thirst-quenching - but is it fairly priced?

Here’s a test of fairness.  Imagine you are lying on the beach on a hot summer day and find yourself craving a cold, satisfying beer.  What price would you be willing to pay to quench your thirst?  Now imagine two alternative scenarios.  In one, the only place within walking distance to buy a beer is the poolside bar of a swanky five-star beachfront hotel.  In the other, there is a rather run-down beachfront grocery store that sells beer.  Imagine further that both the hotel and the grocery store sell the exact same brand and type of beer.  Does your maximum price point change depending on whether you think you are getting the beer from the hotel or the store?  Do you think it is fair for two different establishments to sell the same commodity for a different price?

Those questions were at the heart of a study by a team of behavioral economists and reported in the Journal of Business in 1986 (“Fairness and the Assumptions of Economics” by Daniel Kahneman, Jack Knetsch and Richard Thaler).   Participants (playing the role of the thirsty beachgoer) were told where the beer would come from (ritzy hotel or rundown grocery store) and asked what their maximum permissible price would be.  The results were interesting: respondents who thought their beer was coming from the downmarket store were willing to pay a maximum $1.50 while those who were told the beer would be purchased at the luxury hotel were prepared to shell out $2.65.

What’s so fair about that?  We have to assume that, give or take, the procurement cost to each vendor was roughly the same.  The results of the study seem to indicate a calculus in the minds of the respondents that the beer will inevitably cost more if it comes from the hotel, so they were willing to adjust their own demand curves upwards to meet the perceived point of supply, as opposed to boycotting the transaction opportunity because of a perhaps unfair price differential.  Instinctively that makes sense to me.  Putting myself in the position of the parched beachgoer in the shadow of the ritzy hotel I think I would be more likely to go along with the reality of the $2.65 hotel beer than take a principled stand on the arguable unfairness of a 77% markup.  My experience tells me that it’s simply the way these things work, like it or not.  The results of the Kahneman study say largely the same thing: despite a potentially strong case to be made for the unfairness of the hotel’s pricing scheme, most people willingly go along with its reality and adjust their own internal pricing mechanisms accordingly.

Most of us have been somewhere where we have paid much more for something than we would otherwise – the infamous mini bar and local telephone call surcharges in hotel rooms come to mind.  Ordering a bottle of wine in a restaurant brings about the same experience – I know that a particular 2005 Gigondas retails for $18 at the local wine store but I’ll have to shell out $40 for the same quaff over candlelight and soft music at that romantic little cuisine provençale place down the street.  That $8 bag of peanuts or $40 bottle of wine become reference points – prices we anchor in our brains as reflective of actual experience, and call upon each time we are presented with similar transaction opportunities.  In this process a subtle shift takes place; we are no longer focused on the inherent fairness or not of the underlying state of affairs (high markups in restaurants and hotels) but rather on the fairness of any transaction offered to us in relation to its reference point.  So, going back to the sun-baked beach, if someone offers to go buy a beer for me and tells me the only option is from the hotel bar then my brain calls up the reference point of prior hotel-based transactions and I set my maximum price accordingly.  That $2.65 is an imprecise stab at establishing a benchmark for what the hotel bar should charge for my drink, and as long as it is somewhere in that neighborhood I am okay with the purchase.

salamancan scholars found fairness in the micromarket

Luis Saravia de la Calle, a member of what was known as the Salamancan School of the Late Scholastic period in 15th century Spain, stated that “the just price of a thing is the price which it commonly fetches at the time and place of the deal.”  Interestingly the Salamancans strongly influenced the philosophies of later Austrian School thinkers like Joseph Schumpeter, but also seem to resonate with the more recently emergent tenets of behavioral economics avatars like Kahneman (the 2002 Nobel laureate in economics) and the late Amos Tversky.  In this line of thinking fairness is not some arbitrary notion of a justifiable price based on component costs of production and delivery (like a cost-plus model); if it were, then more people would throw down the gauntlet at the prospect of shelling out 77% more for the same beer just because of where it happens to be sold.  It’s more along the lines of de la Calle’s notion of what prevails at the “time and place of the deal” – which is also what we at Sentrana think of as Pricing 4.0 – the intricate configuration of the needs and propensities of each individual customer at the point of interaction with each individual product.

We may not be able to pinpoint the precise meaning of fairness at all times and all places for all people.  But by better understanding the reference points that anchor buying and selling decisions in the micromarket we have an improved chance of achieving results that are both fair and profitable.

Looking at the human mind this way, as a machine constantly evaluating possible outcomes based on prior knowledge and assigning probability weights to those outcomes, gave rise to the notion of the “Bayesian brain,” a term popularized in 1983 by Geoffrey Hinton of the University of Toronto and Terry Sejnowski of Johns Hopkins University.  This notion has subsequently received a good amount of validation by neuroscientists as they continue to make advances in understanding how the brain really works.  Neuroscientists Alexandre Pouget and David Knill of the University of Rochester in 2004 referred to a “growing body of evidence that human perceptual computations are ‘Bayes optimal’ (“The Bayesian brain: the role of uncertainty in neural coding and computation,” Trends in Neurosciences, vol 27 issue 12, December 2004, pp 712-719).  That’s a fancy way of saying that we make estimations based on likelihood – for example we routinely make estimations about things like the distance from us of an object, or the speed at which it is traveling, based on our prior knowledge of the shape, clarity and movement patterns of such objects and the likelihood that the present reality fits into that a priori knowledge.

So far, so good.  But there is an Achilles heel to our hierarchical mental gymnastics.  Briefly, we may be great at the kind of proposition-within-proposition reasoning that our sales rep exhibited in getting to the essence of the competitive threat posed by the wholesaler’s move to town.  But we humans are generally pretty lame when it comes to computation.  Our intuitive reasoning skills fail at the task of instantaneously calculating that 34 x 57 X 71 = 137,598.  One way that we get around this failing is through heuristics – basically, shortcuts that we use in conditions of uncertainty to help us get from information to evaluation and decision.  Take the example above of evaluating the distance a particular object might be from us.  Now, there is a physics formula we could apply to measuring distance, height, momentum (if moving) and so forth to give us the precise answer as to how far away that bicyclist in the yellow jersey is from us.  But our brains lack the ability to do spontaneous physics equations.  Even if we precisely knew one or more of the variables it would be hard to do an on-the-spot computation.  So we need something else – a proxy, a heuristic.  That something might be clarity.  Can we see the bicyclist clearly?  Can we make out the details of his black helmet with red stripes, and the ‘Elf Aquitaine’ logo on the yellow jersey?  That can give us enough information to call upon our “cyclist in a yellow jersey” neuronal connections and infer a likelihood that he is, say, 50 yards away.

The problem with heuristics is that they are subject to error: not occasional lapses in judgment but systematic, predictable biases.  For example if we use clarity as a heuristic we may overestimate the distance of that cyclist from us if there is poor visibility.  Understanding the role of heuristic errors in human judgment and decision making was one of the main contributions of Amos Tversky and Daniel Kahneman to our understanding of behavioral factors in human decision-making (“Judgment Under Uncertainty: Heuristics and Biases,” Science New Series vol 185 no. 4157 Sep 1974 pp 1124-1131).  Tversky and Kahneman documented specific heuristic errors such as representativeness (drawing broad or sweeping conclusions from a limited data set), availability (assigning the likelihood of an event based on the easiest example that comes to mind, whether or not appropriate, and anchoring (relying heavily on one piece of information when making a decision even if it is irrelevant).

Since heuristic errors are part and parcel of human judgment and decision-making under uncertainty, we have to take this reality into account when we attempt to integrate quantitative modeling methods and qualitative human judgment.  What are the best mathematical tools and frameworks to integrate these two domains?  One area in which we at Sentrana are spending considerable time is that of Bayesian hierarchical modeling. The Bayesian approach is particularly useful in marketing situations such as modeling differences in the needs and wants of customers using both generalized and conditional assumptions involving multiple variables. Bayesian frameworks provide a natural way to pool disparate sources of information. A Bayesian model requires the formulation of prior distributions and the estimation of a likelihood function, which can add complexity to the model-building process.  However we expect future insights and innovations in this area, alongside the development of more robust computation capabilities to bring more firepower to bear on this difficult but potentially valuable quantitative approach.