# How does utilitarianism deal with probabilities?

This is the most frustrating problem I encountered in understanding utilitarianism. If we've chosen the best possible alternative according to the expected value of 'happiness' it brought. Could our action still be considered immoral if the plan gets off track because of uncontrollable factors? (for example, the Butterfly Effect, or any intrinsic risks we've already considered while deciding)

Here is the formalized case I conducted:

Assume happiness can be quantified

There existed 2 choices:

A: has a success rate of P1, bring X amount of happiness. If failed, brings no happiness.

B: will always success, bring Y amount of happiness

where P1*X>Y>0 (i.e. expected value of A is greater than B)

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1. Which one should we choose, according to utilitarianism?

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1. If the answer is A:

If one chose A and the event failed to happen, is his/her choice immoral?

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1. If Yes:

The one chose the best possible choice according to utilitarianism rules, how can he/she be immoral?

If No:

Does this oppose consequentialism? As the behaviour is assessed not only on its consequence.

• This does not have much to do with utilitarianism as such, and illustrates a mathematical paradox of maximizing expected values of anything. In probabilistic situations, giving the quantity to be maximized is not enough, maximizing it is equivalent to maximizing any monotone function of it, but the expected values depend on such a function. Picking one amounts to making a betting choice: high risk high reward (convex), lower risk lower reward (concave), the standard linear choice is in the middle. There is no prescription on betting, maximization problem is only defined when the choice is made Jun 25, 2019 at 10:49

I like this question. Personally I don't think we can since that before the event actually happened, there was no way of knowing what exactly will be the output.

Assume for contradiction that we can see this as immoral. Following your line of logic we play a thought experiment. A is a trail that has P1 probability of being successful.

Say that the trail ends in success but the player failed to choose A, he had chosen B. Since P1<1, then A>B, the choice of B was immoral by your logic.

This complemented with your argument would render both choices to be immoral in some possible situations uncontrollable and unknown beforehand. Since both situations can happen, there is a risk of being considered immoral no matter what the player choose before the output of the game. I think this is fundamentally incorrect. You can either choose A, or B, your cannot choose nothing. Both A and B could be considered immoral depending on outside uncontrollable factors. So I do not think that we can readily claim that the action of A is immoral.

This question goes deeper too. It reminded me of the Good Samaritan law.

Imagine the following situation:

You are a bystander at a train station. A train is approaching, a child is playing dangerously close to the track and at this rate, he will sure to permanently hurt his foot. You can choose to run to him and rescue him, but this action has a probability of (1-P1) that would result in you startling that child to cause him to lost his foot.

Which choice do you think is immoral? If this was hard to you then:

You are a bystander at a train station. A train is approaching, a child is playing dangerously close to the track and at this rate, he will sure to lose his foot and become mutilated for life. You can choose to run to him and rescue him, but this action has a probability of (1-P1) that would result in you startling that child to cause him to completely drop down on to the track.

Which choice do you think is immoral?

Did your action change? Why do you think it changed or didn't change? If it did change then what really changed in the questions (expected values)? Does it say anything about being moral or not?

• Thanks for a detailed answer :). If I interpret it correctly, choosing neither A nor B is immoral despite the final outcome by your logic. Since the situation is "uncontrollable and unknown beforehand" and "there is a risk of being considered immoral no matter what the player choose".
– user40068
Jun 26, 2019 at 8:45
• However, does it imply that concept of morality becomes vague when probability appears? In classical utilitarianism there is a clear line between moral behaviours and immoral ones. But in this case whatever we behave won't be immoral. Then how can we determine what should we do?
– user40068
Jun 26, 2019 at 8:51
• I don't know of a specific literature that dealt with this question but I'm sure there should be some at least. Search the big names like Hume and Mill to see if they talk about this in the classical sense. Jun 27, 2019 at 15:22
• i'd personally prefer the 'best you can do' based on known information argument. we cannot say that a prior act is moral or otherwise based on additional information. so I would use the expected outcome argument which is the best you can do strategy. I speculate the classical utilitarianism would agree with this since I know of no conflict with this view Jun 27, 2019 at 15:26
• I agree the best you can do argument too :D. The problem here is that the action is justified not on its outcome but on its possible outcome, which in a sense opposed consequentialism I suggest. Nevertheless, I will search for historical discussion around this, thanks.
– user40068
Jun 28, 2019 at 0:11

With utilitarianism actions are always judged based on the consequences.

What if the consequence can't be evaluated ? Then you have a high risk of doing something wrong.

You have to remember that utilitarianism is recursive. Therefore you have to act so that your choice has better chances of being the good one, therefore you have to study your options.

So, utilitarinism demands that you be smart so that the choices that you make have a better chance of being the right ones.

If it wasnt so, then you could simply say that morons are exempt from moral choices because they can't evaluate the consequences.