The Red-Bus/Blue-Bus Problem

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While choice simulators have proven eminently useful for simulating buyer behavior, one of the most common simulation models (the Logit or Share of Preference model) has displayed a problematic result often described as the Red-Bus/Blue-Bus problem.  The underlying property leading to this problem is termed IIA, which is shorthand for "Independence from Irrelevant Alternatives."  The basic idea of IIA is that the ratio of any two products' shares should be independent of all other products. This sounds like a good thing, and at first, IIA was regarded as a beneficial property.


However, another way to say the same thing is that an improved product gains share from all other products in proportion to their original shares; and when a product loses share, it loses to others in proportion to their shares.  Stated that way, it is easy to see that IIA implies an unrealistically simple model.  In the real world, products compete unequally with one another and when an existing product is improved, it usually gains most from a subset of products with which it competes most directly.


Imagine a transportation market with two products, cars and red buses, each having a market share of 50%.  Suppose we add a second bus, colored blue.  An IIA simulator would predict that the blue bus would take share equally from the car and red bus, so that the total bus share would become 67%.  But it's clearly more reasonable to expect that the blue bus would take share mostly from the red bus, and that total bus share would remain close to 50%.


It is important to note that some degree of IIA is appropriate and useful within market simulations.  In many markets, there is some degree of randomness to buyer behavior.  It is not that people are irrational, but that buyers must balance the costs of making a utility maximizing decision against the costs of taking the time to make perfect decisions.   It is quite reasonable for rational buyers to make what on the surface may seem as haphazard decisions — especially for low-involvement purchases.  A similar or even duplicate offering could thus be expected to capture more share in the real world than a rational simulation model might suggest.


In general, market simulation models based on disaggregate models of preference (utilities estimated at the individual level) are more immune to IIA difficulties than aggregate models of preference (aggregate logit, as offered by our CBC System).  In addition to modeling respondent preferences at the individual level, there are market simulation methods that help deal with IIA.  These are described in the next sections.


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