Luce’s Choice Axiom
Luce’s choice axiom refers to a theory that describes the behavior of an individual when it comes to making choices. This theory states that, absence or presence of the other items in a pool does not affect the probability of an individual selecting a certain item over the other in that pool.
This kind of selection is considered as having independence from the irrelevant alternatives. When choosing among alternatives, it is very often that probabilities conditioned on set choice appear to govern the responses of an individual. However, with the standard definition of the conditional probability, the ordinary theory of probability is not exactly what is required.
The difficulty can be illustrated using an example. When choosing the means to use while traveling from your home to a different city, you can choose to go by airplane, bus or car. If you choose to travel by car, all uncertainties of traveling with airplane or bus remain since a plane will fly and the bus will run regardless of whether you are in them or not.
Nevertheless, if you choose to travel by airplane or bus, your car will remain in your garage without altering the set in which the car falls. Thus, there is single universal event that underlies the uncertainty’s source. Introduction of Luce’s choice axiom was aimed at constructing a theory that is probability-like for the choice that by-passes universal, fixed sample-space assumption.
Among the areas where Luce’s choice axiom theory has been applied include psychology. Psychological application of this theory gives it historical connections. It is connected to various choice models with L.L being the most prominent in the 1927, Thurstone’s comparative judgment law.
The assumption of this theory is that numerical psychological value exists for alternatives and that the value varies randomly between choice occasions. Thus, values are the random variables. To make choices in different situation, decision makers are assumed to take time in comparing the values. Apart from psychology, Luce’s choice axiom theory has also been applied in economics and marketing research.
Nevertheless, this theory has been subjected to criticism by many scholars and experts with most of them questioning its validity. However, supporters of the theory have stood by its validity. This is because the axiomatic approach value that underlies Luce’s choice axiom is that the theory establishes testable and precise conditions that aid in determining whether a theory can be applied or not.
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