Rational choice theory is a branch of Economics that seeks to model people’s economic and social decision making. To do this it uses a number of tools including Game Theory.

In order to predictably model choices, rational choice economics must assume that people are rational. That is they behave in certain predictable ways. Rationality is not the same as being sensible. We may consider the choices someone makes to be obviously ridiculous but as long as they are logically consistent with that person’s other choices they are likely to be rational. Most people would consider poking yourself in the eye with a stick to be a rather silly thing to do but this does not make it an irrational act in the economic sense as long as the other choices and preferences the individual has are consistent with it. Economists have 4 axioms (rules or laws) of rationality the first 2 of which must hold for us to be able to model people’s behaviour.

 

Partial and Complete PreferencesCompleteness

A person must be able to state a preference order. If I have a choice between an Aston Martin, a Ford Fiesta and enduring an evening with Justin Bieber then completeness states that I must be able to put these in order of preference:

Aston Martin is preferred to Ford and to an evening with Justin Bieber. Completeness says that I must know if a Ford is also preferred to an evening with Justin Bieber.

 

It is perfectly possible to be indifferent – to say that you don’t care whether you have a Fiesta or Justin Bieber but your preferences would not be complete if you did not know which you would prefer. It is important as if you don’t know your preferences then economists can’t work out how you would react given different choices

Formally we would write this as:

For every A and B either A ≥ B or A ≤ B

 

Transitivity


Preferences Violating TransitivityThis is what most people think of when they think of rationality. If I prefer an Aston Martin to a Ford Fiesta and I prefer a Ford Fiesta to an evening with Justin Bieber then logically I must prefer the Aston to Justin. If not a situation like the diagram would result and again it would not be possible to order your preferences and predict your actions.

Formally we would say:

For every A, B and C with A≥B and B≥C we must have A≥C

 

 

Independence within lotteries

By a lottery or probability distribution all we mean is that people make a choice without being certain what the outcome will be. You do this all the time. When you go to the beach you don’t know whether you are choosing a sunny day at the beach, a wet day at the beach or a day in a traffic jam. Weather forecasts and travel news may change the odds but there is still a chance of any one of the three.

Let’s use the same example as our previous axioms but this time we will look at them as a lottery


either

(0.6) Aston Martin + (0.4) Justin BieberLottery1

Or

(0.6) Ford Fiesta + (0.4) Justin Bieber  Lottery2

We know that your preference is Aston, then Fiesta then Bieber so it must follow that you prefer lottery 1 with a 60% chance of getting an Aston to lottery 2 with a 60% chance of getting a Fiesta. That must be the case because each time there is a 40% chance of getting an evening with Justin.

This is really helpful in rational choice theory because it means economists can work the other way. I don’t know your preferences but you have told me that you would choose lottery 1 over lottery 2. That allows me to work out your preference order.

It is quite straightforward with a single set of outcomes and it is unlikely that anyone would make choices that violate this axiom but it gets rather more complicated when we factor in compound lotteries. This is when instead of simply choosing a lottery you choose a lottery within a lottery. Then people’s ability to rationalise between one lottery, each of whose outcomes is a lottery and another lottery with a different set of lotteries as an outcome, becomes highly questionable. While it sounds unlikely that you will be faced with this sort of choice the example of going to the beach shows that many choices that seem straightforward are in fact a lottery of outcomes. An example of this is the Allias Paradox which you can find out more about online.

Formally we would say:

Let p ϵ [0-1] and A, B, and C be three outcomes. A ≥ B if and only if pA + (1-p)C ≥ pB + (1-p)C

  

Continuity

Continuity says that if I have 3 outcomes there must be some probability that would make me indifferent between the best outcome with a risk of the worst and the middle outcome with certainty.

Let’s go back to our example. I have an ‘x’ chance of getting an Aston otherwise I get the evening with Justin. There must be some value of ‘x’ that would make me indifferent between that lottery and getting the Fiesta with certainty. Given the horrific prospect of an evening with Justin you may think that I would rather take the Fiesta every time but it seems reasonable to assume that once the probability of getting the Aston reaches 99% and above I would change my mind.

Formally we would say:

        Let p ϵ [0-1] and A ≥ B ≥ C. There exists a probability p such that B = pA+(1-p)C

 

 

There was quite a bit of detail there so if you are still with me then you have done well. I hope you can see that the axioms of rationality are actually simpler than they look and not especially controversial with the possible exception of independence, which makes logical sense but in a real life situation it is easy to see how people could make inconsistent choices as compound lotteries come into play. If you want to look more at the various axioms then there are an excellent set of videos on each one in this YouTube play list

 

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