Luce's choice axiom
Encyclopedia
In probability theory
, Luce's choice axiom, formulated by R. Duncan Luce
(1959), states that the probability
of selecting one item over another from a pool of many items is not affected by the presence or absence of other items in the pool. Selection of this kind is said to have "independence from irrelevant alternatives
" (IIA).
where w indicates the weight (a measure of some typically salient property) of a particular item.
, where it can be used to model a consumer
's tendency to choose one brand of product over another. It is also found in psychology
, particularly in cognitive science
where it is used to model approximately rational decision processes.
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, Luce's choice axiom, formulated by R. Duncan Luce
R. Duncan Luce
Robert Duncan Luce is the Distinguished Research Professor of Cognitive Science at the University of California, Irvine.Luce received a B.S. in Aeronautical Engineering from the Massachusetts Institute of Technology in 1945, and PhD in Mathematics from the same university in 1950...
(1959), states that the probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
of selecting one item over another from a pool of many items is not affected by the presence or absence of other items in the pool. Selection of this kind is said to have "independence from irrelevant alternatives
Independence of irrelevant alternatives
Independence of irrelevant alternatives is an axiom of decision theory and various social sciences.The word is used in different meanings in different contexts....
" (IIA).
Overview
Mathematically, the axiom states that the probability of selecting item i from a pool of j items is given by:
where w indicates the weight (a measure of some typically salient property) of a particular item.
Applications
The axiom is often encountered in economicsEconomics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
, where it can be used to model a consumer
Consumer
Consumer is a broad label for any individuals or households that use goods generated within the economy. The concept of a consumer occurs in different contexts, so that the usage and significance of the term may vary.-Economics and marketing:...
's tendency to choose one brand of product over another. It is also found in psychology
Psychology
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
, particularly in cognitive science
Cognitive science
Cognitive science is the interdisciplinary scientific study of mind and its processes. It examines what cognition is, what it does and how it works. It includes research on how information is processed , represented, and transformed in behaviour, nervous system or machine...
where it is used to model approximately rational decision processes.