On the Difficulty of Price Modeling

I was recently looking for a clean example of a service or an item that could clearly show the difficulty of the pricing of said service or item. I just found one on Dan Ariely's blog: Locksmiths. Here is the video:






Do you have other examples ?

Human Behavior Modeling Failures

This blog entry entitled Millenium bridge, endogeneity and risk management features two examples of faulty modeling in bridges and value-at-risk models (VaR) that take their roots in their not taking into account human behavior. One but wonders if people were dealing with unknown unknowns when the initial modeling was performed. In a different direction, when one deals with models and human behavior there is always the possibility for subgroups to game the system and make the intended modeling worthless. Here is an example related to ranking academics and researchers.

RMM Example #3: Nuclear Proliferation and Terrorism Risk Assessment.

In the U.S, the nuclear fuel cycle is termed 'one through' as nuclear fuel passes in nuclear power plant only once before being discarded. The debate on whether the country should be reprocessing some of these materials has been an ongoing discussion as early as the 1950's. The problematic is extremely complex and has many stakeholders at the table. A subset of the discussions include the fact that if the U.S. were to ever perform some reprocessing in their civilian fuel cycle, it would provide some grounds for other countries to do the same. For technical reasons, reprocessing is considered to be a good tool for proliferation because as soon as you allow for your nuclear fuel to be reprocessed, you  also open the door to the ability to extract material for "other purposes". Most countries are signatories of the Non Proliferation Treaty (NPT) and as you all know the IAEA is in charge of verifying compliance (all countries that are signatories are subject to yearly visits by IAEA staff) And so, a major technical effort in any type of Research and Development at the U.S. Department of Energy (and other countries that comply with the NPT) revolves around bringing technical solutions to some proliferation issues (as other proliferation issues are political in nature). As part of the recent DOE Nuclear Energy Enabling Technologies Program Workshop, there was an interesting subsection of the meeting dedicated to Proliferation and Terrorism Risk Assessment. I am not a specialist of this particular area, so I will just feature the material presented there for illustration purposes as they all represents some issues commonly found in difficult to solve RMM examples. From the presentation introducing the assessment here were the Goals and Objectives of this sub-meeting:

Solicit views of a broad cross‐section of stakeholders on the following questions:

• Would you favor an expanded R&D effort on proliferation and terrorism risk assessment? Why or why not?
• In what ways have current methodologies been useful, how might R&D make them more effective?
• If an expanded R&D program was initiated, what are promising areas for R&D, areas less worthwhile, and what mix of topics would best balance an expanded R&D portfolio?
• If an expanded R&D program was initiated, what cautions and recommendations should DOE‐NE consider as the program is planned and implemented?

Panel presentations to stimulate the discussion will address:

• Existing state‐of‐the‐art tools and methodologies for proliferation and terrorism risk assessment.
• The potential impact of improved tools and methodologies as well as factors that should be carefully considered in their use and any further development efforts.
• Identification of the challenges, areas for improvement, and gaps associated with broader utilization and acceptance of proliferation and terrorism risk assessment tools and methodologies.
• Identification of promising opportunities for R&D. Broad discussion/input is essential, active participation of all session attendees will: Provide important perspectives on proliferation and terrorism risk assessment R&D and ultimately strengthen capabilities for supporting NE’s development of new reactor and fuel cycle technologies/concepts while minimizing proliferation and terrorism risks.

Why talk about this subject on RMM ? Well I was struck by the type of questions being asked to technical people as they looked like typical questions one would ask in the context of an RMM example.

In Robert Bari's presentation one can read:

"Conveying Results: In particular, what we know about what we do not know" sounded a little too much like the categories discussed in The Modeler's Known Unknowns and Unknown Knowns

In Proliferation Resistance and Proliferation Risk Analysis: Thoughts on a Path Forward by William S. Charlton, one can read:

I wonder about the type of modeling that goes into estimating uncertainties. Finally, in Bill Burchill's slides, one can read on the proliferation pathways the following:

Solution to the "Selling from Novosibirsk" business model riddle

Bernard Beauzamy (the owner of SCM SA) had set up a 500 euros prize for whoever could find a way for the business model riddle featured on Tuesday. Bernard tells me that nobody won the prize, here is the answer:

....The answers we received fall into two categories:

Those who want to send 10 000 left-hand gloves, and then 10 000 right-hand gloves, and declare them of value zero.

This answer does not make sense ! Do you think that the customs will be stupid enough not to observe that they see only left-hand gloves, and only later right-hand gloves ? They would confiscate both, and the sender would go to jail, for attempt to cheat the customs. Many years of jail !

Those who want to create a branch of the company in the destination country, and claim that they would evade the customs this way.
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This answer does not make sense either ! It only reduces the profits, since one has to pay all the people in the local structure. And it changes nothing to the fact that customs tax the final selling price. If you have 10 intermediaries, you will have to give a salary to the ten, and the customer pays the same price, so the producer gets less money. In all circumstances, customs or not, the fewer intermediaries you have, the better you feel.

The answer, as we expected, was not found by anyone, because all our readers, by education or taste, want to build mathematical models, and this is a situation where no model is possible. It defies imagination and logics, and contradicts all existing economical models.

First of all, the solution looks impossible. If we sell each pair at its maximum price, that is 200 Rubles, the customs takes 160, we keep 40, and this is exactly equal to the production cost, so we have no benefit at all. It is even worse if we sell at a lower price.

The solution is this : we have to impose fabrication defects to 5 000 pairs (both left and right gloves). After that, we export 5 000 pairs, of which the left one is normal and the right one is defective (for example a big scar across one finger). These gloves are declared as "fabrication rejects", for a very small price, for instance 20 Rubles a pair. Note that selling and exporting "fabrication rejects" is quite ordinary and legal, and is common practice.

Then, next month, we do the converse : we export 5 000 pairs, of which the left one is defective and the right one is normal. We put all gloves together, and we get 5 000 pairs of normal gloves, which we sell at the maximum price. The total cost is 400 000 Rubles (fabrication), plus 160 000 Rubles (customs). The sales bring 1 000 000 Rubles, so we have a benefit of 840 000 Rubles. We can of course sell the defective gloves, just to have some receipts for the customs.

The ideal solution, but this is a remarkable industrial achievement is to program the fabrication machine so that it put defects on one pair out of two.

We observe that the solution is perfectly legal. Fabrication defects exist and are sold worlwide, for a low price. Each pair is perfectly declared at is correct value.

We said earlier that mathematical modeling is impossible. In fact, this example shows that all Nobel prizes given to economists since 1969 (year of creation of the prize) should be withdrawn, because they have no value at all.

Precisely, we see here that the notion of price is not mathematically well-defined. We cannot talk about the price of a glove, even not of a pair of gloves. We see that the price is not a continuous function, nor an increasing function, nor an additive function. The price of two objects together is not the sum of their individual prices. Still, the economists will build nice models, defective by all parts, and no reassembly can bring them any value !

Remember this : this is a true story, and the man who invented the solution did not know what a mathematical model was and did not have any degree at all…

[P.S: added Dec 4 (3:40PM CST): It's a riddle. One could make the point that this type of business model is not robust. All the countries in the world revise their own laws in order to effectively plug holes such as the one presented here. The ever growing sophistication / complexities of the tax systems in most countries reflects this adaptive behavior. If this system were robust it would be common business practice by now. It may have worked in some countries in the past however. The most important take away from this riddle is that the definition of the price of an item is indeed a difficult problem for which modeling is going to be tricky for a long time]

The RMM LinkedIn Group

As some of you may know, the Robust Mathematical Modeling blog has its own group on LinkedIn. Rodrigo Carvalho is our latest member which put our count to 21.

The 500 euros prize for the solution to the business model riddle ends today in about 7 hours. Good luck!