Economists use three quite different definitions of rationality. None of them correspond to the normal English-language definition. You would be hard-pressed to find any economist admitting to this situation.

Rational (#1): If you prefer B to C and C to D, then you also prefer B to D

Or, as Wikipedia puts it: “When a preference order is both transitive and complete, then it is standard practice to call it a rational preference relation, and the people who comply with it are rational agents.” 

“Complete” means the “transitive” relationship specified in the definition holds no matter what B, C and D mean.

This is a very weak requirement. Dogs and cats are quite rational by this definition. If they like food B more than C and C more than D, they will almost always like B more than D.

Rational (#2): You have “rational expectations” if your prediction of your future economic situation is unbiased (roughly, if you have an equal chance of being high or low).

Or, as Wikipedia puts it: “In economics, “rational expectations” are model-consistent expectations, in that agents inside the model are assumed to “know the model” and on average take the model’s predictions as valid.” Wiki’s explanation corresponds to how conservative economists (the ones who like this idea) use this definition. They build a complex model of the economy and the government and then assume all workers and consumers figure out what will happen for decades to come. But what happens depends on what everyone else thinks will happen. So they assume everyone’s thinking will turn out to be right on average and work out what that means will happen. 

Cats and dogs find this difficult, as do most economists and regular folks. Basically, it’s an assumption that people are geniuses with no biases.

Rational (#3): If you’re playing a game and know the payoffs for winning, losing, and all the in-between possibilities, and if you know your chances for each possible move, then you will move in the way that maximized you expected (average) payoff.

Or, as Aumann and Brandenburger put it: “We call a player rational if he maximizes his utility given his beliefs.” By “utility” (happiness by a fancy name) they basically mean the monetary payoff.

For many simple games, this contains a reasonable dose of #1 and #2. It assumes you like a little more money rather than less and a lot more rather than a little more. And it assumes you can predict something that is not too complicated in a simple game.

The Hidden Problem

Although none of the definitions say this, when economists use these definitions they always assume that your “utility” depends only on your payoff, or what you consume, and you don’t care about anyone else. 

This is a great simplification of reality and it makes it possible to prove surprising things. Rational definition #2 also assumes people don’t have build-in biases regarding what they believe. But, in my view, the most fundamental problem is that people are inherently social animals and that’s what creates social institutions and what makes them function for good or for evil. Leaving that out is leaving out the most important part of how people think.

The Normal Definition

The English language definition of rational does not make this mistake. In English saying someone is rational just means they use logic to try to get what they want. And what they want can include making someone else happy or unhappy.