They're not realistic because they're designed to isolate the relevant intuitions from the noise. Being suspicious of our intuitions about fictional scenarios is fine- but I don't think that lets you get away without updating. These scenarios are easy to generate and have several features in common. I don't expect anyone to give up their utilitarianism on the basis of the above comment-- but a little more skepticism would be good.

Please don't throw around Gödel's Theorem before you've really understood it— that's one thing that makes people look like cranks!

"When does that ever happen and how does answering that question help me be more ethical?"

Very rarely; but pondering such hypotheticals has helped me to see what some of my actual moral intuitions are, once they are stripped of rationalizations (and chances to dodge the question). From that point on, I can reflect on them more effectively.

"Exposed to these situations" means to say that when someone asks about utilitarianism they say, "if there was a fat man in front of a train filled with single parents and you could push him out of the way or let the train run off a cliff what would you do?" To which my reply is, "When does that ever happen and how does answering that question help me be more ethical?"

These thought experiments aren't supposed to make you more ethical, they're supposed to help us understand our morality. If you think there are regularities in ethics- general rules that apply to multiple situations then it helps to concoct scenarios to see how those rules function. Often they're contrived because they are experiments, set up to see how the introduction of a moral principle affects our intuitions. In natural science experimental conditions usually have to be concocted as well. You don't usually find two population groups for whom everything is the same except for one variable, for example.

Digression: if a decision-theoretic model was translated into a set of axiomatic behaviors could you potentially apply Godel's Incompleteness Theorem to prove that simple and consistent is in fact too much to ask?

Agree with orthonormal. Not sure what this would mean. I don't think Godel even does that for arithmetic-- arithmetic is simple (though not trivial) and consistent, it just isn't complete. I have no idea if ethics could be a complete axiomatic system, I haven't done much on completeness beyond predicate calculus and Godel is still a little over my head.

I just mean that any simple set of principles will have to be applied inconsistently to match our intuitions. This, on moral particularism, is relevant.

The main Wikipedia entry for Utilitarianism says:

Utilitarianism is the idea that the moral worth of an action is determined solely by its utility in providing happiness or pleasure as summed among all people. It is thus a form of consequentialism, meaning that the moral worth of an action is determined by its outcome.

Utilitarianism is often described by the phrase "the greatest good for the greatest number of people", and is also known as "the greatest happiness principle". Utility, the good to be maximized, has been defined by various thinkers as happiness or pleasure (versus suffering or pain), although preference utilitarians define it as the satisfaction of preferences.

Where 'preference utilitarians' links back to the short page on preference utilitarianism you referenced. That combined with the description of Peter Singer as the most prominent advocate for preference utilitarianism suggests weighted summing or averaging, though I'm not clear whether there is some specific procedure associated with 'preference utilitarianism'.

Merely satisfying your own preferences is a moral philosophy but it's not utilitarianism. Ethical Egoism maybe or just hedonism. What appears to distinguish utilitarian ethics is that they propose a unique utility function that globally defines what is moral/ethical for all agents.