I really like this explanation:

“Since in the real world it is nearly impossible to know another player’s prefs, a good approximation is to make the assumption of rationality, and let the choices made inform your notion of the player’s utility.”

I’m going to use that one in the future

In this way of looking at it, even many clearly insane people are raional; they just have an unexpected preference set.

–The Formal Definition–
In economics, a rational preference has a specific meaning. There are two requirements:

1. Completeness. For any two options X and Y, you either prefer X to Y, Y to X, or are indifferent.

2. Transitivity: If X is preferred to Y, and Y is preferred to Z, then X must be preferred to Z.

Dealing with preference ordering gets arduous when you have to compare thousands of choices. So economists use “utility functions” as a compact method. This means u(X) > u(Y) only when X is preferred to Y.

A preference can only be represented by a utility function if it is rational.

–What is Irrational?–
Mahesh gives a good definition of irrational. It means that you choose a sub-optimal preference. If you preferred X to Y, but decided to choose Y, then you made an irrational choice.

Or if you preferred X to Y, and Y to Z, but then chose Z over X. This is a topic I discussed in last week’s article of voting.

–To answer Steph’s examples–
Your examples are interesting, and you raise a question of whether the choices are truly irrational. In one sense, no, they are not.

You’re right that people are choosing things that make them happy under full information. They have choice, they are weighing options, and they are making a decision. It’s wrong for me to say it’s irrational just because I would not do those things.

But in another sense, I think the beliefs are irrational. This is because people can be made to have irrational beliefs and then act “optimally.”

When women started smoking in America, they were doing so because celebrities told them it was a liberating experience. It is an example documented in “The Century of the Self.” The narrator explains that it’s completely irrational that smoking would make a woman freer–you become a slave to nicotine and big business. But the image made them feel freer.

And that’s why I call my examples “irrational.” When you look at the payoffs–IF ALL players were rational–then it doesn’t make sense what people are doing.

Valentines day has marked up candy because people buy into the idea. People pay to wait around on an airplane since it sounds fun. Most of us know it’s not really fun.

Somewhere, I would say these strange actions are the result of irrational beliefs. I don’t think people would do these things in the absence of marketing.

–To answer Mahesh–
You caught me–I was using the word irrational lazily. I’ll have to look at those Becker articles; thanks for the pointer.

A similar example I have come across recently is the case of an Indian company that is offering a “plane ride to nowhere” on which passengers board an Airbus 300 in Delhi, are waited on by flight attendants, and receive “in-flight” announcements all while sitting on the ground. (http://www.timesonline.co.uk/tol/news/world/asia/article2558290.ece) To me, paying to sit on an airplane and go nowhere would be completely irrational, but to people who may never get to experience the real thing, I can see how it could be worth it. They are getting utility that you are I may not get – just as people who buy chocolates on Valentine’s Day or buy the latest fashions are getting some sort of utility out of it that is causing them to pay the premium.

I’ve always thought of irrationality in an economic sense to be a decision that is made with asymmetrical information where utility is inconsistent. An example of the former would be buying an airline ticket from Orbitz when you could get the exact same ticket from Expedia for $100 less. If you aren’t aware that Expedia is offering a lower price, you might make the decision to buy the ticket from Orbitz, a decision which I think economists would consider “irrational” – under perfect market conditions, economists would predict that Orbitz would sell zero tickets even if its price was even $1 higher. An example of the latter (taken from Berkeley prof Matthew Rabin) would be that many people prefer $10 today over $15 one week from now, but prefer $15 fifty-one weeks from now over $10 fifty weeks from now.

What is the economic definition of irrational? And are there different degrees of irrationality?