---
title: Shift in expected value of decisions when taking into account welfare of others
author: Issa Rice
created: 2018-01-03
date: 2018-01-03
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---

This page makes a basic point, which is that the expected value of personal
decisions shifts when taking into account others' welfare.

Suppose you have a choice between doing something (M) and not doing the thing
(NM). Suppose also that doing the thing can end up as good (GM) or bad (BM).
For concreteness, and to make the exposition clearer, suppose M is the act of
marriage. In that case, NM is choosing not to marry, GM is a good marriage, and
BM is a bad marriage. Of course, reality is more complicated and there is a
distribution of many outcomes, not just three.

Now suppose the utility of each case is described as follows. Beware that I am
just making up numbers! This is just a proof-of-concept to make the general
point!

|Outcome|Utility for self|Utility for others|
|-------|---------------:|-----------------:|
|NM     | $-10$          | $+100$           |
|GM     | $+10$          | $+110$           |
|BM     | $-20$          | $0$              |

A caricature of the situation goes like this:

NM
:   You don't marry, so you take a personal hit to welfare, because you're
    lonely all your life.  On the other hand, you can still pursue altruistic
    activities mostly normally, so utility for others is high.

GM
:   You marry, and it's a good marriage so are happy. Because you are feeling
    good, your altruistic endeavors also go well, so you get a bonus there.

BM
:   You are in a bad marriage, so you take a hit to utility. Maybe you become
    severely depressed, or commit suicide, or you have to pay alimony so you
    can't donate. The individual capacity to suffer is limited, but your
    altruistic output can suffer dramatically.

Now suppose the probability of GM is 0.6. In that case we obtain:

$$\begin{align}
\mathrm E[u_{\text{self}}(\mathrm{NM})] &= -10 \\
\mathrm E[u_{\text{self}}(\mathrm M)]   &=
    u_\text{self}(\mathrm{GM})p + u_\text{self}(\mathrm{BM}) (1-p) \\
                             &=10p - 20(1-p) \\
                             &= 30p - 20 \\
                             &= -2
\end{align}$$

So selfishly you should marry.

But if we take into account the welfare of others:

$$\begin{align}
\mathrm E[u(\mathrm{NM})] &= -10 +100 = 90 \\
\mathrm E[u(\mathrm M)] &= u(\mathrm{GM})p + u(\mathrm{BM})(1-p) \\
                        &= 120p -20(1-p) \\
                        &= 140p - 20 \\
                        &= 64
\end{align}$$

So you shouldn't marry.

In reality, I don't know what the numbers are, and there are more things to
take into account, like in-between choices, in-between outcomes, the fact that
in the particular case of marriage you can choose among multiple people or the
choice might not appear at all, etc.

Some other possibilities for what the "M" could be, other than marriage:
recreational drug use, frequent travel, risky hobbies, lack of exercise,
suboptimal office ergonomics.

The problem I described matters much more for people with very high "altruistic
potential". This is because while such people probably don't have exceptionally
high ability to feel pleasure or suffer, the value they can provide for others
is orders of magnitude higher than is typical. If you can single-handedly save
a billion lives, avoiding a little bit of boredom can't justify a small chance of death,
because humanity needs you that badly.

Note that some people make a similar argument for high-impact people and time
savings. For instance, they argue that if such people can pay to have their
house cleaned (instead of cleaning it themselves), they should do so to save
time (which can then be spent on high-impact activities). This argument depends
on a high ceiling of innate work hours. If you can only work with high
intensity for four hours per day, it doesn't matter much whether you clean your
house or not, as long as you can get those four hours in.