Independence of Irrelevant Alternatives (IIA)
The concept of Independence of Irrelevant Alternatives (IIA) is used in economics and decision theory to describe the fact that when a third, irrelevant alternative is introduced, the relative preferences between the two alternatives should not change. Thus, if two alternatives are presented, the presence or availability of a third, unrelated or insignificant alternative should not alter the decision-making process or preference.
Simplification of the idea
Let us consider a simple example in order to better understand this concept. Consider the case in which you are given a choice between two flavors of ice cream: chocolate and vanilla. The choice of chocolate expresses your preference. The IIA principle argues that your preference between chocolate and vanilla should not be affected by the addition of a third flavor, such as strawberry. Therefore, regardless of the presence of strawberry, your preference for chocolate should remain the same.
Many economic and social contexts use the IIA principle, such as voting systems, consumer choices, and market competition. In addition, it ensures that the introduction of new alternatives does not alter the relative ranking or choice of existing alternatives.
Nevertheless, the IIA principle has been subject to some criticism and is not always observed in real-world situations. A violation of IIA can occur in situations where complex interactions or contextual factors are present, resulting in a change in preferences and choices when new alternatives are introduced. This phenomenon can be quntified using Hausman-McFadden test in R.
Let’s consider the GSS 2016 dataset and it has been modified to include a new column named “transportation”. This column has four unordered categories which is the core idea behind multinomial logistic regression. The categories are bus, train, car and airplane. We are interested to model the transportation variable to see if this is dependent on family income.
The variables in the dataset are:
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