Utilitarianism wins outright part 5
Giving more arguments for utilitarianism
“And God feels intellectually inadequate compared to John von Neumann.”
—Scott Alexander
John was famous for his thought experiment in which one was equally likely to be all members of society. He argued that ethics has to be impartial—it’s about what we’d do if we were equally likely to be everyone, but acting as a rational agent. As a result of this and other things, he was one of the most revered thinkers of his time with numerous citations.
I’m of course referring to John Harsanyi. I know, not Rawls, who had his seminal idea long after Harsanyi did, before becoming famous by reasoning badly about what one would do from behind the veil of ignorance. Harsanyi’s argument is as follows.
Ethics should be impartial—it should be a realm of rational choice that would be undertaken if one was making decisions for a group, but was equally likely to be any member of the group. This seems to capture what we mean by ethics. If a person does what benefits themselves merely because they don’t care about others, that wouldn’t be an ethical view, for it wouldn’t be impartial.
So, when making ethical decisions one should act as they would if they had an equal chance of being any of the affected parties. Additionally, every member of the group should be VNM rational. This means that their preferences should have the following four features.
Completeness. When choosing between A and B they should either prefer A, prefer B, or be indifferent between A and B. They have to be able to compare any two situations and decide whether one is better, or whether they’re equal.
Transitivity. If they prefer A to B and B to C, they should prefer A to C. Likewise, if they’re indifferent between A and B and indifferent between B and C, they should be indifferent between A and C.
Continuity. If A≥B≥C, then there’s some probability P such that P(C) + (1-P) (A) = B. To illustrate, if I prefer bananas to apples and apples to oranges then there’s some probability, let’s say .5 for which I’d judge certainty of apples to be just as good as (1-.5)=.5 probability of bananas and .5 probability of oranges.
Independence. For a probability between 0 and 1, B≥A only if the value of P(B) + (1-P)(C) ≥ P(A)+(1-P)(C). Basically if B is better than or equal to A, then some probability of B and some probability of C will be better than or equal to the same probability of A and the same probability of C. To illustrate once more, if I prefer bananas to apples, then (using the probability of .5), I’d prefer a .5 chance of bananas and a .5 chance of a car to a .5 chance of apples and a .5 chance of a car.
These combine to form a utility function, which represents the choice worthiness of states of affairs. For this utility function, it has to be the case that a one half chance of 2 utility is equally good to certainty of 1 utility. 2 utility is just defined as the amount of utility that’s sufficiently good for a 50% chance of it to be just as good as certainty of 1 utility.
All of the premises pose major problems if they’re denied that involve dutch book arguments—it would be pretty complex to explain why, but let’s just accept these axioms of rational decision making for now. Well if all the individuals in the group should be vnm rational when making decisions, the group as a whole should similarly be vnm rational. If everyone in the group prefers apples to bananas and bananas to oranges then the group as a whole should prefer apples to bananas and bananas to oranges.
So now as a rational decision maker you’re trying to make decisions for the group, knowing that you’re equally likely to be each member of the group. What decision making procedure should you use to satisfy the axioms? Harsanyi showed that only utilitarianism can satisfy the axioms.
Let’s illustrate this with an example. Suppose you’re deciding whether to take an action that gives 1 person 2 utility or 2 people 1 utility. The above axioms show that you should be indifferent between them. You’re just as likely to be each of the two people, so from your perspective it’s equivalent to a choice between a 1/2 chance of 2 utility and certainty of 1 utility. We saw before that those are equally valuable, a 1/2 chance of 2 utility is by definition equally good to certainty of 1 utility. 2 utility is just the amount of utility for which a 1/2 chance of it will be just as good as certainty of 1 utility. So we can’t just go the Rawlsian route and try to privilege those who are worst off. That is bad math!! The probability theory is crystal clear.
Now let’s say that you’re deciding whether to kill one to save five, and assume that each of the 6 people will have 5 utility. Well, from the perspective of everyone, all of whom have to be impartial, the choice is obvious. A 5/6 chance of 5 utility is better than a 1/6 chance of 5 utility. It is better by a factor of five. These axioms combined with impartiality leave no room for rights, virtue, or anything else that’s not utility function based.
This argument leaves unspecified what things should factor into an individuals utility functions. It could be the case that a person’s utility function corresponds with how many marbles they connect (though the person who invented that utility function would have clearly lost their marbles). This just shows that morality must be the same as universal egoism—it must represent what one would do if they lived everyone’s life and maximized the good things that were experienced throughout all of the lives. You cannot discount certain people, nor can you care about agent centered side constraints. You cannot care about retributivism—if you had an equal chance of being the murderer you wouldn’t support decreasing expected utility by n/p where n is the amount of utility they’d experience absent retribution and p is the number of total people. Additionally, I’ve provided compelling arguments as to what the utility function should be in other articles.
Those who are impartial and rational must be utilitarians. We now have two independent derivations of this principle. And there are many more to come. For those still on the fence, how likely do you think that the incorrect theory would get the right answers historically, win on theoretical virtues, and be derivable from two independent sets of plausible axioms, one deduced by a nobel laureatte.
It’s certainly possible, but I wouldn’t bet on it.