One of the most most powerful ideas I have taken from economics is thinking at the margin. To quote one of Greg Mankiw's principles of economics, "Rational People Think at the Margin". I think like Mankiw occasionally tends toward, this quote is ironically mischievous, and to some extent the mischievousness undermines the profundity of the message. Mankiw is not backing a horse in the old debate of whether "people are rational", or "markets are rational" - the "rational thinking" applies to the analyst, not the actors. So what he is basically saying is "In analyzing a complex system of actors or events in light of possible changes, a rational analyst thinks in terms of how actors/events at the margins are affected by the changes, rather than trying to reason about the affect on all of them, or even an average one".
A good example is if you ask someone "Do mandatory seat belts cause there to be less fatal road accidents?". The immediate common response is, "of course, since fatal accidents can become merely injurious". This is true, but not complete, the followup question is "Do you suppose, by engendering a feeling of safety, that seat belts could cause more dangerous driving, and so more accidents". Here people think about their own driving, and whether it is influenced by their wearing of the seat belt, and conclude it isn't and so answer "No". But it is here that their thinking is less than rational. Yes, most people are good, safe, average drivers in their normal range of experience, and a fairly small accident rate across the population reflects this. But it is the margin where things matter; is there marginal drivers who might feel a little safer with their seat belt on, and so might drive a little closer to the edge? It seems the answer must be yes. So on balance then are mandatory seatbelts good or bad? Well from analysis of actual before/after measurement when laws have been enacted, results are mixed.
This is a fairly unintuitive result, and economists like Steven Landsburg And Steven Levitt have managed to fill books by applying similar reasoning to a range of similar systems, to get similar unintuitive outcomes. The important point is they follow their reasonings with actual experiments to test the reasoning, and it is this that carries the weight of the argument, and allows it to win over the default, naive, intuitive analysis.
Which brings me back to the "ironically mischievous" aspect of Mankiw's principle; that since results from thinking at the margin seldom match with peoples intuition, they are extremely difficult to convince people of over "average case" type thinking. Or in other words, most people are just not rational.