Moral Calculus

Ethical decisions are usually thought of as a philosophical exercise, a qualitative analysis of values that cannot be quantified scientifically or mathematically. The very notion of putting a value on human life seems absurd.

However, I suggest that there is a numerical value we can assign to a human life. That value is one. One-for-one, each life is fundamentally of equal value. Therefore, in a situation where lives are on the line, a mathematical method of morality would place the value of a certain means of saving life that is 100% probable, as 1, and that is 0% probable as 0. Thus an action with a 50% likelihood of saving a life would be valued at 0.5. An action that would cause a person to die with a probability of 100% would be equal to -1.

From this, we can apply Bayesian Probability as a means of calculating much more complex moral dilemmas.

Consider that act that would kill someone, but in the process, save the lives of others (the shooting the gunman example). This act has moral value of (-1) + wX, where X is number of lives that will saved, and w is the weight or probability that these lives will actually be saved as a derivative of the action.

Any given action has a first order moral value, which is determined by its direct effect. For instance, killing someone is a first order -1, a fundamentally evil act. However, such an act may have derivative moral values, their collective indirect effects. This allows for a directly evil act (shooting someone) to have a net good effect (through indirectly saving the lives of others).

Or consider the problem of Adultery. A common criticism of Utilitarianism is that it doesn’t condemn acts like Adultery because at first glance, an act like Adultery seems like it would increase net happiness and therefore be condoned. This does not take into account the probabilities of being caught however. Given uncertainty, it is usually safe to assume a uniform distribution of probabilities, which means that getting caught has a 0.5 probability. We must then compare the utilities of not getting caught, and getting caught. It doesn’t really matter what the exact numbers are, so much as the relative relationship of the values. So for instance, we can say that Adultery in the not getting caught scenario has a +5 to each member of the Adultery, for a total of +10. However, in the getting caught scenario, there is a +5 to the uncoupled member, but a net loss of -20 to the coupled member, and -20 to the wronged partner, due to the potential falling out and loss of trust resulting from the discovered Adultery.

Thus the net total effect of Adultery in the caught scenario is -35. If we assign the probabilities to each scenario, +10 x 0.5 = +5, while -35 x 0.5 = -17.5. +5 – 17.5 = -12.5, therefore the probable net effect of Adultery is actually negative and therefore morally wrong.

But what if getting caught is very unlikely? Well, we can show that to a true agnostic at least, the probability of getting caught must be at least 0.5, because that is the most likely probability that God and an afterlife exist, which would lead eventually to the other partner finding out. But assuming a simplified atheistic view, there is the danger that hypothetically, if the probability of truth not discovered was 1, then this calculation would actually suggest that committing Adultery would be moral.

The previous example is based on subjective happiness, but what if we used a criterion of Eudaimonia, or the objective happiness we would feel if we knew everything? In that case the Adultery scenario looks even more negative.

In this instance, we can say that Adultery in the not getting caught scenario has a +5 to each member of the Adultery, but also a -20 to the partner who is being wronged because that is how much they would suffer if they knew, which is a net -10. In the getting caught scenario, there is a +5 to the uncoupled member, but a net loss of -20 to the coupled member and an additional -20 to the partner being wronged, due to the potential falling out and loss of trust resulting from the discovered Adultery.

As you can see, with a Eudaimonic Utilitarian criterion, even if the probability of truth not discovered was 1, it would still be negative and therefore morally wrong. Thus, whereas Utilitarianism based on subjective happiness bases its case against Adultery on the probability of being caught and the potential negative consequences, Eudaimonic Utilitarianism takes a more solid case that Adultery would always be wrong because regardless the consequences are negative.

Take another more complicated example. What is the actual moral calculus of lying to protect a family of Jews from a Nazi in World War II? In this we assume that if the lie is discovered, you’ll also be killed.

So as you can see, -4 < -2.5, and so telling the lie is justified.

Now look at the strange effect of if there’s just one Jew.

So as you can see, -1 = -1 so this is actually a close moral conundrum that depends heavily on whether or not the truth being discovered is likely. Note that unlike the Adultery scenario, being discovered in the afterlife is not important. Thus, if there is even a slightly greater than 0.5 chance that the lie will be believed, then the correct moral act is to lie.