Here are a few Too long; didn’t read for big schools of thoughts in philosophy. Most of them are explained, then implicitly criticized because I am something of a cynic myself. The Trolley Problem is used in each of them as an example.
Utilitarianism: You try to achieve the greatest good for the greatest number of people. You will choose to pull the lever, killing one person to save five. You look at the big picture, regardless of what happens to individual pixels. The right choice is dictated by a few ethical premises and a lot of math with them. Murder could be justified as long as someone enjoys it enough.
Deontology: You have a few arbitrary premises about what constitutes good, and a very short-sighted way to use them. Respecting those rules is the number one priority, because if everyone did so, nothing bad could happen. You shall not kill, therefore pulling the lever is the wrong choice. You will not tell your kids about Santa Claus, you will not lie about a surprise for a loved one, and you will let a genocide happens if the only way to stop it is to punch Hitler.
Consequentialism: The end not only justifies the mean, but is literally everything. Your actions don’t matter, you will only be judged by how things turned out. Whether you pull the lever or not, you are evil because your decision allowed people to die. Gambling your entire life savings is justified as long as you win.
Egoism: A choice is justified as long as it benefits the person making it. All agents are ethically justified to work in their own self interest, regardless of the rest of the world. It is more justified to steal from the weak and defenseless, because they are less likely to fight back, so your success is more probable, and the negative consequences for you might be smaller. You should pull the lever if an utilitarist is watching you, and you should ignore it if the witness is a deontologist.
Nihilism: Life has no meaning, the world has no meaning, and there is no point to keep writing this definition. There is no difference between dying today or 50 years from now, and since everyone your life will impact will die too, nothing you do matters. You probably won’t kill yourself, because death has no value either, so why waste your efforts to die? You won’t jump off a bridge, but if a car sways towards you, there is no reason to step aside either. You pull the lever if you feel like it, it makes no difference. You will only delay the death of the people on the tracks.
Antinatalism: Life has, on average, a negative value. People will suffer more than they will be happy. Therefore, birth and procreation are immoral acts. It is morally acceptable, and required, to end lives as soon as possible as often as possible to save people from the pain of existence. Some people are against abortion because they think it is murder, some people are pro-choice because they think a women shouldn’t be forced to give birth. The anti-natalist will vote for abortion because it is good for the baby to not be born. You are the one tying people to the tracks.
Stoicism: Pain is but an illusion. All of your unhapiness is your own choice, because you could simply choose to not care about it. There is no reason to abstain from rape and murder, because the other person could just not be unhappy about it. They could have become a nihilist, so you are not doing any wrong by posing actions that they chose to dislike. The lever is none of your business.
Epicureanism: A more positive outlook on Stoicism. Instead of being psychologically immune to pain, you are the only person responsible for your own hapiness, through pleasure. You only need the bare minimum for survival in terms of food, heat, etc. The rest is not only unecessary, but a problem, since it might make you want it more when it’s gone. You can simply choose to be happy and fulfilled with whatever is in your life, since pleasure is subjective. You will pull the lever to allow 5 people to continue being happy, and the dead guy should appreciate that.