A Critique of “Utility”

Economists and other social theorists often take the concept of utility for granted.

In theory, utility is a measure of value. I will denote the utility of X to Y as U(X, Y) or simply U(X) if Y is clear in the context. For a single individual, we can think of utility as a mathematical function that maps objects or outcomes to points on the continuum. This mapping is called a “utility function”. (In this context, “function” has its mathematical meaning, not its ordinary meaning.)

To think about society, we might want to define utility for a group, not just a single individual. Collective utility is typically defined as the sum of individual utility over the collective. This assumes that utility is defined on the same scale for everyone.

The concept of utility is used to model individual and social decision-making. It is used in game theory to define benefits and costs. It is often used in moral philosophy to define the “goodness” of actions and outcomes. In a utilitarian moral theory, collective utility is the measure of goodness, and we have a moral obligation to act in ways that increase it. In economics, it is often assumed that prices measure the utility of goods and services. GDP is often viewed as a measure of collective utility for a society.

The concept of utility is based on an underlying metaphor: thinking of value as a substance. A substance can be quantified, measured, compared, summed over a collection, exchanged, produced, consumed, etc. Metaphorically, we think of U(X, Y) as defining a quantity of a substance that is present in X. We say “How much value does X have?”, as if value is a substance contained in X. We talk about how much value a company produces, or an entire economy produces, as if value is a substance that we produce and consume.

Does this metaphor make sense? Is value like a substance?

In this essay, I will argue that the concept of utility is a convenient fiction.

Utility can be defined in different ways:

• Reproductive utility: U(X, Y) is how much X contributes to the reproductive fitness of Y.
• Desiric utility: U(X, Y) is how much Y psychologically values X.
• Hedonic utility: U(X, Y) is the net effect of X on Y’s experiences of pleasure and pain.
• Energetic utility: U(X, Y) is the amount of work that Y would do for X.
• Monetary utility: U(X, Y) is the amount of money that Y would pay for X.

Let’s consider each of these definitions.

Reproductive Utility

U(X, Y) is how much X contributes to the reproductive fitness of Y.

Reproductive fitness is not a precise notion. There is no right way to quantify reproduction. We could count offspring born, but what if they all die young? We could count offspring that live to adulthood, but what if they don’t reproduce? We could count grandchildren instead of children, or descendants at some other reproductive distance. Each of those measures would be a valid way to compare organisms of the same species, and thus it would be a reasonable way to approximately measure reproductive fitness. Any of them could be useful for thinking about evolution. However, none of them perfectly captures what we mean by “reproductive fitness”.

Regardless of how we decide to measure it, reproductive fitness is a long-term metric. Even if we only counted children, we could not measure it until the end of the reproductive lifespan.

Without measuring reproductive fitness, we can make some general claims about what is adaptive or maladaptive. Survival is generally instrumental to reproduction, so actions that contribute to survival are generally adaptive. Conversely, actions that lead to death are generally maladaptive. Mating activity and parental care are also generally adaptive. Birth control is generally maladaptive.

However, we can’t quantify the effects of a single action on reproductive fitness. Most actions have only a small effect on reproductive fitness. We don’t know all the long-term effects of an action, and we don’t know what would have happened otherwise.

If you see quantitative reasoning about evolution, you should be very skeptical of it. It is probably bogus.

Does it make sense to aggregate reproductive utility over a collective? We could define collective utility as the size of the population. If the population is growing, the members of the collective are reproducing above replacement on average. But this has some problems. First, we need to define the collective. Second, a population can’t grow forever, so collective utility would be limited. After some point, it would become zero-sum. Also, this notion of collective utility doesn’t seem very useful for understanding society or making social decisions.

Reproductive utility is a useful concept for understanding human evolution and human nature. We evolved to reproduce. But reproductive utility cannot be precisely quantified, and it is not very useful for reasoning about the specifics of human action. Action is generated by the brain. It is not proximately based on reproductive utility, even approximately or heuristically. It is based on desire. We do what we want to do.

Desiric Utility

U(X, Y) is how much Y psychologically values X.

What does it mean for Y to psychologically value X?

There are three layers of normativity in the brain. The bottom layer is the emotions, which are innate. They generate motivation. The middle layer is value-knowledge, which is acquired from experience. The top layer is desire, which consists of ideas in the mind.

For example, suppose that you want to eat a hamburger. The motivation to eat comes from the emotion of hunger. The knowledge that hamburgers are good food is value-knowledge, which was learned from experience. The desire to have a hamburger is a conscious idea of what you want.

Which of the layers should we associate with utility?

Motivation is not like a utility function, because it has no representational content. Hunger is not an idea of what you should eat. It is just a type of motivation. The emotion of hunger does not even have the concept of food built into it. We have other emotions, which we can collectively label “taste”, that determine whether something is delicious or disgusting. However, we have to learn what is good to eat from experience. So, motivation is not a candidate for utility.

Value-knowledge is acquired from experience. It can be representational or conceptual. The knowledge that hamburgers are good food is conceptual. It is generic knowledge about a type of thing and its relation to me. Representational value-knowledge consists of attachments to specific things, such as people, objects and places. For example, I value my house. This type of value knowledge involves a representation of the object or entity that is valued.

Since conceptual value-knowledge does not assign value to specific things, it is not like a utility function. Representational value-knowledge does assign value to specific things, so it is more like a utility function. However, it does not assign value to all possible things or outcomes.

Desires are representational. A desire is generated in a context by applying value-knowledge to the current motivational state and information about the current situation. For example, if I am walking past a McDonalds and I am hungry, the desire for a hamburger might be generated by my brain. The desire is a value judgment: “it would be good (for me) to have a hamburger”.

Of the three layers of psychological normativity, desire seems like the best candidate for utility. Desire assigns psychological value to specific objects and outcomes.

If we define utility in terms of value-knowledge, we have the problem that value-knowledge is normally latent and hidden. It is only consciously manifest in desires. The knowledge that hamburgers are good food is always in my brain, but seldom in my mind. It is only active when I am hungry and have the option of eating a hamburger. I value my house, but that value is normally latent. I would only have a conscious desire to protect my house if it was threatened in some way.

If we define utility in terms of desires, we have the problem that desires are transient, contextual, ad hoc and incremental. If I am hungry and walking past a McDonalds, I might want a hamburger. If I am hungry and at home, I might want a sandwich. If I am not hungry, I will not want to eat food. However, if I am concerned about an impending shortage of food, I might have a strong desire to get food and store it. If the utility of X is my desire for X, then it only exists when I want X but do not yet have X.

Before I bought a house, I wanted to buy a house. That conceptual value would often manifest as a conscious desire in my mind. It motivated me to save money, search for a house, and eventually buy a house. Now that I own a house, I value this specific house. The conceptual value of a house is still present in my brain, but it has become attached to a specific object, through a representational value. I no longer have the desire to buy a house. Instead, I periodically have a desire to maintain or improve my house. Clearly, my house has value to me, but how can we convert all of these desires into a measure of utility? Do all of these different desires arise from some underlying, stable utility number? If so, how?

Perhaps we could say that desires reflect incremental utility (what economists call “marginal utility”), rather than absolute utility. Incremental utility is the additional utility of X to Y, given what Y already has. Since I already have a house, I have no desire for a house, because another house would have no incremental utility to me (at least, not if I had to pay for it). When I am hungry and have no other food, a hamburger has incremental utility to me. Once I have one hamburger, a second would have little or no incremental utility to me.

But that raises the question of what the underlying utility is. If desires represent incremental utility, what is absolute utility? Representational value-knowledge assigns value to some things, and this value judgment exists (in some sense) without being manifest in a desire. But other value judgments arise from transient conditions, such as hunger. The brain has nothing like a utility function that maps every possible state of the world to a numeric utility. The brain contains ad hoc value-knowledge, and it generates ad hoc desires in situ.

Another problem with desiric utility is that we can’t measure desires or the underlying value that they reflect. There is no external scale on which we can quantify them. A desire is just information in the brain.

How could you infer the amount of value that I place on my house? You could ask me, but how would I answer the question? There is no common scale that I can use to describe how much I value my house. You could offer to buy it, and thereby discover the price that I would be willing to accept for it. However, that would only reveal the montary value, not the psychological value. (See the critique of monetary value later in this essay.) It would also require that you are willing to pay the lowest price that I would accept.

What value do I place on having clean water, staying warm in the winter, or having light in the evening? I pay for water, gas and electricity, but the payments don’t measure how much I value those things. If they were more expensive, I would pay more. If they were less expensive, I would pay less. What value do I place on air? I never consciously desire air, unless I am swimming underwater, but I need air to live. What utility does it have to me? Infinite? Finite? Does it make any sense to assign utility to the requirements of life?

What value do I place on the lives of my children, or my own life? On what scale would it be defined? How could it be measured?

There is an important distinction between measurement and control. A speedometer measures the speed of a car. It does not control the speed. The gas pedal controls the speed but does not measure it. In a sense, the gas pedal represents the rate at which fuel flows into the engine. However, it is not a measurement of that flow. It controls the flow. Different cars can have the same gas pedal mechanism, but with a different relation between the pedal position and the flow rate.

Psychological value is a control mechanism. It has the psychological function of generating action toward goals. It is not a measurement of something that exists outside our heads. We normally think of value as something external that we are motivated toward, but that is an illusion or a misleading metaphor.

Another issue is that value-knowledge is affected by the social and cultural environment. This raises the question of whether a given value or desire is “authentic” or not. Are your values really yours? Or were they imposed on you by external forces?

If you want a McDonald’s hamburger, is that desire an authentic expression of your self-interest, or was it imposed on you by advertising? If a Muslim woman wants to wear a headscarf, is that desire an authentic expression of her interests, or was it imposed on her by social and cultural pressures?

Another issue is that we view some desires as pathological. Does heroin have utility to a heroin addict? Does suicide have utility to a suicidal person? Does murdering people have utility for a serial killer? If we define utility in terms of psychological value, we cannot critique psychological values, because they are correct by definition.

If we want to aggregate desiric utility over a collective, we have the problem that there is no way to measure it, and there is no common scale for it. What would we sum to get the collective utility of X? We can use a voting scheme to convert individual choices into a collective choice, but choices are not desires. We can use the market to coordinate the desires of individuals, so that they cooperate to collectively satisfy their desires, but the market does not calculate collective utility (see Monetary Utility later in this essay).

Hedonic Utility

U(X, Y) is the net effect of X on Y’s experiences of pleasure and pain.

Rather than defining utility as what the individual wants, we could define it as how he feels. Hedonic utility is pleasure minus pain. U(X, Y) is the net hedonic effect of X on Y: how much X increases Y’s pleasure and/or decreases Y’s pain.

Hedonic utility has its own problems.

Pain and pleasure are qualia. They cannot be directly measured, even by the experiencer. They are simply felt. At most, we can infer them from expressions and actions, to some extent.

I believe that pain and pleasure balance out. If I am right, actions do not affect hedonic utility (although there is a wrinkle at the end of life). Hedonic utility is zero-sum for the individual. However, let’s set that aside for now, and pretend that it is possible to increase or decrease net hedonic utility.

It is difficult to estimate/predict the full effects of an action. For the sake of argument, let’s assume that we can measure pain and pleasure over time. Let’s also assume that we can attribute immediate hedonic effects to actions. So, if you eat a hamburger, and you experience some pleasure as a result, we can measure the pleasure and attribute it to the action. However, that would not be the full hedonic effect of the action. Actions have many effects.

For a hamburger, we can ignore long-term consequences. But we do some things only for their long-term consequences. How could we know the net hedonic effect of buying a car, buying a house, moving from Toronto to Vancouver, or getting married? There is no way to know all the effects of the action, or what would have happened otherwise.

What is the hedonic utility of things that are normally present? What is the hedonic utility of having central heating? If you are used to it, you get no pleasure from it. But maybe it prevents pain, because you would be cold without it. (Again, I am setting aside my zero-sum theory for the sake of argument.) If so, there is some effect, but it is purely hypothetical.

Can we aggregate hedonic utility over a collective? This has the obvious problem that hedonic utility is mind-dependent and thus incommensurable. We could make various assumptions about how social actions affect net hedonic utility, such as that increasing average wealth would increase average happiness. But how could we test those assumptions?

For the sake of argument, let’s assume that we can approximately measure individual hedonic utility (by looking at facial expressions, perhaps). We might be able to extrapolate from what affects individual utility to what affects collective utility. For example, if making an individual wealthier seems to make him happier, we might infer that making everyone wealthier would make everyone happier. However, this type of inference is not necessarily valid. It assumes that individual effects are independent. Some things that people want, such as status and sex, are zero-sum. They can be increased for individuals, but not for everyone.

There are various known problems with hedonic utilitarianism as a moral theory, such as “the utility monster” and Omelas.

Now, I will stop setting aside the theory that pain and pleasure balance out. Clearly, pain and pleasure are causally related. You must be hungry to enjoy food. If you are cold, then you feel pleasure from warming up, but you feel no pleasure from simply being at a normal body temperature. We are not ecstatic because we live in modern civilization, with hot and cold running water, central heating, electric light, refrigerators, TVs, avocadoes in the grocery store, etc. Conversely, our ancestors were not miserable because they lived in premodern conditions. Rich men are not happier than poor men. Beautiful people are not happier than ugly people. Actions cause immediate pain or pleasure, but actions do not affect hedonic utility in the long run, because pain and pleasure balance out.

See How I Rejected Hedonism and Motivation.

Energetic Utility

U(X, Y) is the amount of work that Y would do for X.

In physics, work is force in a direction times distance moved in that direction. More precisely, it is the path-integral of force along a trajectory, but we can think of that integral as the sum of many little movements, each of which has a constant force and direction. The details don’t really matter here.

Most human action is much more complex than simply moving an object in a direction, but we can think of it as “pushing” the world in a “direction” or along a “path of change”. The direction or path is defined by what is desired.

Energetic utility is closely related to desiric utility. Desire is the willingness to do work. We work toward what we desire. Essentially, energetic utility maps desiric utility onto an external, physical scale, through the concept of work.

However, desire does not measure work, and work does not measure desire. Again, there is a distinction between control and measurement.

Also, people have different capacities for doing work. Two people with the same desires might work at very different rates toward those desires. Also, one might do less work than the other because he knows a more efficient way to satisfy the same desire.

As defined, energetic utility is based on a hypothetical: the maximum amount of work that someone would be willing to do. We can observe the work that a person actually does for X, but not the maximum amount of work that he would hypothetically do for X. People try to do the least amount of work necessary to obtain a result. Work done is not a measure of how much something is desired or valued.

Like desiric utility, energetic utility is highly contextual. The energetic price that I am willing to pay for a hamburger depends on the energetic prices of other foods. If I can get a tuna sandwich for one hour of labor, then I will not do more than (roughly) an hour of labor to get a hamburger, because one product can substitute for the other.

Like desiric utility, energetic utility is hidden for most things, because values are normally latent. For example, I would be willing to do work to protect my house from a fire, but that work would only happen if my house was threatened by a fire.

What if we define U(X) as the work done to produce X? This doesn’t fit what we mean by “utility”. First, it is retroactive. It is only defined after X is produced, not before. The point of a utility function is to motivate choices and actions. Second, it doesn’t take efficiency into account. An improvement in the efficiency of producing a type of product would appear (in this metric) as a decline in its utility. Also, we sometimes do things, as individuals or collectives, that we later view as worthless or even harmful, such as building a bridge to nowhere or fighting a war.

Life depends on energy. To survive and reproduce, organisms need to make an energy profit from their labors. They must harvest energy from the environment. Life is work. The ultimate currency of society is also work. Society is based on cooperation, or in other words, work exchange. Thus, it would be very convenient if we could define utility in terms of work/energy. Unfortunately, we can’t.

Monetary Utility

U(X, Y) is the amount of money that Y would pay for X.

Money is a medium of exchange. Monetary value is circular: money has value to one person because money has value to other people. If nobody wanted money, money would be useless. Money is only useful because people want it, and its only use is to exchange it for something else.

A market price is the amount of money that can be exchanged for a certain type of product at the current moment. Of course, that definition hides a lot of complexity. In a market system, a seller can set his own price, but he might not get any buyers if the price is too high. On the other hand, if the price is too low, he could do better by increasing it. So, sellers tend to converge on the same price for the same type of product, other things (such as location) being roughly equal. Prices emerge within markets, and prices tend to balance supply and demand. In a system where prices are determined by the government, other factors (such as availability) balance supply and demand. For simplicity, let’s assume a market system.

Like a desire, a price is a control mechanism, not a measurement. It enables the exchange of a good or service. It balances production and consumption, supply and demand. A price increase creates incentives to increase supply and decrease demand. A price decrease creates incentives to decrease supply and increase demand. That is the function of a price: to balance supply and demand.

Exchange is possible because people value things differently. For example, suppose that a farmer produces more potatoes than he needs to feed his family. Beyond a certain amount, additional potatoes have little psychological value to him. This is what economists call “diminishing marginal utility”. The term “marginal” means “incremental”. Suppose that a fisher is in the same situation: he can catch more fish than he needs to feed his family. However, each could benefit by exchanging some of his production for the production of the other, so that each family would have a more balanced diet. So, each man produces more than he needs for himself, and trades his excess production for the excess production of the other man. Both men benefit from the exchange.

Now, suppose that there are multiple fishers and farmers exchanging the products of their labor. An exchange rate between fish and potatoes will emerge. Potatoes will have a “price” in fish, and fish will have a “price” in potatoes. This price will tend toward an equilibrium that balances both work and psychological value.

In this market, there are two ways to get fish: fishing and farming. You can catch fish, or you can grow potatoes and trade for fish. Likewise, there are two ways to get potatoes: farming and fishing. If it is more energetically efficient to get fish by farming, then people will switch from fishing to farming. Conversely, if it is more energetically efficient to get potatoes by fishing, then farmers will become fishers. The exchange rate will tend to balance the amount of work done by each side.

Exchange also tends to balance the psychological value for each side. Consider the simple example of exchange between two people. If one side values the relationship less, he has more bargaining power to raise his price. This balancing process is made more efficient by a market, because buyers compete for sellers, and sellers compete for buyers.

Like desires, prices are contextual. The price of one product depends on the prices of other products. The price of a product depends on the prices of the inputs to its production. It also depends on the prices of similar products. Prices don’t exist in isolation. Market prices emerge together. Each price is a property of the system as a whole.

Does a price measure the collective desire for a type of product? To some extent, yes. A price depends on supply and demand. Demand is determined by the desires of individuals, but it also depends on how much money they have. Individuals with more money can have a greater effect on a market price. So, demand is not simply an aggregation of individual desires.

What does a market price represent? Nothing, other than itself. It is just the current exchange rate of money for a type of product. It does not represent the psychological value of the product to anyone in particular. If money was a measure of value, exchange would be impossible, because a product would have the same value as its price, and there would be no reason to exchange one for the other. Clearly, in any transaction, the buyer values the product more than the money, and the seller values the money more than the product.

Let’s consider whether money spent is a measure of utility for an individual.

Suppose that a man takes home (after taxes) $3,000 per month. He spends $500 on food, $1,500 on rent and utilities, $500 on various expenses (transportation, clothing, furniture, medical care, etc.) and $500 on entertainment. If money measures value, then he values food and entertainment equally.

Now, suppose that his salary is cut by $500 per month. He still spends $500 on food, but now he spends $0 on entertainment. Clearly, he values food more than entertainment.

When the man had adequate food, he was willing to spend money on entertainment, as an incremental benefit. His desires for food and entertainment depend on what he already has, and how much of each he already has.

We can imagine an experiment in which the man receives dollars one at a time, and must immediately allocate each dollar to some spending category. He doesn’t know how much he will receive. In this experiment, the man will allocate the money to categories in order of decreasing value to him. Survival will come first, then comfort and security, and then entertainment, status-seeking and other luxuries. His priorities will demonstrate what he psychologically values more. However, at each moment, his level of desire for the next incremental benefit might be the same.

We can imagine the same experiment conducted on a social scale. If we slowly increase total production, it will be allocated to different things. If most people are hungry, food production will dominate the economy. When most people are well-fed, comfortable, and safe, a significant amount of economic production will be allocated to luxuries, such as entertainment. If people collectively spend $100 million dollars on food and $100 million dollars on entertainment, it does not follow that they value food and entertainment equally.

The amount of money that an individual spends on X does not measure how much the individual values X. The amount of money that we collectively spend on X does not measure how much we collectively value X.

Desire and monetary value are both incremental. They exist “on the margin”. We cannot treat them as measures of absolute utility.

A monetary aggregate, such as the total amount spent on food, is not a measure of the total value produced — and what would that even mean? We could say (with some caveats) that it measures the allocation of resources to that type of production. If people spend equal amounts on food and entertainment in total, we can say that roughly equal amounts of resources (natural resources and labor together) are allocated to those types of production. But people might value those things very differently.

There are some issues with how natural resources are priced — see Natural Resource Taxation.

Another issue is that some products are used only to compete within the collective, and thus we do not think of them as having collective utility. When survival-related needs are satisfied, people start competing for sex, status and power. Because those goods involve human relationships, they are zero-sum across the entire human collective, and tend to be approximately zero-sum within any large collective, such as a country. In modern civilization, a large percentage of the total labor and resources are used to produce weapons for these competitions, such as beauty products and luxury goods. Even food and drink can function as status symbols.

To be clear, when I say that these goods are “zero-sum”, I am using a mathematical metaphor to express something qualitative. We can’t quantify sex, fame and power. But we can understand that they are zero-sum, because they involve relationships within a collective.

We can increase these goods to some extent. If no one is having sex, we can pair people up, and thereby increase the amount of sex. We can also improve pairings by matching compatible people. At some point, however, we reach the limit of improvement, at which it becomes zero-sum. If everyone has the best possible partner, we can only make one person better off by making another person worse off. For example, one man might want to have a harem of ten women. To satisfy his desire, nine men would have to be celibate, and the women in his harem would have to share one man (which they might not prefer). Setting aside sexbots and other artificial substitutes, we can’t produce more sex in the way that we can produce more material goods, such as food and houses. The same is true for status and power.

See Unsatisfiable Desires.

Think of the trees in a forest growing tall to obtain sunlight. They put considerable resources into increasing their height. It might seem that the trees implicitly value being tall. However, their height is just a way of competing for sunlight. If the trees had more water and other nutrients, they might all grow taller. This would not correspond to an increase in their average reproductive utility. Each tree would be in the same situation as before: competing with the other trees to survive and reproduce.

This shows a general problem with inferring collective utility from individual utility. Something can have utility to each member of a collective, and yet no utility to the collective as a whole.

Markets are a very effective way to coordinate human desires and actions. They don’t work by doing utility calculations. They work by creating incentives. Prices are a control mechanism, not a measure of utility.

It is convenient to think of money as value. After all, it is a “substance” and it is quantifiable. Prices assign quantities of this substance to objects and outcomes. Money has some of the properties that we want in a utility function. But money is not value. It is a medium of exchange.

Summary

It would be very convenient if value was a substance that could be quantified, measured, compared, given, received, aggregated, produced and consumed — but it isn’t.

The concept of utility is useful in some contexts, where we need some way of thinking and talking about value. For example, it is used in game theory to define problems of cooperation, such as the prisoner’s dilemma. In that example, we can interpret utilities as individual levels of desire in a situation, or as rewards in a common currency, such as money. Either way, it is useful to hide all the complexities of psychological value inside a black box called “utility”.

The concept of utility becomes misleading when it is confused with reality. This is a common problem with metaphors. Metaphors make it easier to think, by making abstract things more tangible. Metaphors become misleading when people start taking them literally, and believing that the abstract thing is actually tangible. Value is highly abstract and intangible. In some contexts, it is useful to think of value as a substance. But that metaphor can be misleading.

The concept of utility is a convenient fiction.