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

Question

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.

Answer 1

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.

Answer 2

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.