*This is a simplified, introductory text to ‘**Why I became a utilitarian**’ and ‘**Variable critical level utilitarianism**’*.

* *

## The problem of interpersonal comparability

Is your feeling of pain stronger than the pain experience of someone else? Are you happier than someone else? How can you tell? How can you find out the answers to such questions?

In ethics, increasing each other’s well-being is a good thing (all else equal). But to find the best choices or actions, we need to be able to tell by how much we can increase everyone’s well-being. If I increase my happiness with one unit, is it as much as your increase of happiness with one unit? Perhaps our units of measurement of happiness are different. That makes an interpersonal comparison of well-being difficult. It is like the old philosophical problem: if you and I see a cloudless sky, do we experience the same color blue, or does your experience or perception of blue differ from my experience? Perhaps your blue corresponds to my green and your green to my blue, even if we both call the sky blue?

## The utility function

Our utility is a function of all the things that we value or prefer. We not only value our own happiness and well-being, but we value more things, such as the well-being of others, the fairness of the distribution of happiness amongst people, and so on. These values are all included in the utility function. Hence, if we have different options, we mostly prefer the option that gives us the highest utility. And impartiality implies that we have to pick the option that maximizes total utility (the sum of everyone’s utility). But how do we add up different utilities of different persons if we do not know an interpersonal unit of measurement for utility?

There is an interesting analogy between utility and temperature that I want to explore here. This analogy describes the problem and offers some directions to find a solution.

## The analogy between personal utility and room temperature

Suppose there are two rooms, each having a thermometer. One room contains a mercury thermometer, the other a digital thermometer. The readings of the thermometers are different: the mercury thermometer measures the temperature in terms of degrees Celsius, the digital thermometer has other units. You cannot move the thermometers from one room to the other. The rooms can have different air temperatures. How are we going to find out which room is the warmest?

This is the analogous situation of the interpersonal comparison of utility between two persons. The two rooms correspond to the two brains of two persons. The air temperature corresponds to our objective utilities. The readings on the thermometers correspond to the subjective utilities: our subjective valuations or stated preferences. For example, when I feel a little pain from a small scratch, I give it a subjective utility minus hundred. When you feel extremely happy, you give it a subjective utility plus ten. When you feel very depressed, you give it a utility minus ten. These numbers represent our own subjective preferences for different situations. But we cannot simply compare my numbers with yours. My little pain is not ten times worse than your extreme depression.

The point is: our subjective utility function is not uniquely defined. If I multiply all my subjective utility values with the same positive constant number, or if I add a constant value to all my subjective utility values, it describes the same objective utility. The same goes for the thermometers: different thermometers with units in degrees Celsius, Fahrenheit or Kelvin measure the same objective temperature of a room. So we have to figure out a way to compare different subjective utilities, or to compare the readings on the two different thermometers. Specifically, we have to determine the values 0 and 1.

## Determining the reference point and the unit of scale

Let us start with determining the value 0 for the thermometers. We have to find a reference value. As mentioned before, if we add a constant value to the temperatures, this still gives us a consistent thermometer that measures temperature. What we can do for the temperatures of the two rooms, is to find an extremal value that counts as 0 degrees. Let us see how far we can cool down the first room. As physicists have discovered, there exists an absolute minimum temperature at minus 273 degrees Celsius. So we can take a new unit of temperature, the Kelvin, such that 0 Kelvin corresponds to minus 273 degrees Celsius (and 273 Kelvin corresponds to 0 degrees Celsius). The same can be done with the digital thermometer in the second room. As a result, in terms of the new units of temperature, 0 degrees in the first room corresponds with 0 degrees in the second room.

Next, we have to determine the unit 1 on the thermometers. We can multiply the values on the thermometer with a positive constant and the result will still be a valid (consistent) temperature scale. So how can we determine whether 1 degree on the first thermometer corresponds with 1 degree one the second?

In the case of the two rooms, we can change the environmental temperatures (e.g. seasonal variations in temperature) or heat the rooms, and see how the two thermometers respond. For each room, we can write down the thermometer values under a lot (ideally all) environmental circumstances. For example, the mercury thermometer in the first room measures temperature in units of Kelvin: 290K in the first situation, 315K in the second, and so on. With all these values, we can calculate the standard deviation, a measure that is used in statistics to quantify the amount of variation or dispersion of a set of data values. Next, we can divide all values by this standard deviation. The same can be done with the thermometer in the second room. Now both thermometers have comparable scalings: their new standard deviations are both equal to 1. For example, if the two thermometers had units in Kelvin and degrees Fahrenheit respectively, we can derive that a difference of 1 degree Fahrenheit corresponds with a difference of 0,556 Kelvin. Instead of using the standard deviation, other scalings are possible. For example, we can look for universal natural processes, such as the boiling of water at constant air pressure. The temperature at this boiling point can be used to rescale the thermometer, to determine the unit.

After determining the reference temperature (the value 0) and the unit of scale (the value 1), the two thermometers are now fully comparable. We can follow the same procedure with our personal (subjective) utilities. But here we can have one extra freedom: each of us can freely choose his or her own reference utility level and unit of scale.

Let us start by fixing the reference value. You can choose your reference value of utility that allows us to calculate your relative utilities: the differences between your personal utility values and your reference value. For example, if an option gives you a utility of 10 units, and you take 20 as your reference, then your relative utility becomes minus 10 units. Both positive and negative relative utilities are possible.

Next, we have to fix the unit of scale for our relative utilities. You can think of all possible situations or options, and for each of them you can give your preference or personal relative utility value that measures how strongly you prefer or dislike that option. This gives us a set of numbers. Now we can calculate the standard deviation of this set, and divide all numbers by this standard deviation. I can do the same thing with my personal relative utilities. As a result, our relative utilities have the same range: they become normalized relative utilities. Now we can compare an increase of one unit of my normalized relative utility with one unit of your normalized relative utility.

Other normalizations for our relative utilities are possible as well. For example, you can take your maximum relative utility, and define that as a normalized relative utility of 1. A normalized relative utility between 0 and 1 now corresponds with a subjective preference between your reference point and your maximally preferred state.

You are free to choose your reference value and unit of scale (normalization method), and so am I. Our normalized relative utilities are now completely comparable, so we can add them. As a result, we can now formulate a utilitarian theory that says that we have the choose the option that maximizes the sum of everyone’s normalized relative utilities.

## Population ethics and the relevance of reference points

However, even if you can choose your own reference value freely, you have to be careful. There is a range of possible reference values, from the lowest safe value to the highest safe value. If you pick a reference value outside of this range, and you calculate your normalized relative utilities with this extreme reference value, maximizing the sum of everyone’s normalized relative utilities might result in the choice for a situation that you strongly dislike, such as a situation where you have a negative well-being or where you do not even exist.

Here we enter the area of population ethics, where our choices determine who will exist in the future. The reference value is important, because it helps us avoiding many problems in population ethics (called ‘repugnant’ and ‘sadistic’ conclusions by population ethicists). The moral theory that gives us a duty to maximize the sum of everyone’s normalized relative utilities, is also called variable critical level utilitarianism, where the critical levels of utility are the reference values. Here we see another analogy with room temperatures. The absolute zero temperature (0 Kelvin) actually corresponds with an ideal vacuum in the room (no air molecules present). This empty room is like a non-existing or permanently unconscious person who has no preferences (no utilities).

## From subjective to objective utility

Some problems remain, though. We assumed that people can give their preferences or subjective utilities. Similarly, we assumed that the rooms have thermometers. But what about babies, mentally disabled humans or non-human animals who cannot give us their utility values? What about rooms without thermometers, or with thermometers without displays?

In the case of the rooms, physicists have discovered something very remarkable: the temperature that we can measure corresponds to physical properties of the air in the room. There are several candidates of physical properties: the size of the room, the number of molecules, the velocities of the molecules,…. These are all objective properties that are independent from the readings on a thermometer. It turns out that the temperature is determined by the average velocity of the air molecules (at least if the velocities form a certain statistical distribution of thermal equilibrium). Size matters not: if the number of air molecules increases but they all follow the same velocity distribution, the temperature remains the same. This non-trivial result in physics is very remarkable, because now we can couple the readings on a thermometer with an objective, physical property: the velocities of air molecules.

Can we do the same thing with our utilities? Can we couple our subjective utilities to objective utilities? Is there a connection between your subjective experience of wanting something and some physical properties or processes of your brain? This question is important, for example when we have to compare human well-being with insect well-being. The brains of insects are smaller, so are insects less conscious? Does the size of the brain determine the strength of preferences or the strength of pain experiences? If yes, then the suffering of insects is much smaller than the suffering of whales. But perhaps the strength of preferences and feelings is determined by the speed of neurons firing in the brain? Some insect brains are in some ways faster than human brains (that is why it is so difficult to catch a fly), so that would mean some insects can have stronger experiences (e.g. more pain per second).

The holy grail in neurobiology is finding the connection between brain activities and personal utilities, just like physicists discovered the connection between molecule velocities and room temperatures. When we find this brain-utility connection, we can objectively determine the utility levels of all sentient beings, even of those who cannot communicate their utilities.

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Thanks for the post. 🙂

> The brains of insects are smaller, so are insects less conscious?

Doesn’t the normalization process imply that an insect and a whale will be counted equally? For example, if you normalize between 0 and 1, then the best possible experience for a whale counts equally (relative utility = 1) as for a fly.

> Is there a connection between your subjective experience of wanting something and some physical properties or processes of your brain?

Personally I expect there’s no perfect correlation, though probably there are some metrics one could devise that correlate pretty well with verbal reports of wellbeing. Then there are further judgment calls regarding how to extend these metrics to non-humans with different brain architectures.

The normalization procedure (working with subjective utilities), may indeed come to the conclusion that the maximum subjective utility of an insect equals that of a whale, and this might indeed be different from the objective utility, if objective utility happens to be determined by brain size. The same would go for the thermometers: if temperature happened to be determined by the size of the room or the number of air molecules, we would have two different approaches to measure temperature (one by measuring room size, one by using a thermometer) and comparing temperature scales of different thermometers (by normalization) would give the wrong answers.