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I discharge number 3 and number 4 objection, as a situation where the problem is ill-defined. That is, the ammount of knowledge supposed to have is inverosimile or unkown. And yes, I think the fat guy case is a case of an ethical injunction. But doesn't it slip the predictive power of consequentialism? It may not. I'm more concerned on the problems written below.
I do think you should act for a better outcome. I disagree in completeness and transitiveness of values. http://en.wikipedia.org/wiki/Rational_choice_theory#Other_assumptions That's the cause that utility is not cuantifiable, thus there's not a calculation to show which action is right, thus there's not a best possible action. The problem is that action is highly chaotic (sensitive) to non rational variables, because there are some actions where it is impossible to decide, but something has to be decided. Look, how about the first example here http://en.wikipedia.org/wiki/Framing_effect_(psychology)? I understand that you would choose the same in the first and second question. But what would you choose? A(=C) or B(=D). The answer should be none, just find a way where the 600 hundred people will keep alive. In the meantime, where that option is not possible, there are politics.
By the way, if you believe in utility maximization, explain me Arrow's theorem. I think it disproves utilitarianism.
By the way, I haven't read about consequentialism. Is so wrong in so many levels! Firstly, it is impossible to assign a numbered utility to each action. That is just not understanding human brain. Secondly, it is impossible to sum up utilities, give me an example where summing different people utilities make any sense. Thirdly, it regards the action as an one-time action. But just it isn't. If you teach .people to push the fat guy to kill it. You just not only will have three people less dead. You'll also have a bunch of emotionless people who think it is ok to kill people if it is for the greater good. Fourthly, people don't always come immediately to the truth. You can't say you should kill the fat guy if you really think that's gonna save the other people. The soberby of people might not be a good idea to make them feel they have the power. Fifthly, if utility is not cuantitative, the logic of morality can't be a computation. That's my point. The discovery of reallity might be a calculation, because you go outside to see. On the whole, what a disappointement. This page is so great I can't understand why it understands so poorly morality. I recommend you to read, for example, Weber, who has a detailed theory of value in societies. Or Sartre for a complexity in defining what's right.
I'll try to defend politics. I would be grateful if you debate with me. I argue that values (a generalization of morality) are comprehensible. I, thus, agree with Eliezer in the methaetics sequence. But values are different in a crucial ways to external reallity. I think that external reallity is better to reach by rationality than values. I'll think that because of that the non-rational discurse of politics is a great action. I'll take this as an example of a problem I see in this page at analizing morality. Firstly, which is the difference between values and external reality that I recall? I'll call it "coherence", I'll say external reality is objectivily (inductivily) coherent, and values are objectively incoherent. What do I mean with "coherence"? You may describe a reality in a way such that you encompass a lot of your next observations. But you not always can act in a way such almost all your values you have are considered in the act. That is you can think coherently, you can't act coherently. And it's not a problem of not enough information, or your stupidity.
Let's take two examples: The ethical paradox of a train that is going to kill three people, but you can change it's way, so it kills one guy. Would you pull it? And if it was another number? I'd argue the problem is you valorate not killing personally, but you also feel responsible for the death of more people. But this values may not be rationally compatible.
The abortion problem. You may not kill another human being. But what's a human being? It's not defined a priori, but by society. At the same time, choice is important because there's a problem in telling a woman that because she has it biollogically she might not have a career (imagine a teen pregnancy), thus degradating her life -not that the child life might be great. There is adoption, etc. You may reach dozens of arguments and contraarguments in both sides. I'm not taking a posture here. I'm just illustrating a problem.
Now, I say you can think coherently but not act coherently, why I make the difference? Ok, I think reallity is definite. Something happens or doesn't happens, right? Let's do an experiment! etc. Suppose we were rational utility maximizers. Then, there would be an answer, right? It might be difficult to achieve, but there would be an answer. But we are not. So there's not a value that is strictly better than another one? Yes, there is. The value A is better than B if it includes the reason because B was good, and something more. But because you're human, and you just can'ty fly nor create life clapping your hands, you may not have a coherent action. I might throw philosophical and sociological concepts, but I think I made myself clear. What for then it exists athe polytics, if you can't do nothing? Because there is society.
And that's the point where I wanted to reach. In this page the individual rationality is greatly discovered. But there's not only the individual. Now, if you make a tiny parallelism, you can see that as a person may learn bayensianically, a society may learn the same way. It’s not too difficult to show it, it just mean that social progress exists, and I think you’d agree on that. No, “not being political” doesn’t exists. It just means that your policy is to keep social relationships the way they are. Because you let the individual change, but you don’t incentivize the society change as a whole. In my country this is called “conservative view”. So, sumarizing, I’m recalling one of the many times that a nonrational discurse is morally right. This case is when by defending yourself at the same time your opponent, you let the society to unravel posibilities to act. Politics is not war, politics is peaceful, is human. It’s almost impossible to appasionate about many ideologies because they are strongly incoherent between them. You may not be able to tax some people and not taxing at the same time. But the problem in not appasionate at something beyond reason is that you may not overcome the problems a society has, such as poverty, illness or uneducation. You would limit your solution to techical solutions, barring the possibility to societal solutions. Your country has houses without people and people without houses. That’s irrational. That’s a problem. There are others discurses, such as the artistic discurse that are great and respectful. But at the objective of not writing too long, I’ll stop here.
PS: I’m saying you may not use only rational arguments. I’m not saying you shouldn’t be open. Openness is more fundamental than rationallity.