Happiness-based systems

This is the second of five posts making up my essay on moral calculus.

In the previous post we used desires as our basic observable. However, there are other observables that are commonly used in the realm of ethics and morality. One of the most common is happiness which, in principle, can be measured in the brain. Another observable is suffering.

I will assume for simplicity that a happy person cannot simultaneously be suffering, and vice versa. It therefore makes sense to treat happiness and suffering as two extremes of one continuous scale. However, before moving on, I make a change in terminology, since “happiness” and “suffering” are, to my mind, a little too specific. Instead, I will use “contentment” and “discomfit”. “Contentment” is meant to include pleasurable states like peacefulness, in addition to the feeling of joy that the word “happy” invokes. Similarly, “discomfit” is meant to include unpleasant states such as sadness, in addition to the experience of physical pain that the word “suffering” invokes.

Definition 2.1 Emotional Value

  1. We define the set of negative and positive values on a simple number line as  “discomfit” and “contentment”, respectively. Smaller (more negative) values on the number line represent greater discomfit, while larger (more positive) values on the number line represent greater contentment.
  2. Let us call the number line the “emotional scale”. Although common usage of the word “emotional” refers to a wider range of qualities than discomfit and contentment, we use it here to refer to these two states only. Let us call a particular value on the emotional scale an “emotional value”. As with my previous use of the word “value”, I refer to a numeric value only.
  3. Let values on the emotion scale be measured with some arbitrary unit called “emotons” that can later be scaled to some real unit of brain measurement.

With this definition, we can observe that a very happy brain has an emotional value of, say, 500 emotons, while a very sad brain has an emotional value of, say, -500 emotons.

We wish to investigate the relationships between the emotional values of different brains. However, in order to do so, we must determine how the emotional value of one brain can effect the emotional value of another. Previously, when considering desire-based systems, we noted that one desire could affect another by being fulfilled or thwarted. However, the emotional value of a brain has no such obvious logical relationship to the emotional values of other brains. For instance, increasing the emotional value in one brain does not necessarily increase or decrease the emotional value in another brain.

In order to see how emotional values can affect each other, we must consider the inputs and outputs of brains. The inputs of brains are stimuli from the various senses. The outputs of brains are muscle movements. The only way we are able to communicate our thoughts to the outside world is by moving muscles, whether they be vocal muscles or hand muscles, or leg muscles. I therefore suggest that the very general term “action” describes the currency of communication between brains.

Definition 2.2 Action

An action is an event that is initiated by muscle movement, and which is directly or indirectly detectable by the senses.

There is a particular class of action that affects the emotional value measured in brains. For instance, the act of insulting someone is likely to upset them, thereby moving their brain to a more negative value on the emotion scale. Conversely, embracing someone is likely to comfort them, thereby moving their brain to a more positive value on the emotion scale.

A particular action, however, might cause a small increase in the emotional value of one brain, and a much larger increase in the emotional value of another brain. Indeed, a particular action might simultaneously increase the emotional value of one brain and decrease the emotional value of another. We must therefore conclude that the ability of an action to produce a change in emotional value depends on the brain being considered.

To demonstrate this, I would like to consider an example. However, to do so, I must deal with the issues of relevance encountered in the previous section. When working with desires, it was relatively straightforward to determine which desires were relevant: we started with a “focal” desire that had some special interest, and determined all the other desires that could be influenced by the focal desire. We cannot do the same with actions, because actions do not influence each other in such a straightforward way. Performing one particular action will not necessary cause another action to be performed or to be suppressed. However, we can take advantage of the fact that we are developing systems with an eye to their moral applications. Such applications usually involve a relatively small number of well-defined actions that the moral agent is asked to choose between. We therefore make the assumption that there exists some finite, pre-defined set of relevant actions, which we label A1, A2, A3, etc.

Questions of relevance are not quite settled though. We must also determine which brains are relevant to the problem:

Definition 2.3 Relevant Brains

Given a set of relevant actions, relevant brains are those whose emotional value can be modified by at least one of the actions.

So, for instance, if we are considering whether to give to a particular charity, the action of donating money is relevant, since it has the potential to change the emotional value in the brain of the donor and the  recipients, while the action of walking, say, is irrelevant.

We can now proceed with our example. Consider a set of four relevant actions: A1, A2, A and A4. Using Definition 2.3, we determine that there are three relevant brains: b1, b2, and b3. The potential influence of each action on the emotional value of each brain can be expressed in tabular form, as shown in Table 9.

b1 b2 b3
A1 500 325 150
A2 -10 81 34
A3 -855 -132 -152
A4 203 144 192

Table 9. Changes in emotional value produced by the four actions in the three brains, as measured in our arbitrary units (“emotons”).

Note the similarity of Table 9 to Table 4. In the latter table, we listed the intensity of each desire in each brain. Here, we list the change in emotional value each action can produce in each brain. (I comment further on the analogy between our desire-based and happiness-based systems later.)

Looking at the numbers in Table 9, we see that action A1 is one that generally increases the emotive values of the three brains: it causes the level of contentment to rise. Conversely, action A3 decreases the emotive values of the three brains: it causes the level of contentment to drop (or, put differently, it increases discomfit).

2.1 Changes in happiness

With the example values of Table 9 in place, we pose the following problem:

Problem 3.

We are given:

  1. A set of actions,
  2. The set of brains relevant to this set of actions, and
  3. The set of emotional value changes for each action-brain combination.

How do the actions rank in terms of their ability to produce the biggest positive change in emotional value?

Unsurprisingly, the solution to this problem, like the problem itself, is familiar from our previous work:

Solution 3.

Define the rank of each action as the sum of its emotional value changes for all relevant brains. The action with the highest rank is the one which produces the highest net increase in emotional value.

Solution 3 asks us to sum the values in each row of Table 9. We show the resulting rankings in Table 10. We also provide normalized rankings, which make the relative rankings of the actions a little easier to discern.

b1 b2 b3 Ranking Normalized Ranking
A1 500 325 150 975 1
A2 -10 81 34 105 0.59
A3 -855 -132 -152 -1139 0
A4 203 144 192 539 0.79

Table 10. Changes in emotional value produced by the four actions in the three brains, together with rankings computed as the sum of all values in a given row.

As expected, action A1 ranks the highest: it causes substantial increases in the emotional values of all three brains. Similarly, action A3 ranks the lowest because it causes decreases in the emotional values of all three brains. Overall, the remaining two actions (A2 and A4) are moderately ranked because they cause modest increases in emotional value in most (or all) brains, with the exception of only one small decrease (action A­­2 decreases the emotional value of brain b1).

2.2 Accounting for initial emotional values

Instead of posing Problem 3, we could pose a slightly different problem:

Problem 4.

We are given:

  1. A set of actions,
  2. The set of brains relevant to this set of actions, and
  3. The set of emotional value changes for each action-brain combination.

How do the actions rank in terms of their ability to raise the minimum emotional value in the set?

Before we consider a solution, let us devise a set of initial emotional values for each brain in our example:

b1 b2 b3
Initial emotional value 1240 1186 1169

Table 11. The initial emotional value of each brain.

We offer the following solution to Problem 4:

Solution 4.

Let the minimum initial emotional value in the given set be Emin.

For each action, apply the following steps:

  1. Add to the initial emotional values the changes in emotional value prescribed for the action.
  2. Determine the new minimum emotional value Fmin. This is the ranking of the action.

Getting back to our example, we can see from Table 11 that the minimum emotional value is 1169 emotons, associated with brain b3. Next, we compute the ranking of each action. The first action changes the three brains by the following amounts (Table 10): 500, 325, and 150 emotons, respectively. We add these values to the three initial emotional values in Table 11 to give the three new values 1740, 1511, and 1319. The new minimum value is now 1319, associated with brain b3. The difference between the new and old minima is the 150 emotons we have just added, and that is the ranking for the first action.  We proceed in the same way with the remaining three actions, yielding the information in Table 12.

b1 b2 b3 Ranking

(New Minimum)

Normalized Ranking
A1 1740 1511 1319 1319 0.96
A2 1230 1267 1203 1203 0.59
A3 385 1054 1017 1017 0
A4 1443 1330 1361 1330 1

Table 12. Final emotional values produced by the four actions in the three brains, together with rankings computed as the difference between the old and new minimum value.

We now see that the action with the highest ranking is A4. This action results in a higher minimum emotion value across the set of relevant brains than any other action. It is thus likely to be ranked higher than actions that produce large net changes in emotional values (such as A1). In many cases, however, an action that produces high increases in emotional value in all relevant brains will also produce the greatest increase in the minimum emotional value.

Note that we could specify a new problem in which we are asked to rank actions in terms of their ability to raise the maximum emotional value among the relevant brains. This problem would proceed in the same way as Problem 4, but would use as rankings the new maximum emotional value rather than the new minimum value.

Before moving on to the next post, I make the same observation as I did at the end of our desire-based work, namely that the problems we have considered here are not exhaustive, but represent some sample of the total population of possible problems.

Next post on moral calculus.

Previous post on moral calculus.


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