How People Choose – A Primer On Choice Research

This article provides a brief summary of the history of that science, including its logic and some of the thinkers who developed it.

Rational Economic Man
Traditional economics invents a convenient fiction that allows it to simplify and to think about how humans make decisions. This fiction, "rational economic man," is a "utility maximizer." That is, he seeks to do what is best for him economically. If two cars are identical but one is cheaper, he buys the cheaper one; if the same type of checking account pays him interest at Bank of America but not at Citibank, he opens the account at Bank of America; and so on. Many of us behave like rational economic man, much of the time.

The Psychology of Choice
Unfortunately, the fiction of rational economic man turns out to be a little too simple to use. He always picks the product with the highest utility, but when real humans choose, they may not have their facts straight about all of the products they could choose, or they're preferences could change day-to-day. Add to that, there are just really a lot of products from which to choose. It took a while for economists to account for all this complexity, and they did so with the help of a pair of mathematical psychologists.

First, in 1927, L.L. Thurstone was working on a theory of scaling and psychological measurement for survey research. As part of his work, he noted a difference between what respondents perceive and what is true. Applied to economics, this means there is difference between the true value (V) a product may have for me and my perception of its utility (U):

Because this difference, ε, is itself a variable with a statistical distribution, it is a "random variable" in math-speak, and so utility models that took advantage of Thurstone's insight were called "random utility models."

In 1959 a second mathematical psychologist, R. Duncan Luce, created a formula he called the "choice axiom:

In words, the chance of choosing a certain alternative A (a certain car, or checking account or restaurant) is proportional to a function of the utility of that alternative divided by the sum of the functions of the utilities of all the alternatives we have to choose from.

Luce's choice axiom explains a lot about choices we see in marketing research. For example, Why do I lose share when my satisfaction scores stay the same (or rise)? Well, it could be competitors raised their scores even more than you did, so the denominator grows faster than the numerator. Alternatively, maybe new competitors have entered the market, which is another way to make the denominator grow faster than the numerator.

Extension to an Attribute Model
So random utility theory and the choice axiom are pretty cool. They provide some tidy math to describe choices. But as marketing researchers, we want to do more than just describe choices, we want to explain them.

In 1974, economist Dan McFadden extended Luce's choice axiom to a statistical model incorporating the effect of attributes. First, he suggested the function to use in Luce's choice axiom is the exponential function*, e, the reverse of the logarithmic function:

Coincidentally, if you just multiply by 1 instead of using the exponential function in Luce's equation, you get a function that predicts how pigeons make choices – now you know one more difference between humans and pigeons.

McFadden's model also allows us to compute coefficients (or relative strengths) for attributes that sum to total product utilities, like this, where each "b" is a different strength:

That little ε on the end of the equation is the same error term (the same difference between real and perceived utility) identified by Thurstone.

This is helpful stuff. You'll notice the structure of this utility model is an additive, linear model (it is "additive" because the terms are connected by addition signs; it is "linear" because none of the Xs get squared or cubed or anything funky like that). This is the same as the familiar structure of models based on regression analysis.

So now we can describe the choices people make with tidy math and understand those choices in terms of how various attributes (like price, brand and various product features) affect them. This is handy information indeed, and it is part of what won McFadden the Nobel Prize in economics in 2000.

It is also the model to use in brand equity and competitive loyalty models, if we want to portray customers' choices realistically.

Adding Experimental Design
Cool as McFadden's model (today called "multinomial logit") is, it looks backwards: we model choices people made (or would make) using the attributes (or perceived attributes) that currently exist in the market. But markets are dynamic, and there's always and forever some brand adding a new bell or whistle, changing a price, or putting a picture of Jessica Simpson on its package.

At this point, a marketing professor, Jordan Louviere, made choice models more practical still. In 1983, he and an experimental design expert, George Woodworth, extended McFadden's model by marrying it with an experimental design theory (much as Paul Green had done 10 years earlier, combining regression analysis and experimental design to produce conjoint analysis). Now we can run future looking multinomial logit models. We can also create hypothetical scenarios, populated by experimentally designed alternatives, with new and existing attributes, and then have respondents make choices among them.

This form of conjoint analysis (known as "choice-based conjoint analysis," and, less precisely, as "discrete choice modeling," or DCM) is the engine driving conjoint analysis for product optimization, portfolio optimization, and pricing studies.

A Dissenting View: EBA
Not everyone liked McFadden's simple additive utility model. Another mathematical psychologist, Amos Tversky, described choice differently. He suggested we make choices using an "elimination by aspects" (EBA) strategy:

It's hay fever season, so you go to the store to buy an allergy remedy. Wow, there are a lot of allergy drugs! So you start to simplify. You don't want to be sleepy, so you want a "non-drowsy" product. You don't like the medicine taste, so you won't be buying any of those nasty-tasting liquids. You don't want a store brand, and you avoid all brands with pseudoephedrine in them. You keep making these eliminations until you get down to a single product, and then you buy it.

That's "elimination by aspects."

Technically, models like McFadden's are called "compensatory" (because of their additive nature, doing badly on one attribute can be "compensated" for by doing well on another – I don't like the color of the car at the lot, but since they've marked it down $2,800, I guess I can live with it). On the other hand we call models like Tversky's "non-compensatory" (I don't care how much they knock off the price, my pizza had a rat on it!)

So the non-compensatory EBA model describes a lot of my choices, too. Unfortunately, EBA models took way too much computing time to solve. As a result, EBA models have not appeared in the world of applied marketing research.

Until recently, that is. An academic named Richard Batsell and his colleagues have recently figured out how to run EBA models very simply, and from deceptively simple inputs. We are not aware of any commercial applications (or even interest outside of our company) of this work to date, but Maritz Research is consulting with Batsell and experimenting with his version of EBA analysis for our brand research products, so stay tuned for further developments.

Integrating EBA and compensatory choice models
It's also nice to have your cake and eat it, too, and there are a couple of ways of integrating Tversky's EBA into McFadden's conditional logit model.

• Consultant/academic Joffre Swait did so with a "constrained cutoff" conjoint model he showed at a conference in 1998 (he also published it, though you may not have noticed – he tried to get it into People, but the best he could do was Transportation Research: Part B in 2001; and a more reader-friendly version appeared last year in the Marketing Research magazine).
• More recently, academics Tim Gilbride and Greg Allenby came up with an even more fully-featured Bayesian way to combine the two models.

Summary
All of us in marketing and marketing research owe a debt of gratitude to these academicians. They have pushed the envelope in ways that turned the study of consumer choice into a science and allowed us to explain and predict behavior in ways that were unimaginable only a few years ago. This science is growing at an exponential pace and will continue to improve the practice of marketing research for some time to come.

* An exponential function is one in which a constant base (in this case e, which at a value of approximately 2.718 is the base of the natural log system) gets raised to the power of some variable (in this case the utility of a choice alternative)

Keith Chrzan
Keith Chrzan is the Vice President, Marketing Sciences Group at Maritz Research. Keith has 20 years of experience on the client and supplier sides of the marketing research industry. His experience includes positions as Director of Marketing Research at Boehringer Mannheim Diagnostics and Managing Director of Marketing Sciences at IntelliQuest, Inc., an Austin Texas-based marketing research consultancy serving the technology industry.

An industry leader in the area of choice experiments, Keith frequent speaker at the American Marketing Association’s Advanced Research Techniques Forum, the Sawtooth Software Conference and the INFORMS Marketing Sciences Conference. He is also the inventor of partial profile conjoint analysis and configuration conjoint analysis and has a paper about using choice models to inform strategy for medical instruments in the 2001 issue of The Journal of Product and Brand Management.

Keith received an M.B.A. in marketing from Indiana University and a B.A. in philosophy of religion from the University of Notre Dame.

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