What are the logical problems of solving the trolley problem with chance?

I want to ask people what do they think about solving the most standard trolley problem (1 person on a track, 5 on the other, nobody knows each other, you are the trolley driver) with chance? Throwing a coin seems like it is too simple. The solution I'm thinking about is rolling a dice, and say if you get 1 save the one person, and if you get 2 or higher save the group of people.

That way, you make the chance of surviving per person the same. That seems good to me! Can you think of formal problems with this? The most serious one I have heard is from an existentialist or Kantian view, that'd be denying your own powers of reason by leaving it to chance. I think it is the opposite. It is precisely because of me being a rational animal using those powers---say thinking that ideally every life is worth saving---that I conclude using the dice is (at least apparently) the fairest thing for me to do.

EDIT:

I think I have a way of explaining myself more. I'm going to assume that my actions about the trolley problem can only provide the world with some "goodness" G (for now assume finite, bare with me for a little), and I want to distribute that G as equally as possible between the 6 involved people to be fair.

Given the initial description of the trolley problem, I can send that G to the one person, or send that G to the five people. To give give a number, say it is 6000. I'll evaluate goodness by the average value of the distribution of G, and unfairness as the variance of the distribution of G (justice and fairness will be maximal when the differences among subjects are minimal,and so the std dev. will be minimal too).

A) I pull the lever and I send G to the five people, then I give 1200 to each, so the G distribution looks like this 0 1200 1200 1200 1200 1200, average G is 1000, std dev of G = 490

B) I don't pull the lever, and send G to the 1 person, then 6000 0 0 0 0 0, average G = 1000, std dev of G = 2459

so A) is better than B), same good, less unfair.

Now bring my roll the dice solution C) Roll the dice, so with a chance of 1/6 I get the distribution 6000 0 0 0 0 0 and with 5/6 I get the distribution 0 1200 1200 1200 1200 1200 then the average distribution taking into account the probs. is 1000 1000 1000 1000 1000 1000 Average = 1000, std dev = 0

For completeness, here is the case D) where instead of a dice you use a coin flip: distribution is 3000 600 600 600 600 600, avg = 1000, std dev = 816 (better than B but not A)

Then C is even better! It is the only way of keeping the same average goodness and also minimizing unfairness.

Now of course, saving a life cannot be assigned a number, but there is no problem, take the limit G --> inf, my solution is still the only one that minimizes the std dev of the goodness. Just to clarify, given the description of the trolley problem I cannot take G and directly distribute it among the 6 people, because I cannot "half-save" or "1/6-save" a person's life.

I think some people say that A) is better because you give every alive person 1200, which is greater than 1000, but I think the cheating part is that you would be somewhat ignoring the other person.

• Well, the expected number of deaths rises if you do that, compared to if you just kill the one person. Specifically, you would expect 5/6 * 1 + 1/6 * 5 = 1.666... deaths if you roll your die, compared to only 1 if you just kill the 1. Commented Feb 19, 2022 at 19:52
• Right. I'm maximizing chance of living per person, all six people considered. A) With dice, all of them have 1/6, the average is 1/6, and the variance (unfairness) is zero. B) No dice, if you don't move the lever, the distribution of chance per person is 1/6,0,0,0,0,0. The average is 1/36, and the unfairness is 0.07. C) No dice, if you do pull the lever, the distribution per person is 0, 1/6,1/6,1/6,1/6,1/6, the average is 5/36, and the unfairness is also 0.07.So, definitely C) is better than B), but, A) is still better than C) ! The average is larger 1/6 > 5/36 and the "unfairness" is lower. Commented Feb 19, 2022 at 22:53
• Does this answer your question? What are the ethical problems with flipping a coin to decide in the trolley problem? Commented Feb 19, 2022 at 22:55
• @causative I think if we just limit ourselves to maximizing life/minimizing death then pulling the lever and saving the five is the obvious answer, but in that case there is no trolley problem to begin with. I guess I maximize the chance of saving lives subject to the constraint of also minimizing "unfairness" when distributing that chance Commented Feb 19, 2022 at 23:44
• It's not probability homework, it's a moral dilemma. Commented Feb 20, 2022 at 1:51

Isn't that just a convoluted way of saying you want to save more people?

Also what do you mean by:

That way, you make the chance of surviving per person the same.

Because you don't. Previously with the coin flip the chance for every person to survive it was 50:50. Either they are in the lucky group or they aren't. Both the single person and the group as well as any member in the group had the exact same chance.

Now the chance to survive is unequal. For every person in the group it's 5/6 and for the single person it's 1/6. How is that fair to the single person, who's essentially disadvantaged even before the random event?

I mean you could argue that saving more people is better, but then why do you jump through the hoops of making coin flips or dice rolls at all? On the contrary if that were your position then you'd make it worse by upping the chance of the singular person, even if it's just a little.

I also shared my 2cents in that other thread in terms of the different options and how they play out: https://philosophy.stackexchange.com/a/91711/57988

Also this isn't correct:

Now of course, saving a life cannot be assigned a number, but there is no problem, take the limit G --> inf, my solution is still the only one that minimizes the std dev of the goodness.

if you let G go to infinity than you have `5*infinity + 0` or `5*0 +infinity` and your std dev is `sqrt(5*inf/6) = inf` or `sqrt(1*inf/6) = inf`. So you'd actually have the same level on unfairness because of how the infinite isn't rational.

• I mean the probability per capita, so the group has a 5/6 total, but 1/6 per capita, and so does the single person. That's what is equally distributed. It's not a cop-out as I'm not shying away from consequences. I'm using rationality to still try to choose the best (the least bad) given the facts. As for the std dev, both of your formulas are wrong, it is G/sqrt(6) or G/(5*sqrt(6)). But it doesn't matter because you first need to average the distributions with the dice probs, and then you get G/6 for everyone, so even with G->inf you do get zero unfairness because they are all equal Commented Jun 20, 2022 at 20:09
• Due to that scenario each person within a group has the probability of survival of the whole group as they can't survive independent of the group. So there is no per capita and that's not additive. The problem is that you can rationalize pretty much any outcome of that scenario the question is just what your priorities and moral assumptions are. en.wikipedia.org/wiki/… Commented Jun 20, 2022 at 20:20
• You can define a probability per capita without a problem in this scenario Commented Jun 22, 2022 at 5:23
• Oh you can define lots of things but what's the meaning behind it if it's a figure that applies to almost no one in this problem? Commented Jun 22, 2022 at 6:50
• Exactly, the thing is that it does apply to everyone in this problem Commented Jun 23, 2022 at 12:53

I guess I maximize the chance of saving lives subject to the constraint of also minimizing "unfairness" when distributing that chance.

Not really. You try to balance fairness and survival, but that's not very useful.

For fairness, consider you need to choose which track to lie on if you know the decider will flip a coin. Does not matter, right? But what if you know the decider uses your dice method?

Of course instead of deciding between fairness and maximizing lives you can also try to find a middle ground. But there are infinite ways those two ideals could be balanced and weighed. But none of those different ways objectively give appropriate weight to each ideal, unless you can prove a given distribution is the "correct" split between those ideals.

So your method is not helping with the trolley problem philosophically, but can be applied to other decision making problems with proportional gain for the stakeholders and proportional claims to the payout.

• I'm not sure I followed the "choose your track" point. I think the trolley problem would change a lot if you can choose which track to be on. However, I do like the idea of thinking how the people on the track will feel. Say there is time between the decision and the moment the trolley accident happens. I think if you pull the lever and save the 5, the person in the other track could legitimately complain that he wasn't given a fair chance of surviving. With the dice, I think no one could complain because they were all given a fair chance and the rest was just random. Commented Feb 20, 2022 at 5:26
• Asking you to choose which of the potential victims to be does not change the trolley problem, it just means analyzing the same issue from different point of views. Given a 50/50 coin toss makes it irrelevant which position to choose, this is the most fair model compared to one where it it most desirable to be in a larger group. And the group of 5 people can very well complain that you waste 5 lives based on the throw of a dice. Commented Feb 20, 2022 at 9:40
• However, psychologically, you might throw the dice as explained, but then chose to save the 5 people in any case. That way you save lives, but the poor single person will at least die believing they had a fair chance. But then a coin toss also works. Commented Feb 20, 2022 at 9:55
• I think if we keep increasing the number of people in the group from 5 to 10, 100, a million ... it'll become clear that the simple coin flip is not the fair thing to do. Of course in that case you wouldn't throw a dice, but use a random number generator within 1 and N, the number of people in the group. I think they could always complain about not being saved, but they couldn't complain that they weren't all given an equal chance of being saved. Commented Feb 20, 2022 at 22:38
• Maybe you could calculate the std dev for the coin flip for limit G --> inf. And add that to your question. Commented Feb 20, 2022 at 23:54