Update 2: More on non-existent people

This is an update to my essay on morality.

In Update 1, I discussed the affects on my moral calculus of cases in which relevant people did not exist for some of the relevant actions. I was led to make a rather unsatisfactory assumption about what LOD should be associated with a non-existent person in order to allow the calculus to produce a well-defined result.

In this update, I propose a deeper reworking of the calculus that removes the need to find LOD differences for individual people before and after a given action. This, in turn, removes the need to define an appropriate LOD for a non-existent person. (In fact, as it turns out, such an LOD actually arises naturally from the new calculus, but I will discuss this later.)

Let me summarize the basic steps of the original calculus before I present the modification. The basic steps were as follows:

  1. For a given person and action, calculate the difference in time-averaged (per diem) LOD that the person would experience if the action were performed compared to if it were not performed.
  2. For each action, add up these differences for all relevant people.
  3. The action with the smallest (or most negative) result is the preferred action, since it causes the greatest net decrease in LOD among the relevant people.

The problem arises in the first step of this procedure. For cases in which a person does not exist for a particular action, the LOD difference required from step 1 is ill-defined. To circumvent this problem, we delay differencing until contributions from individual people have been added together. The new sequence is as follows:

  1. For a given person and action, sum the action utilities for all the desires associated with that person and action, if the person exists for that action.
  2. For a given action, add the utilities of all existing people, and divide by the number of existing people. This yields a per capita utility for the relevant, extant population.
  3. The preferred action is that which has the smallest (or most negative) per capita utility.

Let us return to the example used in the original essay, and see what results the new algorithm produces. Later, we will look at the same example modified to include a non-existent person.

In the original essay, step 1 in the new algorithm, i.e. the computation of desire utilities was already performed, and presented in Table 5, which I reproduce below.

Table 5. Desire utility for each action.

Adam Bella Carly
a 750 450 -1850
b 0 -650 -2000
c 100 100 -700
d 200 -250 -2550
e 1600 1150 250

The second step is to add the utilities of each action together, and divide by the number of extant people for that action. In this case, of course, all three people exist for every action, so we’ll always be dividing by 3.  The per capita utilities are as follows:

Table U1. Per capita utilities.

 action per capita utility
a -217
b -883
c -167
d -867
e 1000

According to step 3, the preferred action is that which has the lowest (most negative) per capita utility. This would make action b the preferred action. This is the same result as before. Indeed, by comparing the values in Table U1 with the values in the total column of Table 6 in the original essay, we see that the results of the new algorithm are identical to those of the old, except for a constant factor of 100, and are therefore ranked exactly the same. (The factor of 100 appears because I’m dividing utilities by 3 to get per capita numbers, whereas the original algorithm was dividing utilities by 300 to get per diem numbers.)

Now let us reconsider the example with one small change. Suppose that for the performance of action d, Carly does not exist. We therefore cannot define a utility for Carly for action d, and we therefore put a “X” symbol in the relevant cell of Table 5:

Table 5. Desire utility for each action.

Adam Bella Carly
a 750 450 -1850
b 0 -650 -2000
c 100 100 -700
d 200 -250 X
e 1600 1150 250

This time, when we add up the desire utilities of each action d, we only have two numbers to work with (Adam’s and Bella’s numbers), and we therefore divide by 2 to get the per capita utility. The utilities for the other actions remain unchanged, because they still have three people associated with them. We therefore have the values in Table U2:

Table U2. Per capita utilities with non-existence.

 action per capita utility
a -217
b -883
c -167
d -25
e 1000

Action d now has a per capita utility of -25, rather than -867. It therefore slips from being the second ranked action to the fourth. This makes sense because the non-existence of Carly for action d means that her very favorable utility of -2550 in the original example also ceases to exist. In other words, performing action d does not have the huge benefit of dropping Carly’s LOD, because Carly does not exist if this action is performed.

To conclude, let us consider what average LOD we would need to assign to Carly for action d in the original algorithm if we wished the outcome to be the same as in Table U2. Keeping in mind that there is a factor of 100 difference in Table U2 values and the average LOD changes of Table 6, what we want is an average LOD change for action d of -25/100 = -0.25, since this would produce exactly the same ranking of action d relative to the other actions that we see in Table U2.

For action d, the average LOD changes for Adam and Bella are (from Table 6) 0.67 and -0.83, respectively. We therefore seek the number L such that

0.67 – 0.83 + L = -0.25

The solution is L = -0.08.  This number is the average LOD for Carly (under action d) that we would have to assume were true if Carly did not exist under action d, in order to get the same final results with the old algorithm that we do with the new algorithm.

In Update 1, I suggested that we used some typical value of LOD for non-existent people. If we assume that the per diem LODs in Table 6 cover typical ranges, we would probably have assumed something like -0.76, which is the mean of all 15 values in Table 6. If we had used this value, the total per diem LOD for action d would have been 0.67 – 0.83 – 0.76 = -0.93. This would not have changed the overall rankings of the actions, but it may have done so in a different example. Finally, we note that the equivalent LOD of -0.08 for the non-existent Carly applies only to her, and only to action d. A different equivalent LOD would arise if Carly were non-existent for some other action, or if some other person were non-existent for action d.

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