Differences in independence of irrelevant alternatives at individual vs aggregate levels, and at single pair vs full choice set

The concept of 'independence of irrelevant alternatives' (IIA) was originally developed at the individual level. Real-world applications of choice modeling in fields such as marketing, transportation, and political science, however, generally occur at the aggregate level. Here, we investigate the relationship between the IIA assumptions at the two levels, and identify variables moderating this relationship. Specifically in this research, we prove that under some particular conditions, validity of the IIA assumption at the individual level leads to validity (or violation) of IIA at the aggregate level. Analogous to the above, past literature has focused on evaluating IIA violations or otherwise for a single pair of alternatives. Real-world managers, on the other hand, need to look at possible IIA violations between all possible pairs of alternatives in a choice set; this focus on the full choice set is necessary for making appropriate marketing strategy decisions. In this research, we argue that it is more relevant to focus on the full choice set. We first identify IIA relationships at the single pair level, and then build on those findings to identify IIA relationships at the full choice set level. One of the important findings at the full choice set level is that there must exist preference homogeneity or IIA is violated at the aggregate level, when there is no violation at the individual level.