chance that the money remains in our pocket. The expected utility of this option is:

Option two (buying a lottery ticket):

We assume the first prize of the lottery is $11 million, and subsequent winners do not receive significant amounts worth discussing. Therefore, we disregard them. The rule of the lottery game is that we must choose 6 numbers from among 59 numbers; meaning the probability of winning first prize is 1 in 45 million. (Of course, without considering the possibility that two people pick the same set of numbers and have to split the prize). This probability is calculated as follows:

For $1, we can choose two sets of six numbers. In this case, the probability of our winning first prize becomes 2 in 45 million. Now we can calculate the expected utility of option two:

Cost-benefit analysis shows that the expected utility of buying a lottery ticket is 48 cents, and the expected utility of not buying a lottery ticket is $1. The reasonable economic course of action is to maximize expected utility, which means buying a lottery ticket is not a rational act. But why do so many people buy lottery tickets? We will explain later that decision theory is a type of prescriptive knowledge;[6] that is, it states what a rational person should do to make a decision, not what they actually do. Humans in the world make many irrational decisions every day that are inconsistent with decision theory.

Knowing the expected utility helps us understand what the reasonable decision is in uncertain situations. Casinos become wealthy because they are masters of calculating expected utility. However, expected utility is not always measured in money, because money is not the only thing that is desirable for people. Nevertheless, if a desirable matter is at stake that cannot be measured in money, one can still decide by calculating expected utility. In that case, as in the previous examples, we must estimate the utility of all options and calculate how much each option might lead us to what we want. Then we multiply the probability of each option by its value and choose the option with the highest expected utility. We will provide one or two examples of this type of decision-making as well.

Example Four

You are invited somewhere for dinner and ask the host: "Should I bring something for dinner or not?" and the host replies: "Drinks for dinner are on you." In the evening, you set off for the host's house and want to pick up drinks on the way; but you have no idea what the food is, and consequently, you do not know whether to buy soda or doogh. Unfortunately, you have left the piece of paper with the host's phone number at home and cannot call to ask the host. Therefore, you remain hesitant. Based on what you know of your friends, you consider two possibilities: that dinner is either abgoosht or pizza. If it is abgoosht, soda is not very suitable, and if it is pizza, doogh is not a good choice. As bad luck would have it, you are short on money and can only buy one of these two drinks. What do you do? Do you buy soda or doogh?

Decision theory says to calculate the expected utility of each option. First, you must determine the utility of the options. You can draw a utility matrix that has four options:

1. If dinner is abgoosht and you buy doogh, your choice is correct. (Desirable)

2. If dinner is ābgusht and you buy soda, your choice is incorrect. (Undesirable)

3. If dinner is pizza and you buy soda, your choice is correct. (Desirable)

4. If dinner is pizza and you buy doogh, your choice is incorrect. (Undesirable)

Now, to calculate expected utility, you must quantify these four options; that is, assign a numerical value to each. You consider a numerical range from +10 to -10 and quantify the options as follows:

Option 1: +10

Option 2: -10

Option 3: +10

Option 4: -10

Now you must proceed to calculate the probability of each option. What is the probability that dinner is ābgusht, and what is the probability that dinner is pizza? What dinner the host has made is not up to you. You only have control over buying the beverage. However, you remember that your friend’s spouse said long ago that they would invite you over for ābgusht one night. For this reason, it is more probable that dinner is ābgusht. You guess, for example, there is a 70 percent probability that dinner is ābgusht. Now the expected utility of each option can be estimated:

Expected utility of Option 1:

Expected utility of Option 2:

Expected utility of Option 3:

Expected utility of Option 4:

To calculate the expected utility of each decision when a decision has multiple outcomes, you must calculate the sum of the expected utilities of each individual outcome. Then you must add together the potential gains and losses of the options. If you buy doogh, in the unlucky scenario the expected utility is -3 and in the lucky scenario the expected utility is 7, the sum of which is 4. But if you buy soda, in the unlucky scenario the expected utility is -7 and in the lucky scenario the expected utility is 3, the sum of which is -4. You must always maximize expected utility. So decision theory says buy doogh.

Example 5

This example of calculating expected utility relates to a subject that has fundamentally nothing to do with money; namely, the subject of faith. For this purpose, we formulate Blaise Pascal’s “Gambler’s Argument” in the framework of expected utility. Of course, Pascal himself did not use this concept; but his argument can be formulated this way.[7] Pascal was interested both in the concept of infinity and in decision theory, and he incorporated both into this argument. He believed that belief in God is a rational belief. In his view, whether God exists or not, belief in His existence is compatible with reason.

Pascal’s argument can also be presented in matrix form. Accordingly, we have two options before us: first, that God exists, and second, that God does not exist. In the face of each option, we also have two states: I believe God exists, or I do not believe God exists. So in total we are dealing with 4 states:

State one: God does not exist and I believe God does not exist.

In this state, my belief is correct. This state is a desirable one. So to quantify it, we give it 100 points.

State two: God does not exist; but I believe God exists.

In this state, my belief is incorrect. So to quantify it, we give it 0 points. But perhaps we should deduct from this score; because in this state I also become somewhat disappointed. Let’s give it a score of -10.

State three: God exists and I believe God exists.

This state is the most desirable of all, and its score is infinity (∞); because in this state, I will go to eternal paradise and live an everlasting life there.

State four: God exists; but I believe God does not exist.

This state is the most undesirable of all, and its score is negative infinity (-∞); because in this state, I am met with eternal punishment and everlasting hell.

Now we must calculate the expected utility for each state, and then sum the values separately for believing and not believing. Before that, we know that adding any number to infinity does not increase infinity:

If I do not believe in the existence of God, the expected utility of disbelief becomes:

If I believe in the existence of God, the expected utility of faith becomes:

But why didn't we calculate the probability of each option to multiply it by the option's value when computing expected utility? Because we are dealing with infinity, and therefore, the probability of God's existence or non-existence no longer matters. No matter how small and negligible the probability of God's existence, when multiplied by infinity, the expected utility still becomes infinity.

As we said, a rational person maximizes expected utility. The expected utility of faith is infinity, and the expected utility of disbelief is negative infinity. Therefore, reason dictates faith.

Note that our discussion is not about whether Pascal's Wager is a sound argument for proving God's existence. Many critiques have been leveled against this argument. Our intention was to show an example of applying the concept of expected utility without monetary value being involved.

Cognitive Pitfalls in Estimating Expected Utility

As we said, the basic formula for expected utility has two parts:

1_ Calculating the probability of each outcome;

2_ Estimating the utility and value that each decision holds for us.

But the problem is that we humans are inept at estimating both parts and are subject to numerous errors and biases in both. It is not a bad idea to briefly point out some biases and errors in each part below.

Bias in Calculating Probabilities

We humans are very poor at calculating probabilities, and despite our many capabilities, our probabilistic intuitions were not well-honed in evolution. For example, consider this question:

Which option is more probable: that someone gets pickpocketed in Tehran, or that someone gets pickpocketed in Khak-e Sefid (a high-crime neighborhood in Tehran)?

Many people answer this question by saying: "Khak-e Sefid." But Khak-e Sefid is inside Tehran; that is, all pickpockets in Khak-e Sefid are Tehrani pickpockets. So the probability of being pickpocketed in Khak-e Sefid cannot be greater than the probability of being pickpocketed in Tehran. Yet why do some people say Khak-e Sefid? Because of the image they have of Khak-e Sefid in their minds. People's conception of Khak-e Sefid is a poor neighborhood that is a haven for criminals and drug dealers. Consequently, they estimate that there are more pickpockets there. But the word "Tehran" brings to mind the space of middle-class and upper-class urbanites; that is, a place where pickpockets are not much in view. People form probabilities based on the vivid images they have in their minds; but mental imagery is often not a good guide for estimating probabilities. For this reason, it leads us into error in calculating probabilities.

Consider another example. Farzaneh is thirty-one years old, speaks frankly and directly, and is very intelligent. She has a bachelor's degree in philosophy. During her student years, she was deeply concerned with social justice. In your opinion, what does Farzaneh do today? Among the following three options, which is the most probable and which is the least probable?

Option 1: Farzaneh works in a bookstore.

Option 2: Farzaneh is an insurance company salesperson.

Option 3: Farzaneh works in a bookstore and attends yoga classes.

In response to this question, many people say that option 3 is the most probable. But the probability of option 3 is less than the probability of option 1. Why? Because anyone who works in a bookstore and learns yoga necessarily works in a bookstore. In other words, the probability of 1 and 2 occurring together is less than the probability of 1 occurring alone and the probability of 2 occurring alone. Why do people err in estimating this probability? Because they estimate probability with the help of images. That Farzaneh works in a bookstore and learns yoga fits better with the image given of her. The same error occurs in estimating the probability of 1 or 2. To clarify the matter, consider the following example.

Maryam believes in motivational and success discussions and is into fortune-telling and astrology. Which option is more probable about her?

Option 1: Maryam reads Tarot.

Option 2: Maryam reads Tarot or is an accountant.

Regarding Maryam, many people will likely say option one is more probable; whereas base probabilities tell us that the probability of "A or B" occurring is greater than the probability of "A" occurring alone and the probability of "B" occurring alone. The probability that someone is an accountant or a fortune-teller is greater than the probability that they are only a fortune-teller; but the information given about Maryam's life interferes and creates an image that makes us think she most likely reads Tarot.

Our human intuitions in statistics and probability are far more fallible than they appear. John Allen Paulos[8], the twentieth-century American mathematician, said that we humans lack numeracy; that is, we are illiterate in arithmetic, mathematics, and logical calculations, and this illiteracy has unfortunate consequences for us. The following example shows how our intuitive estimate of probability can be completely baseless.

Suppose there is a test to diagnose a specific type of disease. Suppose there is a 1 percent probability that an error occurs in the test and the result is falsely shown as positive or negative; that is, in a statistical population of those afflicted with the disease, the test result for 99 percent of individuals is positive, and in another statistical population not afflicted with this disease, the test for 99 percent of individuals is negative. Now suppose an individual named Reza takes the test and his test result is positive. How likely is it that Reza actually has this disease?

Most answer 99 percent; that is, equal to the accuracy of the test. But this answer is completely wrong. Why? Because the problem's data is simply not sufficient to reach the correct answer! To reach the correct answer, we must know the base rate of the disease's incidence.

For example, suppose 1 in every 1000 people has this disease; that is, out of every 1000 people, 999 are healthy and 1 is sick. With this description, we must consider four states:

State 1: Since the test shows the correct result 99 percent of the time, out of 999 people, the number of those whom the test shows as healthy and who are truly healthy (i.e., the test did not err in diagnosing their health) is 989 people. We calculate this number as follows: 989 = 999 × 0.99.

State 2: Since the test has a 1 percent error rate, out of 999 people, the number of those whom the test shows as sick but who are truly healthy is approximately 10 people. We calculate this number as follows: 10 ~ 999 × 0.01.

State 3: Regarding the one person who has the disease, considering the test's error rate, there is a 99 percent probability that the result is correct and the patient is truly sick.

State 4: Regarding the one person who has the disease, considering the test's error rate, there is a 1 percent probability that the result is incorrect; that is, there is a 1 percent probability that someone whom the test shows as sick is healthy.

According to the information given, Reza's test result has come back positive. Therefore, the situation is one of two possibilities: Reza is either among the patients who are truly ill (state 3) or among those who are healthy but the test has mistakenly shown them as ill (state 2). So the probability that Reza is truly ill and the test has erred becomes:

The probability that Reza is truly ill is 1 in 11; that is, there is approximately a 9.09 percent chance that he is actually afflicted. In this case, even though Reza's test was positive, there is more than a 90 percent probability that he is not ill.

Now suppose we change the base rate of the disease. This time, assume that out of every 1000 people, 100 have the disease, and the test's error rate remains the same as before. In this scenario, if Reza's test result is positive, what is the probability that he is truly ill?

In this case, out of every 1000 people, 900 are healthy. However, given the test's 1 percent error rate, 9 of these individuals are ill and their test results were erroneous. Again, considering the test's error rate, out of the 100 ill people, 99 are truly ill and the test did not err regarding them. Now, the probability that Reza, whose test result is positive, is truly ill becomes: ; meaning there is approximately a 92 percent chance that Reza is truly ill.

Do you see how changing the base rate of incidence alters the probability of Reza being ill? Therefore, the answer to the question posed is not uniform. But because our probabilistic intuitions are undeveloped, we humans are inattentive to the base rate. This error is known as the "base rate fallacy"[9].[10]

In summary, to calculate the expected utility of choices, we must calculate the probability of each outcome, and calculating probabilities can be very misleading.

Bias in Estimating Utilities

Human valuations are also sometimes incoherent and biased. For example, if we are to choose things right now for our future consumption, our choices will likely be varied; but if we are to choose something to consume right now, we usually do not choose with much variety. For instance, if we go to a large store and are to buy snacks for our consumption next week, we buy a whole bunch of odds and ends: various types of chips, puffs, biscuits, and things like that; but if we are to buy snacks each day next week only for that same day, we will probably buy the same item every day.

Another point is that judgment about what is desirable to us is highly related to the context in which the judgment is made. To put it better, the surrounding environment can be very misleading in decision-making. We evaluate things by comparing them, and this comparison takes place in a specific environment and context. Sellers know this well and use it abundantly to achieve their goals. For example, real estate agencies first show a bad house to the client, and this makes the subsequent house or houses appear much more appealing to the client.

Labels and titles also affect what we deem desirable, causing us to overestimate or underestimate the desirability of things. Previously, researchers at Stanford University and the California Institute of Technology conducted an interesting experiment in this area. The experiment involved asking a number of volunteers to taste juices that were in different bottles. The participants had no particular expertise in the taste of juice and only drank juice occasionally. The juice bottles were labeled with prices: $5, $10, $35, $45, $90; but the juice in the $10 bottle was exactly the same as the juice in the $90 bottle, and the juice in the $5 bottle was exactly the same as the juice in the $45 bottle. Nevertheless, in the participants' view, the degree of desirability of the juices was determined not by the juice itself, but by its price label. In other words, the participants preferred the more expensive juice. During the experiment, the participants' brains were imaged, and it was observed that when a person saw the $90 juice, the pleasure centers in their brain showed a stronger reaction than when they saw the $10 juice, even though the juice inside the bottles was identical.

Tradesmen, profiteers, and large corporations exploit these human biases. They must make the customer's desires constantly change so that, through this, they can sell their new goods. To gain more profit, they are in a dual situation: on the one hand, they want the customer to be satisfied with the product they bought and remain loyal to their products, and on the other hand, they want the customer to be dissatisfied with the previously purchased product in some respect and want to buy the new model. Therefore, they are compelled to insinuate that the purchased product is good, but there is a new model that is better than the previous one.

In fact, companies and manufacturers create a sense of false need in us. In other words, even though the previous product still functions properly and meets our needs in the best way, they use tricks to make us think that the old product is no longer functional. Some contemporary thinkers call this "perceived obsolescence"[11]; that is, instilling the perception that the product no longer meets our needs and must be replaced with a newer model. Numbering products is one of these tricks. For example, with this very trick, they insinuate that the iPhone 4 no longer serves our needs and we must replace it with the iPhone 6. With such tricks, they constantly compel us to buy the newest product.

In summary, our psychological mechanisms as humans may cause us to misestimate the value of options. Part of this error also comes back to how others think about the desirability of things. How the crowd and the masses of people estimate the value of things affects our perspective. But is considering what the masses desire to be desirable a rational thing to do?

The Wisdom of Crowds, the Folly of Crowds

James Surowiecki[12] has written a book called The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations.[13] The main subject of this book is how, in the information age, one can use collective knowledge in individual life. In this work, Surowiecki gives interesting examples of collective knowledge; for instance, psychologists give a jar containing beans to many people and ask each of them to guess the number of beans in the jar separately. The participants in this test make various guesses. Some guesses are much lower than the actual number of beans, and some are much higher. Nevertheless, psychologists see that the average of the guesses is very close to the actual number of beans. Surowiecki says that if you repeat this experiment ten times with ten jars of beans, each time one or two people will estimate the number better than the rest; but after each time, the group's performance improves.

A famous example in this regard is the story of Sir Francis Galton, the nineteenth- and early-twentieth-century British scientist and cousin of Charles Darwin. Galton was an advocate of eugenics and believed that some people are inherently more intelligent, and that the state should prevent the reproduction of the dull-witted and less talented. He did not believe for a moment that the masses of people possessed any intelligence or wisdom.

In the autumn of 1906, the eighty-five-year-old Galton attended a fair: the West of England Fat Stock and Poultry Exhibition.[14] A contest was held at the exhibition. An ox was put on display, and people were asked to guess its weight after it had been slaughtered and its innards removed. Participants bought a ticket for sixpence and wrote their guess on it. The closest guess would then win a prize.

Eight hundred people took part in the contest. The participants came from various groups. Butchers and cattle farmers would probably make more accurate estimates, as it was their trade. Yet all sorts of people entered the contest. Galton, who was a haughty aristocrat, said in his contempt for the masses: "The average guess of those competing in the contest is probably as accurate as the average vote of electors in determining a worthy candidate."

Galton, who was interested in statistics, conducted an experiment. When the contest was over, he took all the tickets from the organizers. Of the 800 tickets, 13 were invalid. He sorted the remaining 787 tickets by their values and found their median (the median in statistics differs from the mean. The median is the number below which half the data falls and above which the other half falls). This number was 465 kilograms. The actual weight of the slaughtered ox was 543 kilograms. In other words, the median of the data was close to the true figure, with an error of less than one percent. The result was not very pleasing to the aristocratic, anti-democratic Galton, who advocated eugenics. Galton had, of course, found the median of the data; but later researchers also calculated the mean of that data, and interestingly, the mean of the data was also astonishingly accurate. The mean of the data was 542 kilograms—that is, just one kilogram less than the actual weight of the ox!

Another astonishing story dates back to 1968, when an American submarine disappeared in the North Atlantic and the navy could not find it, until finally a young officer did something unusual. He gathered a number of experts who understood submarines and had good geographical and geological knowledge of the North Atlantic. He gave them all the necessary information and asked each of them to separately estimate the cause of the submarine's sinking and its likely location. He kept the experts apart. They were not allowed to share their opinions with one another or criticize each other. Then, using Bayesian analysis,[15] he aggregated all the experts' estimates and calculated their mean. The result was interesting. It was not the case that one individual's estimate pointed to the exact location of the sinking; yet the mean of the estimates almost indicated the correct location of the submarine. The submarine's location was only 400 meters away from what the mean of the estimates had arrived at.

Can the wisdom of crowds always be trusted?

Relying on collective wisdom sometimes provides a clue for reaching the truth; but there is no guarantee that it will always lead us to the truth. Social psychologists and some philosophers call the approximate clues and signs that might be a path to the truth and correctly indicate a problem, heuristics.[16] These signs sometimes come as friends and sometimes as foes. Sometimes they guide and sometimes they mislead. Relying on collective wisdom is a method of estimation; a method that sometimes hits the mark and sometimes may lead us into error. If we are in a situation where no one knows the correct answer and everyone merely repeats what others say—that is, if we are dealing with a kind of pervasive ignorance—relying on collective wisdom will certainly mislead us.

As we said, to estimate the expected utility of anything we must assess its value for ourselves. But collective stupidity sometimes causes us to err in estimating the utility of something. In the examples we reviewed, reliance on collective wisdom led individuals to the correct result. In those examples (Galton's example and the lost submarine), each individual had assessed the matter separately, and no one had incited or compelled others to accept their assessment. Therefore, it can be said that if individual assessments are aggregated, they may lead us to the correct result. But when groups and decision-making individuals exert psychological influence on one another, "collective wisdom" probably gives way to "collective stupidity."

For reliance on collective wisdom to lead us to a correct estimate, people's ignorance must not be uniformly distributed; rather, there must be various forms of individual ignorance so that diverse ignorances moderate one another. The uniform distribution of ignorance among humans leads to a phenomenon that economists call "information cascade"[17] . In fact, the subjective and imprecise estimates of many individuals cascade incorrect information to the entire population. When many people repeat incorrect information and reinforce each other's views, others, who naturally tend to follow the crowd and align with the mass of people, assume that information must be correct.

The phenomenon of "herd behavior" has also been addressed in other scientific disciplines. In social psychology, a series of experiments known as the "Asch conformity experiments"[18] have been conducted, which clearly demonstrate humans' tendency to conform to the group and avoid standing out. In informal logic, accepting or imposing a belief merely because the masses believe it is recognized as a fallacy and is called the "appeal to the majority fallacy."[19] In any case, in estimating expected utility, information cascades and collective stupidity may cause us to obtain a flawed picture of our desired things.

We said that decision theory tells us that for rational decision-making we must calculate expected utility: by multiplying probability by utility. But we humans perform poorly in estimating both probabilities and utility. And when we have to put these two together, our task becomes even more difficult. The following example helps clarify the discussion.

Suppose we learn that a deadly influenza is about to break out in America, and if it is not contained, 600 people will die. Two programs are proposed to combat this influenza. If Program A is implemented, 200 people will be saved, and if Program B is implemented, there is a one-third probability that 600 people will be saved and a two-thirds probability that no one will be saved. Given this, which program should be implemented? 72 percent of those asked this question voted for Program A. But what does decision theory say?

According to decision theory, these two options are no different; because the expected utility of both is the same. It is clear that the expected utility of Program A is 200 people. The expected utility of Program B is as follows:

Now consider the same previous example with two different programs: If Program C is implemented, 400 people will die, and if Program D is implemented, there is a one-third probability that no one will die and a two-thirds probability that everyone will die. Of those asked which program to pursue, 78 percent said Program D. But what does decision theory tell us?

The expected utility of both programs is the same. If Program C is implemented, 400 people die; meaning 200 people survive. So the expected utility of Program C is 200. The expected utility of Program D is calculated as follows:

In other words, in Program C, 400 people die, and in Program D, the number of deaths is as follows:

You see that both numbers are the same. Therefore, decision theory tells us that Programs A, B, C, and D all have the same expected utility.

اما چرا آدم‌ها در چنین مواقعی در تصمیم‌گیری‌های خود خطا می‌کنند؟ برنامۀ الف و برنامۀ ب در قالب نجات‌پیداکردن آدم‌ها صورت‌بندی شده است. به‌بیان بهتر، اگر بین دو گزینه مخیر باشیم که در یکی جان آدم‌ها حتماً نجات پیدا کند و در دیگری جان آدم‌ها احتمالاً نجات پیدا کند، گزینۀ اول را انتخاب می‌کنیم. برنامۀ پ و برنامۀ ت در قالب مرگ‌ومیر آدم‌ها صورت‌بندی شده است. اگر گزینه‌ای در قالب مرگ‌ومیر حتمی صورت‌بندی شود، آن را انتخاب نمی‌کنیم. درواقع، وقتی گزینه‌هایی پیش رو باشد که احتمال زیان در آن‌ها می‌رود، آدم‌ها معمولاً خطرگریزند و وقتی گزینه‌هایی پیش رو باشد که احتمال سود در آن‌ها می‌رود، آدم‌ها معمولاً خطرپذیرند. پس شیوۀ صورت‌بندی مسئله است که در انتخاب ما تأثیر دارد و به ذهن ما سمت‌وسو می‌دهد؛ درصورتی‌که منطقاً سود و زیان در همۀ گزینه‌ها یکی است. آنچه در اینجا در انتخاب ما تعیین‌کننده است، خطرگریزی و خطرپذیری است.

مثال بالا و بعضی از مثال‌هایی که پیش‌تر آمد، از دنیِل کانِمَن[20] و عاموس تِوِرسکی[21] است. توضیحی هم که دربارۀ علت سوگیری ذهن آدمی ذکر شد، برمی‌گردد به «نظریۀ چشم‌انداز» که کانِمَن و تِوِرسکی آن را عرضه کرده‌اند. کانِمَن برای نشان‌دادن همین سوگیری‌ها و برای نظریۀ چشم‌انداز، جایزۀ نوبل اقتصاد را برد (البته تِوِرسکی آن موقع از دنیا رفته بود). بااین‌حال، جالب است که کانِمَن و تِوِرسکی هیچ‌یک اقتصاددان نبودند؛ بلکه هر دو روان‌شناس بودند.

نظریۀ چشم‌انداز (که کانِمَن و تِوِرسکی آن را در مقاله‌ای به همین نام مطرح کردند و کانِمَن بعدها آن را در کتاب مشهور خود، تفکر روی دور تند و تفکر روی دور کند، بسط داد) دربارۀ این است که مردم چطور باتوجه‌به چشم‌انداز سود و زیان (و نه صرفاً براساس پیامد نهایی) تصمیم می‌گیرند.[22] در بحث آن‌ها «چشم‌انداز» یعنی نتیجه‌های محتملِ تصمیم که میزان احتمال وقوع هریک را قبل از تصمیم‌گیری می‌توان تخمین زد.

پیش‌تر گفتیم که نظریۀ تصمیم‌گیری نظریه‌ای تجویزی است؛ یعنی دربارۀ این می‌گوید که آدم‌ها چطور باید تصمیم عقل‌پسند بگیرند. اما نظریۀ چشم‌انداز نظریه‌ای توصیفی است؛ یعنی دربارۀ این می‌گوید که آدم‌ها در عمل چطور تصمیم می‌گیرند. نظریۀ تصمیم‌گیری به ما می‌گوید هر تصمیم چه وقت عاقلانه است؛ ولی چنان‌که گفتیم، گاه ما آدم‌ها تصمیم‌های نابخردانه می‌گیریم و این برخاسته از دو عامل است: یا احتمالات را درست محاسبه نمی‌کنیم و به‌جای توسل به آمار، به تصویر ذهنی خود اتکا می‌کنیم؛ یا محیط پیرامونی در تصمیم‌گیری راهزنی می‌کند و ذهنمان را در شناخت مطلوبش گمراه می‌سازد.

اما نظریۀ تصمیم‌گیری مشکلات دیگری نیز دارد. کانِمَن و تِوِرسکی احتیاط می‌کنند و نمی‌گویند که برآوردکردن سود و زیان باتوجه‌به خطرگریزی و خطرپذیری کاری است یکسره نابخردانه؛ اما طبق نظریۀ تصمیم‌گیری، این نحوۀ محاسبه اصلاً عقلانی نیست. برای فهم بهتر موضوع، خوب است از مفهومی کمک بگیریم که دیرزمانی است در زبان اقتصاددان‌ها رواج دارد و به آن می‌گویند «مطلوبیت حاشیه‌ای کاهنده». منظور از این اصطلاح این است که افزوده‌شدن یک واحد به یک چیز لزوماً افزوده‌شدن یک واحد به مطلوبیت آن نیست. درواقع، اگر چیزی بیشتر شود، چه‌بسا ارزش هر تک‌واحد از آن چیز کم شود. برای مثال، هزار تومان برای کسی که میلیاردها تومان ثروت دارد، به‌اندازۀ هزار تومان برای کارتن‌خواب ارزش ندارد.

البته «مطلوبیت حاشیه‌ای کاهنده» نظریۀ تصمیم‌گیری را نقض نمی‌کند و با آن همخوان است؛ اما کانِمَن و تِوِرسکی می‌گویند دربارۀ سود و زیان هم باید کار مشابهی کرد. به‌عبارت گویاتر، در بعضی مواقع شاید معقول این باشد که آدمی بیشتر دل‌مشغولِ حفظ مقداری از مطلوبِ به‌دست‌آمده‌اش باشد تا به‌دست‌آوردن همان مقدار از آن. برای مثال، فرض کنید سالانه ۵۰۰میلیون تومان درآمد دارید و با این پول راحت زندگی می‌کنید. فکر ازدست‌دادن این ۵۰۰میلیون تومان وحشتناک است؛ ولی فکر به‌دست‌آوردن ۵۰۰میلیون تومانِ دیگر، خوشایند است. حال می‌توان پرسید: آیا مطلوبیت به‌دست‌آوردن ۵۰۰میلیون تومانِ دیگر در سال با نامطلوبیت ازدست‌دادن آن ۵۰۰میلیون تومانِ خودتان برابری می‌کند؟ احتمالاً نه. پس گاهی نامطلوبیت ازدست‌دادن چیزی با مطلوبیت به‌دست‌آوردن همان مقدار از آن چیز یکسان نیست. باوجوداین، نظریۀ تصمیم‌گیری به ما می‌گوید برآوردکردن سود و زیان به این شیوه همیشه نامعقول است. پس ظاهراً نظریۀ تصمیم‌گیری محدودیت‌هایی دارد و این نظریه از بعضی خصلت‌های روان آدمی در تصمیم‌گیری غفلت کرده است. شاید هم باید تفسیر دیگری از این نظریه به دست داد.

مطلوبیت منتظره و ارزش جان آدمی

تاجری به‌اسم تونی بولیمور در ژانویۀ ۱۹۹۷ تصمیم می‌گیرد در مسابقۀ قایق‌رانی، دور دنیا را بگردد. در مسیر مسابقه، به آب‌های سرد اقیانوس منجمد جنوبی می‌رسد و در آنجا قایقش در میان بادهای طوفانی و امواج سهمگین واژگون می‌شود. تونی چهار روز زیر بدنۀ قایق گیر می‌افتد و خبری از او نمی‌رسد. مردم همه گمان می‌کنند او جان داده است؛ اما سرانجام نیروهای دفاع استرالیا در یکی از گسترده‌ترین و پرهزینه‌ترین عملیات‌های نجات، او را پیدا می‌کنند و جانش را نجات می‌دهند.[23]

اما آیا این عملیات پُرهزینه برای نجات جان یک انسان ارزشش را داشت؟ اگر بختِ نجات بسیار ناچیز باشد و هزینۀ نجات گزاف، آیا باز جامعۀ مدنی و دولت باید هزینۀ نجات را بپردازند؟ سقف این هزینه چقدر است؟ اساساً آیا می‌توان روی جان انسان قیمت گذاشت؟ برای روشن‌ترشدن بحث، خوب است ماجرای یکی از خودروهای کارخانۀ فورد را در اینجا نقل کنیم که در بین فیلسوفان اخلاقِ کاربردی بسیار بحث‌انگیز بوده است.[24]

پینتو اسم خودرویی است که از ۱۹۷۱ تا ۱۹۸۰ در کارخانۀ فورد ساخته می‌شد. پینتو قرار بود رقیب فولکس‌واگن باشد و باعث شود واردات خودروهای ژاپنی به آمریکا کم شود. در آن زمان معمولاً ۲۳ ماه طول می‌کشید تا خودرو به تولید انبوه برسد. فورد ظرف ۲۵ ماه پینتو را کامل کرد. لی آیاکوکا[25]، رئیس بخش تولید، دستور داده بود که وزن پینتو نباید سرِ سروزنی بیشتر از ۹۰۷ کیلوگرم شود و ساخت خودرو نباید یک پنی هم بیشتر از ۲هزار دلار خرج بردارد.

پینتو مخزن گازی در قسمت عقبش داشت که به‌دلیل کوتاهی‌های کارخانه، فاجعه‌ساز شد. دست‌کم ۵۰۰ نفر به‌علت ایراد مخزن گاز پینتو جان باختند. بعد از آن، دعواهای حقوقی فراوانی علیه فورد طرح شد و در خلال همین دعواهای حقوقی، جزئیات کار رو شد. در برنامه‌ریزیِ قبل از تولید، جای دیگری برای این مخزن گاز در نظر گرفته بودند. پیشنهاد این بود که مخزن گاز پینتو مثل مخزن گاز خودروی دیگری از کارخانۀ فورد، یعنی خودرویِ کاپری، باشد. در کاپری، برخلاف پینتو، مخزن گاز زیر اَکسِل پشت خودرو در دیفرانسیل قرار نمی‌گیرد؛ بلکه بالای آن قرار می‌گیرد و تعبیۀ این مکان برای مخزن گاز در این خودرو موفق بوده است. فورد این شیوه را به‌خوبی آزمایش کرده و تأیید کرده بود که اگر با سرعتِ زیاد هم خودرو ضربه‌ای ببیند، مخزن در امان است.

بااین‌همه، چرا فورد این روش را در ساخت پینتو به کار نگرفت؟ ظاهراً دلیلش فضای صندوق‌عقب خودرو بود. بعدها یکی از مهندسان فورد این را توضیح داد: «مسئله اصلاً امنیت نبود. مهم فضای صندوق‌عقب خودرو بود. شاید باور نکنید رقابت بر سر فضای صندوق‌عقب چقدر شدید است. توجه کنید که اگر مخزن پینتو را مثل مخزن کاپری می‌ساختیم، فقط یک دست چوب گلف در صندوق‌عقب جا می‌شد.»[26]

Ford could have solved this problem with some modifications to the Pinto. It knew that by installing a fire‑retardant shield on the gas tank, this issue could be prevented and the lives of hundreds of people could be saved. But this would cost $11 per vehicle, which, given the mass production of this car, would impose a significant cost on the factory. Moreover, it conflicted with Lee Iacocca's estimate that the car should not cost a penny more than $2,000.

Ford refused to spend $11 per vehicle and install this part; because, according to its cost‑benefit analysis, this action was not justified. In fact, it calculated how much this action would cost it and how much benefit it would bring; that is, it calculated the potential benefits and potential costs of each action in order to make a rational decision by weighing the expected utility of each step. The details of Ford's calculations came to light during the trial. Ford's estimate showed that the potential benefit of installing this part was $49.5 million; but the cost of installing this part on every single Pinto, with that mass production volume (12.5 million vehicles), would be $137 million. Therefore, it was clear that the potential costs of installing this part far exceeded its potential benefits.

But how did Ford calculate the potential benefit of installing the part and arrive at $49.5 million? Ford predicted that without adding this part, 2,100 vehicles would catch fire and, as a result of these fires, 180 people would die annually. They also estimated that each injured person would cost $67,000. But what about those who died? How should they have calculated this? There was no choice but to quantify the damage. In the cost‑benefit analysis of this case, how did they calculate this? What value did they place on human lives? Ford at that time estimated the death of each human being at $200,000. In 1972, the National Highway Traffic Safety Administration (NHTSA)[27] had reported that the value of each human life was $287,175. Ford's estimate was slightly lower than the U.S. government's estimate.

In this way, Ford was forced to put a price on human life and trade on it. But this seems repugnant. Isn't putting a price on human life horrifying? The issue is not that they underestimated the price of human life. The matter is not about numbers at all. It is as if the very act of pricing human life is terrifying. How can one put a price on a human life?

The Myth of the Infinite Value of Human Life

Apparently, the behavior Ford exhibited in pricing human lives is considered distasteful and immoral by many. The source of this perception is probably that many people believe the value of human life is incalculable and cannot be priced; because human life has infinite value. But can one assign a value equal to infinity to human life? This statement is not precise or correct, and several arguments can be made against it.

The First Argument Against the Idea That Every Human Life Has Infinite Value

With a simple calculation concerning infinity, it can be shown that it is impossible for the value of every human life to be infinite. We know that if we add any number to infinity, the result is still infinity. Also, if we multiply any finite number by infinity, the product is still infinity. By this reckoning, if the value of every human life is infinite, the value of one person's life becomes equal to the value of any number of people's lives; because the product of any number multiplied by infinity is infinity. Therefore, if the value of every human life is infinite, the death of one million people or one billion people becomes equal to the death of one person. But is this reasonable?

A thought experiment[28] clarifies this matter further. Suppose we are forced to choose between two options. If we choose the first option, only one person dies, and if we choose the second option, most of the inhabitants of the Earth die. Is there no difference between these two options? Apparently, common sense dictates that we choose the first option; whereas if the value of every human life were infinite, these two options would be no different.

The Second Argument Against the Infinite Value of Every Human Life

It seems that the belief held by some that the value of every human life is infinite is more of an emotional reaction, conveying the message that human life is not worthless and is, in fact, the most valuable thing a person possesses. Nevertheless, in the real world, we usually do not act in accordance with such a belief.

We humans practically risk our lives for things we value. For example, every time we cross the street, we accept a certain amount of risk and believe it is worth taking that risk. We go to amusement parks and engage in high-risk recreations because we think it is worth it (even if we lose our lives in the process). We also accept the dangers of mountaineering to conquer a peak. This is while if we assigned infinite value to our lives, we would never endanger them, or at least we would take fewer risks.

To put it more clearly, people believe the value of human life is infinite, yet it seems each person places a value on their own life. In fact, our behavior shows that we ourselves estimate the value of our lives, and when the cost of having safety becomes heavy, we are not willing to pay it. When we leave the house in a Pride, we know our car is not very safe and we are accepting some risk. Nevertheless, we get in the Pride and go. If we commuted in an armored tank, this risk would likely be much lower, but reducing the risk is not worth the cost. Also, not leaving the house would provide more safety, but no one is willing to adhere to that. Given these circumstances, it seems we do not assign infinite value to our own lives.

The Third Argument Against the Infinite Value of Every Human Life

If every human life has infinite value, then any two human lives are worth exactly the same amount, because infinity equals infinity. But is this claim acceptable? Again, a thought experiment clarifies the matter. Suppose we have two options before us and can only choose one, and with our choice, we can save only one human life: a healthy, intelligent eighteen-year-old teenager and a frail, decrepit eighty-year-old man. If we can only save one of these two, which should we choose? It seems our moral and rational intuition tells us we should save the teenager, even if the cost is the death of the eighty-year-old man. So, it appears that not every life has infinite value, because not all lives have equal value. However, one might quibble with this argument.

The first objection that could be raised against this argument is: "Doesn't this choice somehow promote ageism?" In response, it must be said that this is not the case. Firstly, we should note that in this thought experiment, we are "compelled" to make a choice, and it is not the case that someone making such a choice is necessarily an advocate for systematic discrimination against the elderly. Secondly, the thought experiment can be modified so that reason dictates sacrificing the younger individual. Suppose we are forced to choose between these two options: a ten-year-old child with no hope of survival, whom doctors say will die next year, and a seventy-year-old man who is healthy and athletic and is expected to live for at least another twenty years. In this situation, it seems sacrificing the ten-year-old child is more reasonable. Therefore, this choice is not necessarily based on age.

Another objection that can be raised against this argument is: “When we say that human life has infinite value, we say this in a general sense. If we are told to choose between person A and person B and we know nothing about either of them, we have no measure for choosing. This is while, in the thought experiment above, we are only saving a part of the two people’s lives, not their entire lives. In fact, the eighteen-year-old teenager might live to be eighty, and if we choose him, we have saved 62 years of life; but when we choose the eighty-year-old man, even if he lives to be ninety, we have only saved 10 years of life. So it is not the case that in this thought experiment we have chosen between the lives of two people; rather, we have chosen between the number of years the two people can live.” This objection seems to be correct. However, this objection helps us clarify the claim that all lives are equally valuable. It must be said that it is not the case that people’s lives have equal value “in every respect.” If we are forced to choose between two people, one of whom has more years ahead of them to live and the other fewer, it is rational to sacrifice the latter.

This idea that every human life is worth the same amount has another problem. To demonstrate this problem, we must modify the previous thought experiment somewhat. Suppose we are forced to choose between these two options: saving the life of someone whose destiny in life is misery and wretchedness, and saving the life of someone who has a plan and design for their life and whose life is very fruitful and useful. Let us make these two examples more precise. Suppose we are forced to choose one of the following:

1_ Saving the life of a drug addict who is a thief and destitute;

2_ Saving the life of a doctor who researches cancer and whose research will likely bear fruit before long.

If, for example, due to a shortage of medical resources, we are compelled, does reason not dictate that we save the life of the latter at the cost of losing the life of the former? Suppose we can know everything about both of their lives. One life is full of pain, humiliation, and abjection, and the other is brimming with pleasure, virtue, and achievement. We can only save one life. What does reason dictate?

Again, one can object that when we compare the lives of these two people, it is not the value of their lives that is being compared; rather, we are comparing and evaluating other things. The objector says this thought experiment does not show that one life is more valuable than another; rather, it shows that happiness is better than pain and suffering, or that having achievements is better than being destitute. The value of these two lives is the same. It is the content of each of these two lives that differs. In other words, the lives of these two people, insofar as they are lives, are no different from each other; but what has transpired in their lives does not have the same value. This objection separates the “form of life” (life in itself) from the “content of life” (happiness or misery).

Nevertheless, what meaning does the abstract and formal concept of life, separate from the content of life, have? My life is my life because of the content it has. The value of my life lies in its content. It seems that content must be taken into account, and if we take content into account, it is as if not all lives have the same value.

It seems meaningless to say, in the true and non-metaphorical sense of the phrase, that human life has infinite value. This statement means that all human lives have equal value, and this belief that all human lives have the same value is only defensible if we understand it in a narrow, closed, and minimal sense; meaning that we say the mere fact that one life is the life of person A and another life is the life of person B does not make the value of one of those two lives greater or lesser.

This statement seems correct and falls under a general concept in ethics that Kant called universalizability.[29] According to this concept, if doing something in a particular context is impermissible for one person, then doing that thing in the same context is impermissible for everyone. Therefore, merely knowing that we are dealing with the life of person A and the life of person B, without having any other knowledge about these two individuals, we cannot differentiate between the value of these two lives; because every life is someone's life. It seems only in this minimal sense can one defend the claim that the value of all lives is equal. Thus, every life has its own content, and content causes the value of lives to differ (for example, flourishing is better than failure, happiness is better than misery, prosperity is better than poverty). Once content comes into play, we must come to terms with the fact that people's lives do not have the same value.

Now let us return to the Pinto affair. According to what we have said, one cannot defend the notion that the value of anyone's life is infinite, and also, if content is involved, one cannot defend the notion that all people's lives have the same value. But why did we dislike the fact that the Ford company put a price on human lives? Why was the Ford company's action horrifying and disgusting? Is this feeling of disgust that afflicted us upon encountering the Ford company's decision an inappropriate emotion, entirely devoid of cognition? We must explore this emotion a little. Emotion is not always devoid of cognitive content, and sometimes an appropriate and fitting emotion gives a person important clues.

Probably, what offends one in this affair is not the statement that everyone's life has a value and that the value of all lives is not equal; rather, it is that measuring the value of a human life with money and putting a price on it is unpleasant and disgusts us. Of course, this does not mean that if a human life were measured with money, its price would be infinite. The point is that the lives of those put at risk are not measurable with money; that is, money and life are incommensurable.[30] In other words, money contains one type of value, and life contains another type of value. What offends the audience is that Ford imagined these two values are of the same type and conflated them.

With all this, one can look at the Ford company's decision somewhat sympathetically. Perhaps it could be said that the decision the Ford company made has been misinterpreted, and one can offer a different interpretation of their actions. In fact, despite appearances, their calculations need not be interpreted as wanting to put a price on human lives. One could say that the Ford company wanted to calculate how likely it was that lawsuits filed against it would succeed, and how much the company would lose if the Pinto's design caused fatalities.

But what about the U.S. National Highway Traffic Safety Administration? Was its pricing of human lives an ethical and correct act? The reality is that in public policymaking, economists believe one must assign a value to human life that can be measured, and this is practically important. For example, if we want to dig a tunnel through a mountain, there is a possibility that someone or some people will lose their lives in the process. So, one must determine whether this undertaking is worth its outcome. The price placed on human lives in these studies is mainly based on how much income the individual is likely to earn in the remainder of their life. This figure clearly has application in legal cases. In the jurisprudence and laws of our country, the function of diyeh or blood money is the same. If we accept this sympathetic interpretation of the Ford company's decision, it can be said that the estimate Ford made based on cost-benefit analysis is not, in the strict sense of the word, an estimate of the value of human life; rather, it is an estimate of the average amount that would be awarded against the company in court if fatal accidents occurred.

With all these explanations, we may still not accept this interpretation of Ford's actions and our sense of revulsion may not be diminished; because the wrongdoing of the Ford factory was not merely that it assigned an incorrect value to human life, but the flaw in its action was that it fundamentally did not think about the value of human life and thought only about money. To put it more precisely, the lives of flesh-and-blood people were at risk, and Ford was calculating with an abacus for money and only thought about how much money they might have to pay if they were sued.

As we said, the value of human life cannot be measured with money; because money and life, although both are valuable, each possesses a type of value, and these two types of value are not translatable into one another. Therefore, it is not the case that if one is endangered, the other takes its place. Nevertheless, in an emergency situation, one might be "compensated" with the other; but to endanger people's lives merely for more money is not morally right.

But with what else can human life not be measured? So far, our thought experiments have been about sacrificing someone's life to save the life of another person or many other people; that is, we have valued and gauged human life against human life. This valuation seems correct. But if someone says that the value of human life can only be measured against human life and cannot be measured against any other value, to what extent is this statement correct? We must see whether an acceptable thought experiment can be constructed in which the rational thing to do is to sacrifice human life for another value, or not. In other words, is there anything worth dying for? Probably most of us think such a thing exists. But if we ask what things are worth sacrificing our sweet life for, we mostly name another person; for example, we say we are willing to die to save the life of our child or our beloved. Also, when we can save the lives of others through self-sacrifice and giving up our own life, we might consent to this; like the combatants who show sacrifice and devotion on the battlefields. Nevertheless, in these examples, we are again measuring human life against human life. The question is: Is there anything besides human life whose value makes it worth a human dying for it? It can be said that when giving up one's own life can relieve the suffering and pain of many people, it is worth sacrificing our life for this goal. In this case, a person's dying does not prevent anyone's death; but it can prevent torture, intimidation, and torment and make life better for many other human beings. If we accept this analysis, we must say that the value of human life is not separate from other values and it is not the case that it cannot be measured against any other value.

So far, in reflecting on whether there is anything worth a human life, we have examined an individual who personally decides about their own life and whether to sacrifice their life for something or not. But sacrificing someone else's life to achieve a value we deem higher is a different discussion. We might praise someone who dies while climbing Mount Everest, or perhaps praise one of their qualities; but if someone sacrifices the life of their companion or friend to conquer Mount Everest and says achieving such a goal was worth this act, we will probably be disgusted by them. In such situations, in addition to the individual's life, a fundamental right has been trampled: their right to determine their own destiny. In fact, everyone has the right to sacrifice their own life if they wish. This right cannot be taken from someone, and one cannot choose on their behalf. But is there anything else, besides the lives of others, so valuable that it is worth sacrificing the life of another person or persons for it?

The Coronavirus Disease and the Dilemma of Allocating Scarce Resources

This article is being written at a time when a deadly viral disease called Corona has become a pandemic. Today's situation more or less resembles the state of apocalyptic novels and films; novels such as Camus' The Plague, Saramago's Blindness, Kurt Vonnegut's Slaughterhouse-Five. Corona has spread across the entire globe and left no place safe. From poor countries to the affluent nations of Northern Europe, all have been brought to their knees by the Coronavirus. Just a day or two ago, Boris Johnson, the Prime Minister of Britain, and before him the spouse of the Prime Minister of Canada, contracted this disease.

The disease has moved past the epidemic stage and become a pandemic. Doctors and specialists speculate that soon, due to the increase in the number of infected individuals, even the medical facilities of advanced countries will face severe shortages, and all nations will encounter great difficulty in treating the masses of patients. In the meantime, we must think in advance about the ethical dilemmas concerning the allocation of scarce resources.

It is clear that if the situation were such that medical facilities were available for everyone, the humane duty of healthcare system workers would be to attend to everyone with fairness. But unfortunately, the world we live in is a world of scarcity, and humans are always compelled to strike a kind of balance between their desires and the limited resources at their disposal to fulfill those desires.

Economists use the term "opportunity cost"[31] to refer to this concept. Simply put, opportunity cost means that using any limited resource to fulfill any goal entails losing the opportunity to use that resource for other goals. Therefore, in any matter, one must decide in such a way that the opportunity cost is lower and the expected utility is higher. The sensitivity of such decisions is doubled in emergency situations. More precisely, in an emergency situation, resources are scarcer, the demand for resources is greater, and the opportunity cost is higher. Hence, one must decide more judiciously and proceed more consciously.

As we said, in confronting the Corona pandemic, clinics, hospitals, and other medical centers will sooner or later be compelled to intervene in how services are provided and to make choices. In this situation, many ethical dilemmas and questions grip the staff and those involved in the healthcare system. Among these, the most important problem is how to ration scarce medical resources and services and make them available to everyone in the most effective way. Their interventions in these matters can be examined in three areas: interventions related to prevention, interventions related to diagnosis, and interventions related to treatment. In all three areas, careful prioritization must be carried out.

With the Corona pandemic, we are facing a shortage of resources in all three areas of prevention, diagnosis, and treatment. In the area of prevention, we are faced with a shortage of personal protective equipment (items such as masks, gloves, and alcohol) and vaccines (if such a vaccine is found). In the area of diagnosis, we are grappling with a shortage of test kits, as well as a shortage of hospitals and healthcare system staff. In the area of treatment, in addition to a shortage of hospitals, the number of intensive care unit beds, and healthcare system staff, we are faced with a shortage of medicine[32] and equipment such as ventilators. This is where choice comes into play, along with cost-benefit analysis and the estimation of expected utility.

As we previously discussed in detail, the value of a human life is not infinite, nor is it the case that all lives are equally valuable. Therefore, the rational course of action in this regard consists of maximizing expected utility in the domain of health; that is, increasing life expectancy or increasing the quality of life, or increasing both.

But before entering the discussion, it is good to consider one or two objections:

First objection: Shouldn't all patients have equal access to medical services? Doesn't prioritizing patients based on expected utility fuel a kind of discrimination and injustice?

در پاسخ باید گفت در وضعیت آرمانی که وفور منابع موجب می‌شود خدمات درمانی در دسترسِ همۀ بیماران باشد، این حرف اخلاقاً درست است؛ اما در وضعیت اضطراری که مقدار منابع درمانی از تعداد متقاضیان درمان بسیار کم‌تر است، از انتخاب میان بیماران گزیری نیست. بااین‌همه، این انتخاب باید عاقلانه باشد. در این وضع، روش کارآمد برای تصمیم‌گیری، توسل به مطلوبیت منتظره است.

ایراد دوم: چرا نباید منابع را صرفاً به کسانی اختصاص دهیم که بیشترین نیاز را به آن‌ها دارند؟ کسی که بیماری سخت‌تری دارد، فارغ از سن‌وسال و مطلوبیت منتظره‌ای که برای جامعه دارد، باید در اولویت دریافت خدمات درمانی باشد.[33]

در پاسخ باید گفت هرچند شدت بیماری و نیاز بیمار به درمان از عوامل مهم در اختصاص‌دادن امکانات درمانی است، این عامل را نباید یگانه عامل دخیل در انتخاب دانست؛ دست‌کم به سه دلیل:

دلیل اول

باز آزمایشی فکری را در نظر بگیرید. فرد الف به بیماری حاد و مهلکی مبتلاست که امید چندانی به درمانش نیست و درعین‌حال، حفظ زندگی این بیمار هزینۀ هنگفتی دارد؛ مثلاً هزینه‌ای برابر با هزینۀ درمان ده بیمار دیگر که بیماری آن‌ها به‌شدتِ بیماری بیمار الف نیست. در این حالت، به نظر نمی‌رسد عقل سلیم حکم کند که از جان آن ده بیمار صرف‌نظر کنیم. این هزینه به فایده‌اش نمی‌ارزد و استفاده از منابع به این شکل، کارایی مطلوب را ندارد و مطلوبیت منتظره را افزایش نمی‌دهد. اگر منابع به‌قدر کافی بود، البته همۀ بیماران باید به‌یکسان خدمات درمانی می‌گرفتند؛ ولی وقتی منابع کمیاب است، باید دید مطلوبیت منتظرۀ هر تصمیم برای جامعه چقدر است و آن را بیشینه کرد.

دلیل دوم

به نظر می‌رسد رویکردی که می‌گوید منابع درمانی صرفاً باید به نیازمندترین‌ها اختصاص پیدا کند، گاه از انصاف و عدالت به‌دور است. با این نگاه، فقط مبتلایان به بیماری‌های مهلک‌اند که خدمات درمانی می‌گیرند؛ حال‌آنکه مبتلایان به بیماری‌های مزمنی که بالقوه مرگ‌بار است، مغفول می‌مانند. برای مثال، بیمار مبتلا به آنژین قلبی که خطر حملۀ قلبی در کمین اوست، خدمات درمانی دریافت نمی‌کند؛ درصورتی‌که او هم بیماری مهلکی دارد (منتها بیماری‌اش بالقوه مهلک است و هنوز از قوه به فعل درنیامده است). بااین‌وصف، به نظر می‌رسد اینکه صرفاً برپایۀ نیازِ بیمار، منابع درمانی را اختصاص دهند، نه‌تنها شیوۀ کارآمدی نیست، بلکه گاه دور از انصاف است.

دلیل سوم

گاه ناچاریم از میان بیمارانی که وضع یکسانی دارند و نیازشان به خدمات درمانی به یک اندازه است، کسانی را انتخاب کنیم. در این حالت، پیش‌بینی پزشکان دربارۀ آیندۀ بیماران (پیش‌بینی‌ای که به آن «پیش‌آگهی»[34] می‌گویند) فرق معناداری ندارد. درنتیجه، برای تصمیم‌گیری، به ملاک دیگری به‌جز نیاز بیمار به درمان نیاز داریم.

***

جانِ آدمی ارزش بسیار دارد؛ البته نه بی‌نهایت. نیز جان همۀ آدم‌ها به یک مقدار نمی‌ارزد. ارزش جان بعضی از ارزش جان بعضی دیگر بیشتر است. ظاهراً در نگاه نخست و با درنظرگرفتن پاره‌ای قیود، اینکه منابع را برپایۀ معیار بیشینه‌کردن مطلوبیت منتظره برای جامعه به عده‌ای اختصاص دهند، گزینۀ معقول و کارآمدی است و یکی از ملاک‌های معقول برای این کار که درباره‌اش اجماع نسبی وجود دارد، بیشینه‌کردن سال‌های زندگی است. قید «در نگاه نخست»[35] را به این سبب افزوده‌ایم که ممکن است گاهی پاره‌ای ملاک‌های دیگر که ارزش بیشتری دارد، بر این ملاک بچربد. درواقع، اصل بر این ملاک است؛ مگر اینکه ملاحظات اخلاقی و عقلانی مهم‌تری پیش بیاید که ناچار شویم این ملاک را جرح‌وتعدیل کنیم. در این میان، ارزش‌های اخلاقی پایه‌ای وجود دارد که در کنار مطلوبیت منتظره، سرنخ‌هایی برای انتخاب اخلاقی و عقلانی به دست می‌دهد. پیش از اشاره به این ارزش‌ها، ذکر سه نکته لازم است.

Firstly, as we saw in the Pinto car example, the value of human life cannot be measured in money. Therefore, in healthcare, any allocation of resources based on money and the creation of financial competition to access medical resources is morally reprehensible. Even if this is the current and common practice in our world today, the healthcare system should not ethically submit to it. The efforts of the government and public policymakers should be such that the means for treating people from every class, regardless of their financial ability, are provided. In fact, wealth should not be a determining factor in receiving healthcare services. This becomes especially important when pandemics occur.

Secondly, political power and fame should not cause discrimination in the provision of healthcare services. Here, we can advance the same reasons we discussed regarding the value of money and its comparison with the value of human life, concerning the value of political power and fame and their relation to the value of human life. To put it more clearly, human life has a value that cannot be measured against the value of power and fame. For the allocation of medical resources, being a politician or being famous is not considered an ethical and rational criterion.

Thirdly, the selection of a patient for the allocation of scarce resources should not be arbitrary and unsystematic; for example, the fact that a patient is a close friend or relative of healthcare system staff, or that a physician dislikes the patient's appearance, demeanor, or accent, or that the patient has been recommended, should not influence the provision of healthcare services. Likewise, the patient's religion, nationality, and race should not have any effect on this matter. Such selections have absolutely no rational or ethical basis.

Four Fundamental Ethical Values in Confronting a Pandemic

In a situation where a pandemic has emerged, four fundamental ethical values can be considered guiding lights. Each of these four values is not useful on its own; rather, we must move back and forth between them and strike a balance among them. In this way, by keeping these four criteria in mind and according to our estimate of expected utility, we can make a fair, reasonable, and contradiction-free decision.[36]

1_ Maximizing the Benefits Derived from Scarce Resources

This ethical value is, in fact, the maximization of expected utility and the efficient allocation of resources. In other words, in such a situation, resources must be utilized in a way that, firstly, more years of life and, secondly, more lives are saved.[37] Therefore, how many years of a patient's life likely remain is important. In an equal situation, treating those who will live longer after treatment yields greater expected utility. Consequently, this group is prioritized for receiving healthcare services. Also, patients whose probability of recovery after treatment is higher are prioritized over patients whose probability of recovery after treatment is lower, and over patients who will likely recover without treatment. It is evident that young patients whose illness is severe and who are at risk of dying young are prioritized. In an equal situation, providing healthcare services to someone whose remaining years of life will be in full health is superior to providing healthcare services to someone whose remaining years of life will be grappling with illness and infirmity.[38] Nevertheless, in a situation where we are facing pandemics, we may become so pressed for time that we do not have the opportunity to predict the patient's future quality of life. Therefore, in this situation, this task may become unnecessary.

2_ Treating People Equally

In a situation of resource scarcity, the requirement of fair treatment of clients generally means that priority should be given to those who arrived earlier; just like when people queue for something and their position in the queue is determinative. The queue is the same for everyone and is a requirement of egalitarian treatment of clients. Of course, there is another way, which is drawing lots and random admission of patients.

Nevertheless, it seems that with regard to COVID-19, queuing is not a suitable solution; that is, prioritizing the provision of medical services based on early arrival does not have the necessary efficiency. This results in those who fell ill later (possibly because they took public health recommendations more seriously) being excluded from the circle of treatment. Also, since COVID-19 is highly contagious, maintaining distance from others is important, and queuing likely disrupts social distancing.

Another approach for dealing fairly with patients is to offer them medical services based on the physician's prognosis of the patient; that is, the physician, considering the patient's condition, predicts the future course of their illness and, in this way, advances the treatment process in line with maximizing expected utility. However, the question remains as to which patient, from among the multitude of patients, should be selected for such assessments. This can be done randomly or by drawing lots. If physicians are under time constraints and there is no opportunity for a proper prognostic estimate for all patients, drawing lots is a good solution.

3. Promoting Instrumental Value and Rewarding It

Some individuals, in addition to their lives being valuable, have instrumental value in saving the lives of others. These individuals are more valuable than others because their existence is essential for combating the disease. The researcher, physician, nurse, paramedic, nursing assistant, hospital cleaner, and even the hospital doorman all belong to this group, and saving their lives increases expected utility. Accordingly, treatment priority is with those who can play an effective role in saving the lives of others, as well as those who have played a role in saving others' lives in the past. Among this group, under equal conditions, treatment priority is with those who are exposed to greater risk and also those for whom finding a replacement is difficult. In addition, all healthcare system personnel must be prioritized for receiving personal protective equipment. They must also be given assurance that if their lives are endangered, they will have treatment priority.

Prioritizing this group in treatment, even if we are not certain they will return to healthcare work after treatment, is necessary for two reasons: firstly, because they have accepted a high-risk job, and showing gratitude to them is morally obligatory; secondly, because if we do not do so, other healthcare system personnel, upon seeing this neglect and ingratitude, may withdraw from their work.

Another noteworthy point relates to our duty towards these individuals and not discriminating in appreciating them, as well as in providing services to them and preventive care for them. We are obligated towards all those who risk their lives to save the lives of others. The fact that physicians and nurses are more visible should not make us overlook the role of lower-ranking staff.

4. Prioritizing Sicker Patients

Under equal conditions and with regard to maximizing expected utility, those whose illness is more severe or who, if their probability of death from the disease is high, do not have much time, are a priority. This value also shows that the prioritization strategy based on time of arrival is not very efficient in treating this disease; because the sicker patient has a greater need for treatment and is the priority. Prioritization based on time of arrival is useful for treating diseases where the individual will not perish if they wait for treatment.

***

An important point to note in this discussion is that we must distinguish between the allocation of prevention resources, diagnostic resources, and treatment resources, and organize priorities appropriately in each case. For the COVID vaccine, which serves as prevention, children and younger people should not be prioritized, because the disease is more dangerous for the elderly. It seems the right of vaccine priority is first with healthcare workers and then with the elderly. At the same time, one must be sensitive to scientific evidence and change prioritization in light of changing scientific evidence. For example, if a young patient had instrumental value (i.e., was a healthcare worker) and if studies showed that the best way to reduce the spread of the virus was to vaccinate young people, then maximizing society's expected utility requires that they be prioritized. Also, if the vaccine is insufficient for all eligible individuals, fairness dictates a lottery. For COVID diagnostic testing, priority is also with healthcare workers and, next, with older people. Conversely, for allocating ICU beds and ventilators, which are treatment resources, prioritization must be based on the physician's prognostic judgment. In this case, younger people with more severe illness are prioritized, and those whose likelihood of survival is very low have lower priority for using ICU beds.[39]

Finally, in allocating resources to COVID patients and patients with other fatal diseases (e.g., cancer and heart disease), no discrimination should be made. Contracting COVID is not in itself a factor for prioritization; for instance, a physician with a history of severe allergy who is likely to show a fatal allergic reaction (known as anaphylaxis) has priority for using a ventilator over a COVID patient who is not a healthcare worker.

Therefore, by utilizing the concept of expected utility and keeping in mind the four ethical principles mentioned, the use of prevention, diagnostic, and treatment resources can be managed and prioritized in an ethical and rational manner.

.

---

.

[1]. A summary of this article was published in Management Communication Quarterly (Issue 120, May 2020). With thanks to my dear friend, Mohammad Yousefi-Shirazi, who undertook the editing of the text.

[2]. decision theory

[3] . One of the excellent and highly readable sources on this:

An Introduction to Decision Theory, Martin Peterson, Cambridge University Press, 2009.

[4]. expected utility

[5]. Of course, a distinction can be made between expected utility and expected value; but this distinction and other subtle distinctions of this kind are not relevant to our discussion.

[6]. An Introduction to Decision Theory, Martin Peterson, Cambridge University Press, 2009, P.3.

[7]. I have taken this example and the previous one from the following source:

The Philosopher’s Toolkit: How to Be the Most Rational Person in Any Room, Patrick Grim, Published by the Great Courses, 2013, 358-377.

A similar formulation of Pascal's Wager argument can be seen in the following source:

Logic, Graham Priest, translated by Bahram Asadian, Tehran: Mahi, pp. 142-150.

[8]. John Allen Paulos

[9]. base rate fallacy

[10] . This example is taken from the following source:

Your Deceptive Mind: A Scientific Guide to Critical Thinking Skills, Steven Novella, Full transcript Published by The Great Courses Company, 2012, P. 210.

I am grateful to my thoughtful mathematician friend, dear Arash Kamali, for providing me with a more comprehensible formulation of this problem than Steven Novella's formulation.

[11]. perceived obsolescence

[12]. James Surowieki

[13]. The Wisdom of Crowds, Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations

[14]. West of England Fat Stock and Poultry Exhibition

[15]. bayesian analysis

[16]. heuristic

[17]. information cascade

[18]. Asch conformity experiments

[19]. Ad populum fallacy

[20]. Daniel Kahneman

[21]. Amos Tversky

[22]. “Prospect Theory: An Analysis of Decision Making Under Risk”

[23]. Medical ethics (A Very Short Introduction), Tony hope, Oxford University Press, 2004. P. 26

[24]. The Ford Pinto Case: A Study in Applied Ethics, Business, and Technology, SUNY series, 1994

[25]. Lee Iacocca

[26]. Management Business Ethics, Straight Talk About How to Do It Right, Linda K. Trevino, Katherine A. Nelson, John Wiley & Sons, INC., P. 66

[27]. National Highway Traffic Safety Administration (NHTSA)

[28]. Thought experiments have long been a method of reasoning among scientists and philosophers. For a collection of important thought experiments in the history of ideas, see: Analytic Philosophy: Problems and Perspectives, Ali Paya, Tehran: Tarh-e No, 1st ed., 1382, pp. 529-570.

[29]. universalizability

[30]. incommensurable

[31]. opportunity cost

[32]. Of course, there is still no specific drug available to treat this disease; but even the drugs that alleviate the condition are scarce.

[33]. In medical ethics, this model is called the needs-based model.

[34]. prognosis

[35]. prima facie

[36]. These four moral values ultimately increase expected utility, either directly or indirectly. To the best of my knowledge, the article whose details appear below is one of the first important sources to examine these four values in connection with COVID-19. In this section, I have tried not to introduce anything contrary to the consensus of the theoretical authors and merely to expand the theoretical backing for the positions, and with some additions, to contribute to the discussion. With thanks to my dear friend, Dr. Shahram Paydar, who brought the following article to my attention:

“Fair Allocation of Scarce Medical Resources in the Time of Covid-19”, The New England Journal of Medicine, March 23, 2020, Ezekiel J. Emanuel, Govind Persad, et al.

https://www.nejm.org/doi/full/10.1056/NEJMsb2005114?query=RP

[37]. Of course, there is disagreement about which of these two takes priority. The question of whether resources should be allocated so that more people survive with shorter lifespans, or fewer people survive with longer lifespans, is known as the “distribution problem.”

[38]. Of course, there is disagreement regarding selection based on “quality of life.” Consider these two examples.

First example: Suppose Person A and Person B both have a fatal but treatable disease, and their conditions (age, past health status, etc.) are identical. With treatment, Person A will live another 5 years, and Person B will live another 25 years. Due to resource scarcity, doctors can only provide medical services to one of these two individuals. In this case, consequentialists and non-consequentialists agree that treating Person B is more obligatory.

Second example: Suppose Person P and Person T have a fatal but treatable disease, and their situations are identical. If treated, each can continue living for another 10 years; the difference being that Person P will suffer from paralysis of the lower limbs for all those ten years, while Person T is healthy. Resources are scarce, and one of these two must inevitably be chosen for treatment. The rule of maximizing expected utility says that, under identical conditions, saving Person T takes priority because their life will be of higher quality in the remaining ten years. However, not all ethicists agree here. Some Kantian ethicists believe that quality of life is not a good criterion for this choice. For example, see:

“Dignity, Disability and Lifespan”, Journal of Applied Philosophy, SAMUEL J. KERSTEIN, 2017; 34: 635-50.

[39]. Fundamentally, some ethicists believe that in this situation, if a person’s post-treatment life expectancy is estimated to be less than one year, they should be excluded from the treatment pool:

"Triage: Care of the Critically Ill and Injured During Pandemics and Disasters Consensus Statement". Christian MD, Sprung CL, King MA, et al. CHEST Chest 2014; 146: 4

.

---

.

PDF file of Kaveh Behbahani's article entitled "Rational Decision-Making, Expected Utility, and the Value of Human Life":

Download from Server One | Server Two

.

---

.

Panjereh has published the part of the above article that specifically concerns the prioritization of healthcare resource allocation in light of resource scarcity and increased admissions during the pandemic here.

The Omid Islamic Association of Shiraz University of Medical Sciences also held a conversation with Kaveh Behbahani in an Instagram Live titled "Does every human life have infinite value?", which can be viewed on YouTube and Aparat.

.

---

.